“My dear Admiral,—I have just completed the perusal of your very interesting volume on ‘The Colours of Double Stars,’ kindly presented to me by Dr. Lee in your name and his; and I thank you for the gratification it has afforded me.“What you say on the subject of variable stars has called to my recollection an idea which first occurred to me shortly after the discovery of the periodicity of the increase and decrease in the number and frequency of solar spots. I am aware that such increase and decrease is not continuous, and that the variation is not such as materially to affect the Sun’s brightness. Still, in point of fact, is not our own Sun a variable star—however slightly—with a period, tolerably well defined, of about eleven years? And may not the more marked character of other variable stars be owing to similar causes to those which produce the spots in our sun, acting with greater regularity and intensity?“If you think it deserving attention, pray favour me with youropinion of my theory. Possibly it may have been suggested previously, but if so, I am not aware of the fact.“I remain, my dear Admiral, yours faithfully,“Rowland Hill.“Admiral Smyth, F.R.S., &c., &c., &c.”Shortly afterwards I received a very friendly letter from Mrs. Smyth, the tenor of which will be sufficiently understood from what follows:—“Hampstead, 20th January, 1865.“Dear Mrs. Smyth,—Many thanks for your letter. Pray don’t let the Admiral withdraw himself from his present work. My theory can wait, or I may find an opportunity of consulting some other authority.“Our kindest regards.“Very truly yours,“Rowland Hill.”I accordingly, on the 14th February following, addressed a letter—similar to the one to Admiral Smyth—to my friend, Mr. Warren De La Rue, then President—as Admiral Smyth had once been—of the Astronomical Society; but although Mr. De La Rue took much trouble to ascertain whether my theory had, as he thought, been suggested before, it was not till long afterwards that he was able to give any definite information on the subject.In a letter of July 9th, 1866, Mr. De La Rue drew my attention to a paper by Mr. Balfour Stewart in the Transactions of the Royal Society of Edinburgh, which, in the opinion of Mr. De La Rue, “gives a very explicit enunciation” of the theory.On referring to the paper in question (Vol.XXIII, part iii.), I found that it was read on the 18th April, 1864, and the following is an extract from a memorandum which I made on the subject:—“Indirectly, by showing a probable connexion between the maxima and minima of Sun-spots and the rotation of Jupiter about the Sun, and by suggesting that the periodic variations of the stars is caused by the rotation of large planets about them, Mr. Balfour Stewart has, I think, forestalled me.” Perhaps, however, I may be justified in doubting whether the enunciation here given is very explicit.Before proceeding, it is necessary to digress for a moment. When a boy I was fond of reading books of elementary science. Ioccasionally met with statements which puzzled me—which appeared to me to be wrong—but assuming, as children do, the infallibility of the author—or perhaps I should say of a printed book—I naturally came to the conclusion that my own understanding was in fault, and became greatly disheartened. After awhile—I forget on what occasion—I applied for solution of the puzzle to my father, who, possessing a large amount of general information, was well qualified to advise. To my great delight, he assured me that I was right and the author wrong. My unqualified faith in printed statements was now, of course, at an end; and a habit was gradually formed of mentally criticising almost everything I read—a habit which, however useful in early life, is, as I have found in old age, a cause of much waste of thinking power when the amount is so reduced as to render economy of essential importance.Still, through the greater part of my life this habit of reading critically, combined as it was with the power of rapid calculation, has been of great use to me, especially in my contests with the Post Office, and, after I had joined the Department, in the revision of the thousands of Reports, Returns, and Minutes prepared by other officers.In general literature, if the author attempt to deal with science, the chance of a blunder appears to be great. Even Lord Macaulay could not always do so with safety, as appears from the following passage:—“In America the Spanish territories [in 1698] spread from the equator northward and southwardthrough all the signs of the Zodiacfar into the temperate zone.”[367]What can be the meaning of the words which I have marked for Italics?Mrs. Oliphant, too, whose admirable stories I never miss reading, says, in one of her latest, “there was a new moon making her wayupwardsin the pale sky.”[368]There is no writer to whom I feel more grateful than to Miss Edgeworth. When a boy I read her delightful stories with the greatest possible interest, and I feel sure that they had considerable influence in the formation of my character. Unfortunately, however, they are frequently disfigured by scientific errors. Thus, in her admirable story of “The Good Aunt,” the following passage occurs: “My dearest Aunt,” cried he [Charles], stopping her hand, as she was giving her diamond ear-rings to Mr. Carat—“stay, my dearest aunt, one instant, till I have seen whether this is a good day for selling diamonds.”“O, my dear young gentleman, no day in the Jewish calendar more proper for de purchase,” said the Jew.“For the purchase! yes,” said Charles, “but for the sale?”“My love,” said his aunt, “surely you are not so foolish as to think there are lucky and unlucky days.”“No, I don’t mean anything about lucky and unlucky days,” said Charles, running up to consult the barometer; “but what I mean is not foolish indeed; in some book I’ve read that the dealers in diamonds buy them when the air is light, and sell them when it is heavy, if they can, because their scales are so nice that they vary with the change in the atmosphere.”Now, as the metallic weights are of greater specific gravity than the diamonds, the interests of the dealers—so far as they are affected by change of atmosphere—must be to buy when the air isheavyand sell when it islight. An increase of density in the air would, of course, reduce the gravity of both diamonds and weights, but not equally: the diamonds, being the more bulky, would lose gravity more than the weights, and consequently would weigh less. If it were possible that the air should increase in density till it became as heavy, bulk for bulk, as the diamonds, they would float therein, or, in other words, weigh nothing at all.I well remember when, as a boy, I first read this admirable story, how much I was puzzled by the mistake in question.An error, occasionally met with in novels, is as follows. A wonderful marksman has to exhibit his powers, which he does thus:—He throws into the air two birds—or perhaps inanimate objects—as two apples; then,waiting till both are in a line with himself, sends his arrow or bullet through both. A slight consideration will show that, in a vast majority of cases, no amount of waiting would suffice.Another prevailing error is, that a person simply standing by the side of a pool can see his own reflection from the surface—Narcissus must have found some support which enabled him to lean over the fountain.But it is in books especially intended to teach elementary science that such errors are most to be regretted.A few years since I purchased for some of my grandchildren the eighth edition of “The Seasons,” by Mrs. Marcet. It is an admirable work, highly interesting and useful; but before placing it in the hands of my grandchildren, I thought it necessary to read it myself—a very pleasing task, by-the-by—and to correct any errors I might find. As examples, I may mention that in Volume I.snow is described as frozen rain; that in Volume IV.bothstones in a flour-mill are said to revolve; and that the description in the same volume of a marine steam engine is very incorrect.Again, few books are better calculated to interest boys than Dr. Parris’s “Philosophy in Sport,” but when, in the year 1829, I bought a copy for the School-Library at Bruce Castle, I found it necessary, before placing it there, to make numerous corrections to which I drew the attention of the author, who, in a letter dated March 18th, 1829, still in my possession, thanks me for my communication, and admits some of the errors, though not all.As a specimen of the admitted errors, I give the following:—“Mr. Seymour now informed his young pupils that he had an experiment to exhibit, which would further illustrate, in a very pleasing manner, the truth of the doctrine ofvis inertiæ. He accordingly inverted a wine-glass, and placed a shilling on its foot; and having pushed it suddenly along the table,the coin flew off towards the operator, or in a direction opposite to that in which the glass was moving.”[369]My correction is as follows: “The coin would fall nearly in a perpendicular direction, but inclined a littletowardsthe direction in which the glass was moving, owing to the friction between the glass and coin.”As a specimen of the non-admitted errors, I give the following: “He had ignorantly fired a quantity of oxygen and hydrogen gases in a tin vessel; the consequence of the combustion was the immediate formation of avacuum; and what happened? Why, the pressure of the external air, not being any longer balanced by elastic matter in the interior of the apparatus, crushed it with violence, as any other enormous weight might have done; and so ended the accident, which report magnified into a most awful catastrophe.”[370]My correction is as follows: “The first effect of the combustion was toexpandthe air in the vessel, and thisexpansionit was that caused the accident.”On which the author, after quoting my correction, replies, “Now you will allow me to say that here you have fallen into an error; I am perfectly correct in saying that the accident arose from the external pressure of the atmosphere; for remember that the vessel contained a mixture of oxygen and hydrogen gases, which, bycombustion, immediately combined and formed water, leaving an almost perfect vacuum in the interior.”If any one entertain a doubt as to which of us is correct, I would suggest his filling a small bladder with the proper mixture of oxygen and hydrogen, and exploding it by electrical means; as I did nearly sixty years ago. The bladder will be destroyed; but, according to Dr. Parris’s view, it should simply collapse.But even men of unquestionable scientific knowledge are not always correct. The late Professor Phillips, in his able and interesting Address as President of the British Association in 1865, after noticing Foucault’s recent admeasurement of the velocity of light, proceeded as follows:—“By this experiment the velocity of light appears to be less, sensibly less, than was previously admitted; and this conclusion is of the highest interest. For, as by assuming too long a radius for the orbit of Jupiter, the calculated rate of light-movement was too great; so now, by employing the more exact rate and the same measures of time, we can correct the estimated distance of Jupiter and all the other planets from the Sun.”[371]Professor Phillips’s great forte was geology, not astronomy. To any one familiar with the means by which Römer determined the velocity of light, it is unnecessary to point out that, although his observations were made on the satellites of Jupiter, the radius of Jupiter’s orbit has nothing to do with the problem. The only material facts are, first, thedifferencebetween the maximum and minimum distance of Jupiter from the earth,—that is to say (disregarding eccentricity) the diameter of the earth’s orbit; and, secondly, the effect which this varying distance has on the times at which the eclipses apparently take place. This effect Römer found to extend to about 16 minutes—and he thence concluded that light occupied 16 minutes in travelling across the earth’s orbit.With the view of rendering the above intelligible to those not familiar with the subject, I offer the following illustration:—Suppose it to be known that about a certain hour a gun will be fired at a remote spot, the direction of which, but not the distance, is known, and that two persons (A. and B.) arrange to avail themselves of the opportunity for ascertaining, approximately, the velocity of sound; then, each being furnished with a good watch marking seconds, A. places himself at a certain spot, and B. at a known distance—say a mile—from A., and in a direction opposite to that of the gun, so that B.’s distance from the gun shall be a mile greater than A.’s—the actual distance in either case is unimportant.Each now records the exact moment at which he hears the report; and if the gun be fired repeatedly, several such records are made, in order to give a more accurate result.A. and B. then meet and compare notes. They, of course, find that A.’s time is in each instance earlier than B.’s. The average of the several differences would be about 4¾ seconds—showing that sound travels a mile in that time.[372]The mode of procedure here described is, of course, not that actually adopted for determining the velocity of sound, but it is a practicable mode, and is selected because it is analogous to that adopted by Römer for determining the velocity of light.A copy of Professor Phillips’s Address was sent to me immediately after its delivery, and, on my detecting the error, I endeavoured to induce a friend of his, deservedly eminent as a practical astronomer, to draw the Professor’s attention thereto, with a view to its correction before the publication of the permanent report of the Society’s proceedings; but, unfortunately, the attempt did not succeed.In another similar case, however, as appears by the following correspondence between the Astronomer Royal and myself, I was more successful:—“Hampstead, N.W.“1868—June 17.[373]“My dear Sir,—Pray accept my thanks for the copy of your Report. It came while I was at Brighton; but, since my return home, I have read it with great interest. I felt it a great privation not to be able to attend the Visitation.“Will you allow me to request your attention to what appear to me to be serious errors in the recent annual Address of the President of the Astronomical Society? They will be found in the last paragraph of page 119 of the ‘Monthly Notices’ for February. To save you trouble, I have extracted the part in question, and have underlined the words which I think erroneous. ‘At the present time the Earth is about three millions of miles nearer to the Sun in our northerly winter than in our summer; our coldest month is about 60° Fh. colder than our hottest, and our winter lasts for about eight dayslongerthan our summer. M. Leverrier has calculatedthat 200,000 years ago the Earth approached the Sun by upwards of ten millions of miles nearer in winter than in summer: the winters were then nearly a monthlongerthan the summers, and in the latitude of London there was a difference of about 112° Fh. between the hottest and the coldest periods of the year.’“If you find that I am right, perhaps you will have the kindness to draw Mr. Pritchard’s attention to the errors, with a view to their correction before the Address is printed in the ‘Transactions.’ I would write to Mr. Pritchard myself, but that, as I could not speak with authority, I might give offence.“I have watched the subsequent monthly numbers in the expectation of finding a correction, but none has appeared.“Faithfully yours,“Rowland Hill.“The Astronomer Royal, &c., &c., &c.”The Astronomer Royal promptly replied as follows:—“Royal Observatory, Greenwich, London, S.E.“1868—June 18.“My dear Sir,—I will duly bring before Mr. Pritchard the substance of your note of yesterday.“The two clauses which you have cited are, on the face of them, erroneous; and in the first the fault clearly is in the wordlonger. In the second, the fault may be in the wordnearer. For, during the period through which the great eccentricity prevails, the semi-revolution in the precession of the equinoxes may have reversed the seasons.“It would seem that Mr. Pritchard has had in view the table in ‘Lyell’s Principles of Geology,’ Vol.I., p. 293. In the notes continued on p. 294, the references are to the case of winter in aphelion.“The subject is a thorny one, but well worth your attention.“I am, my dear Sir, yours very truly,“G. B. Airy“Sir Rowland Hill, K.C.B., &c., &c., &c.”I am not aware how the passage in question stands in the Society’s Transactions.[374]The following narrative seems to show that in a progressive science like Astronomy even the highest authority is not infallible.Some sixty years ago, my attention having been accidentally drawn to a tide-mill for grinding corn, I began to consider what was the source of the power employed, and came to the conclusion that it was the momentum of the earth’s revolution on its axis. The next question I asked myself was—could such power be diverted, in however slight a degree, without drawing, as it were, on the stock? Further consideration showed me that the draught required for grinding the corn was trifling in comparison with that employed in grinding the pebbles on every seashore upon the earth’s surface; and, consequently, that the drain on the earth’s momentum might suffice in the course of ages to effect an appreciable retardation in the earth’s diurnal revolution.I now, as usual in case of difficulty, applied to my father. He could detect no fault in my reasoning, but informed me that Laplace had demonstrated in his great work (“La Mécanique Céleste”) that the time occupied in the earth’s diurnal revolution is absolutely invariable. Of course both my father and I accepted the authority as unquestionable; but I never could fully satisfy my mind on the subject, and for the greater part of my life it was a standing puzzle.It may be stated briefly that Laplace’s demonstration appears to have rested mainly on the fact that his Lunar Tables, if employed in calculating backwards certain eclipses of the Sun which happened about 2,000 years ago, give results agreeing so nearly with the ancient records as altogether to exclude the possibility of any appreciable increase in the length of the sidereal day during that long period.But in the year 1866 Professor Adams (really the first discoverer of the planet Neptune) received the Gold Medal of the Astronomical Society for, among other recent claims, the discovery of an error in the data on which Laplace constructed his Lunar Tables which vitiates the above demonstration.The details of this important discovery—and the co-operation therein of M. Delaunay—were fully and ably stated by Mr. Warren De La Rue, then President of the Society, on the presentation of the Medal.[375]And the position of the question two years later is concisely stated as follows by the Rev. Charles Pritchard, in an Addendum to his address as President in 1868:—“At present, then, the case stands thus,—the Lunar Tables, if calculated on the principles of gravitation alone, as expounded by Messrs. Adams andDelaunay, and as confirmed by other mathematicians, will not exactly represent the moon’s true place at intervals separated by 2,000 years, provided the length of the day is assumed to be uniform and unaltered during the whole of the intervening period. There are grounds, however, for at least suspecting that, owing to the effects of tidal action, the diurnal rotation is, and has been, in a state of extremely minute retardation; but the mathematical difficulties of the case, owing greatly to the interposition of terrestrial continents, are so great that no definite quantitative results have hitherto been attainable. The solution of the difficulty is one of those questions which are reserved for the Astronomy of the future.”[376]I need not say that this confirmation of the truth of my early conjecture proved highly gratifying. I have only to add that the increase during the last 2,000 years in the length of the sidereal day is generally estimated at about the eightieth part of a second; but the estimate has, I apprehend, no better foundation than this—namely, that since the recent correction in the Lunar Tables an assumed increase to the extent in question has become necessary in order to make the backward calculation of the ancient eclipses agree with the records as to time.I have found it very difficult at my age (little less than fourscore), and with my mental powers seriously impaired, to deal, however imperfectly, with a subject so abstruse as that now under consideration; and I think it by no means improbable that there may be some error in my statement of facts or in my argument thereon.All that I can say is that I have done my best to render intelligible to ordinary readers an important advance in modern Astronomy—interesting in itself, irrespective of its remote and accidental connection with my own biography.The following very gratifying letter from the Astronomer Royal may perhaps be appropriately given here. It is in reply to my congratulations when, in recognition of his great public services, he was made a K.C.B.:—“Flamsteed House, Greenwich Park, London, S.E.“1872—June 22.“My dear Sir,—I could scarcely have had a more gratifying letter in reference to the public compliment just paid to me from any one than that from yourself. I can truly say that it has been my secretpride to do what can be done by a person in my position for public service; and whose recognition of this can be more grateful than that of one who—by efforts in a similar strain, but on an infinitely larger scale—has almost changed the face of the civilized world?“My wife (I am hesitating between two titles, not knowing which is at the present moment correct, but being quite sure of that which I have written) begs me to convey to you her acknowledgment of your kind message.“I am, my dear Sir, very truly yours,“G. B. Airy.”APPENDIX B.[See p. 71.]“PREFACE TO THE LAWS OF THE SOCIETY FOR LITERARY AND SCIENTIFIC IMPROVEMENT.“In presenting to the public ‘The Laws and Regulations of the Society for Literary and Scientific Improvement,’ its members feel it their duty briefly to state the motives which influenced them in the formation of such an establishment, and to explain their reasons for occasionally deviating in the construction of their Laws from the systems which are generally adopted for the governance of similar bodies.“The experience of almost every one who has passed the time usually devoted to education, but who still feels desirous of improvement, must have convinced him of the difficulty of regularly devoting his leisure hours to the object he has in view, from the want of constantly acting motives, and the absence of regulations which can enforce the observance of stated times. However strong the resolutions he has made, and whatever may be his conviction of the necessity of adhering to them, trivial engagements which might easily be avoided, will furnish him, from time to time, with excuses to himself for his neglect of study: thus may he spend year after year, constantly wishing for improvement, but as constantly neglecting the means of it, and old age may come upon him before he has accomplished the object of his desires; then will he look back with regret on the many opportunities he has lost, and acknowledge in despair that the time is gone by.“Under these impressions, a few individuals who are desirous of extending their literary and scientific knowledge, have endeavoured to establish a society for that purpose; convinced that by so doing they have provided most powerful motives for mental improvement.“It has been thought highly desirable, that every member of the society should be, as nearly as possible, upon an equality, that all may feel alike interested in the success of the whole. In order to accomplish this important object, every regular auditor is expected, according to the rules of the society, to deliver a lecture in his turn. Thus, instead of the society being divided into two parties, one consisting of lecturers, the other of critics, every member feels himself called upon to listen to the others with candour and attention, as he is aware that the time will come when he shall require the same consideration from them. It will be observed also, on a perusal of the laws, that each lecture is followed by a discussion. Thus care is insured on the part of the lecturer that he shall not attempt a subject which he has not well studied; and an opportunity is given to every member to obtain an explanation of anything advanced, which he may not have understood, or to express his opinions on the questions that may arise, and, by these means, correct or confirm his own ideas. But the principal advantage of a discussion is, that it calls forth the individual exertion of every member, by inviting each to take a part in the general instruction, and thus affording constant inducements to private reading and study.“In a town so populous as Birmingham, and which for superiority in art is dependent on the discoveries of science, it cannot be doubted that many individuals may be found who are desirous of intellectual advancement. For such persons ‘The Society for Literary and Scientific Improvement’ was established; and they are respectfully and earnestly invited to lend their assistance towards the promotion of its objects. The society cannot promise that they shall meet with any considerable talent or learning among its members; but in mixing with their equals, with young men of similar tastes and similar pursuits, they may hope to find in a generous emulation most powerful motives for application and perseverance.“The details of management of a society like this, may, on a superficial view, appear of little importance; those, however, who have had opportunities of closer examination, will, it is presumed, agree with the members of this Institution, in considering an attention to such particulars as necessary, not only to the well-being, but to the permanent existence of an association, for whatever purpose it may be formed.“With views like these, the ‘Society for Literary and Scientific Improvement’ have been anxious to establish a mode of electingthe Committee, that should secure (as nearly as possible), an accurate representation of the whole body; not only because it appeared reasonable that the members would feel interested in the welfare of the Institution, in proportion as the arrangements and regulations met their own views and wishes, but because experience proves that, owing to imperfect methods of choosing those who are to direct the affairs of a society, the whole sway sometimes gets into the hands of a small party, and is exercised, perhaps unconsciously, in a way that renders many persons indifferent, and alienates others, until all becomes listlessness, decay, and dissolution.“Men of worth and talent, of every denomination in religion and politics, will be welcome members of the society; and to prevent any unpleasant collision of opinions, it has been thought advisable to exclude altogether the discussion of subjects which have reference to peculiarities in religious belief, or to the political speculations of the day; the important questions which respect the wealth of nations, however, as they have no connexion with passing politics, are considered as among the proper objects for the society’s attention.“Such gentlemen as may feel desirous of improving their minds by engaging in establishments of a nature similar to this, but who, on account of their residing at a distance from any large town, have not hitherto had the opportunity, will, it is hoped, be induced by the regulations respecting corresponding members, to join the society; and they may depend upon meeting with every attention, whenever the Committee shall be favoured with their communications.”APPENDIX C.[See p. 93.]CUBE ROOTS.The mode of extracting the roots ofexact cubeswhich I taught the boys, and which was probably that adopted by Zerah Colbourn, will be best shown by an example. Suppose the question to be, What is the cube root of 596,947,688? This looks like a formidable array of figures, and a schoolboy, resorting to the usual mode of extracting the root, would fill his slate with figures, and perhaps occupy an hour in the process. Zerah Colbourn or my class would have solved the question in a minute, and without making any figures at all. My class would have proceeded as follows: They would first fix in their memories the number of millions (596) and the last figure of the cube (8), disregarding all other figures. Then, knowing the cubes of all numbers from 1 to 12 inclusive, they would at once see that the first or left-hand figure of the root must be 8; and deducting the cube of 8 (512) from 596, they would obtain a remainder of 84. This they would compare with the difference between the cube of 8 (512) and the cube of 9 (729), that is to say, with 217; and seeing that it was nearly four-tenths of such difference, they would conclude that the second figure of the root was 4. The third or last figure of the root would require no calculation, the terminal figure of anexactcube always indicating the terminal figure of its root—thus 8 gives 2. The cube root, therefore, is 842. In this process there is some risk of error as regards the second figure of the root, especially when the third figure is large; but with practice an expert calculator is able to pay due regard to that and certain other qualifications which I could not explain without making this note unduly long. As already stated, Zerah Colbourn did occasionally blunder in the second figure; and this circumstance assisted me in discovering the above process, which I have little doubt is the one he followed. If, instead of an exactcube, another number of nine figures be taken, the determination of the third figure of the root, instead of being the easiest, becomes by far the most difficult part of the calculation.[This part of the explanation was written by Sir Rowland Hill, as a note to the Prefatory Memoir, before the year 1871. What follows was added in 1875.]Rule for extracting the roots of imperfect cubes divisible into three periods:—1. Find first and second figures as described above.2. Deduct cube of first figure from the first period (of the number whose root is to be extracted), modified, if necessary, as hereafter described.3. Then multiply the number (expressed by both figures) by each figure in succession, and by 3.4. Deduct the product (or the significant figures thereof—see example), from the remainder obtained as above. (See 2).5. Divide the remaindernowobtained by the square of the number expressed by both figures (see 3), multiplied by 3—dropping insignificant figures (see example),—and the quotient will be the last figure (or 3rd figure) of the root.I can confidently affirm from experience that there is nothing in the above calculations too difficult for those who, possessing a natural aptitude, are thoroughly well practised in mental arithmetic. I doubt, however, whether the mode just described be exactly that which we followed; our actual mode, looking at the results as described above (which is in exact accordance with my Journal), must, I think, have been more facile; but as it is fully fifty years since I gave any thought to the subject, and as, in the eightieth year of my age, I find my brain unequal to further investigation, I must be contented with the result at which I have arrived.It must be remarked, however, that cases will arise when some modification of the process will be necessary. As, for instance, when the first period of the cube is comparatively light, it may be necessary to include therein one or more figures of the second period treated as decimals; indeed, if the first period consist of a single figure, it will be better to incorporate it with the second period, and treat both together as one period,[377]relative magnitude in the first period dealt with being important as a means of securing accuracy in the last figure of the root. But expert calculators soon learn toadopt necessary modifications, and by the “give-and-take” process to bring out the correct result. Indeed, I find it recorded in my Journal that “small errors will sometimes arise which, under unfavourable circumstances, will occasionally amount to a unit.” These observations it must be understood to apply only to the extraction of the roots of imperfect cubes, which Zerah Colbourn invariably refused to attempt. When the cube is perfect, the last figure of the root, as shown in the text, requires no calculation at all.Example.What is the cube root of 596,947,687?[Note.—This is the number treated above, except that in the unit’s place 7 is substituted for 8, in order to render the number an imperfect cube; so slight a change, however—though rendering it necessary tocalculatethe last figure of the root,—will still leave the root as before.]Following the rule, we find the first and second figures of the root in the manner described above. They are 8 and 4.We next calculate the third or last figure of the root.As the first figure of the second period of the cube is so large, it will be unsafe to disregard it. Call the first period, therefore, 596·9; all other figures may be neglected.596·9mill.(2)8³ =512”84·9”(3) deduct 84 x 8 x 4 x 3 = (roughly)80·6”(5) divide by 84² x 3 = (88 x 80 x 3)[378]= 2·14·32Quotient—2, which is the third or last figure of the root.[Note.—I have not encumbered the above figures with the ciphers which should accompany them, as, to the expert calculator, this will be needless.]The root, therefore, is 842.It is stated in the text that my pupils could extract the cube roots of numbers ranging as high as 2,000,000,000. In the ordinary mode this number would be divided, as above, into four periods; but my pupils treated the 2,000 as one period, the approximate root of which is of course 12, the cube of 12 being 1,728.APPENDIX D.[See p. 202.]VERNIER PENDULUM.Bruce Castle, Tottenham,June 7th, 1832.To the Council of the Royal Astronomical Society.Gentlemen,—In troubling you with the following sketch of an improvement in astronomical clocks, I have a two-fold object. First, to obtain the loan of the necessary instruments, should you consider the plan worth prosecuting; and, secondly, to avail myself of the suggestions of such members of the Society as are more experienced than myself in the minute details of practical astronomy. The objects of the proposed improvement are: To supply an apparatus capable of measuring time to a small fraction of a second, and to make the determination of the exact time a matter of calm and deliberate inquiry, and thus to avoid the errors which must frequently arise from the hurry attending the present method.In order to accomplish these objects, I propose to make use of the principle of the Vernier, by suspending in front of the clock an additional pendulum somewhat shorter than that of the clock, and so placed that the coincidence of the two when vertical may be determined by means similar to those used by Captain Kater; this additional or Vernier pendulum to be put in motion at the instant of observation by means of a trigger under the command of the observer at the telescope, and its vibrations reckoned till a coincidence takes place between it and the clock pendulum. This pendulum may have a maintaining power and an index to save the trouble of counting. When at rest, the Vernier pendulum must of course be raised to the extent of its oscillation.The results of experiments commenced with very imperfect instruments about two years and a-half ago, and continued at intervals to the present time, appear to be as follows:—When a Vernier pendulum, vibrating once in ·9 second, or 10 times in 9 seconds, is employed, its coincidences with the seconds pendulum of the clock may be determined to a single vibration with the greatest ease by the unassisted eye, and thus, of course, tenths of a second are readily estimated.When a Vernier pendulum vibrating once in ·99 second, or 100 times in 99 seconds, is employed, its coincidences with the seconds pendulum of the clock may also be determined to a single vibration, but not without the aid of a telescope. By these means hundredths of a second are measured without much difficulty.In order to avoid the inconvenience of having to suspend sometimes one pendulum and sometimes the other, and also to escape the loss of time which, if the hundredths pendulum were constantly used, would arise when the observer wished to estimate tenths of a second only, I propose to adopt the following arrangement:—To employ a single Vernier pendulum of such a length as to vibrate once in 8·99 second, or a thousand times in 899 seconds. This pendulum differs so slightly from the tenths pendulum (making ten vibrations in 8·99 seconds, instead of 9 seconds), that for estimating tenths of a second it is practically the same, while it affords the means of measuring hundredths of a second also. Its operation will be best understood by an example:—Suppose the interval to be measured by means of the Vernier to be ·24 second. At the second and third vibrations of the Vernier pendulum after its release there would be approximate coincidences between it and the clock pendulum, showing the fraction of time to be between two-tenths and three-tenths of a second. The coincidence at the second vibration would, however, be somewhat nearer than that at the third. At the twelfth vibration there would be another approximate coincidence somewhat closer than the first. At the twenty-second vibration there would be a yet closer coincidence. At the thirty-second one closer still, and at the forty-second vibration the coincidence would be the most accurate of the series. Thus it appears that the tenths of a second may be known by counting single vibrations of the Vernier pendulum till a coincidence of some kind occurs, and that the hundredths of a second may be determined by counting the decades of vibrations, or all the coincidences after the first, until the most exact coincidence arises.By the use of the Vernier pendulum, when connected with anindex, all chance of error in reading the clock will, it is conceived, be avoided. Having touched the trigger at the moment of observation, the observer has, as it were, registered the time, and he may examine the clock at his leisure, for it is manifest that a comparison of the index of the Vernier pendulum with that of the clock will at any time determine the moment of observation. It will also be seen that, should the observer omit to notice the first coincidence of the pendulums, no inconvenience except delay will arise, because the same coincidences will occur in a regular series as long as the pendulums continue in motion.There are a few provisions necessary for extreme accuracy which, in this hasty sketch, it would be out of place to notice. I will just mention, however, that the apparatus contains within itself the means of measuring what may be calledthe mean error of the observer, or the average interval which, as regards the particular individual, elapses between the instant of observation and the release of the Vernier pendulum.To subject the plan which I have here attempted hastily to describe to a rigid trial will require instruments of much greater accuracy than those which I can command, and if the Society possess a good clock not now in use, I shall feel extremely obliged if I can obtain the loan of it. An additional pendulum the requisite length, is not, I presume, to be found among the Society’s instruments.I have the honour to be, Gentlemen,Your obedient servant,Rowland Hill.APPENDIX E.[See p. 205.]COACH COMPANY.Two (or more) principal offices to be established in convenient places for business—say,one near the Bank, and one near the Regent Circus, Piccadilly; these offices to communicate with each other by means of omnibuses.Coaches and omnibuses to radiate from these offices to all parts of the environs of London.A country office to be established at the extremity of each route.The town to be divided into small districts, and the country into larger, each with a house for the receipt and distribution ofparcels. (Shopkeepers who have goods to distribute in the neighbourhood may undertake this). These stations to be, as far as practicable, on the routes of the coaches.The principal and the country offices to be receiving and distributing houses, each for its own district.Each coach in coming from the country to collect parcels from the stations on its route, bringing them to its principal office. On going out, to carry parcels for distribution from the principal office to the same stations. Thus every parcel will pass through one or other of the principal offices. (Exceptions can be made, if desirable, with respect to parcels which would otherwise pass twice over the ground, viz., those received at stations between the principal office and the place of their destination; but the first arrangement would be by far the most simple).Stations not on a coach route must transfer parcels to the nearest stations which are on a route, and receive parcels from the same. [Qy. A small extra charge].Places to be booked at any station for any coach; a memorandum being transmitted to the principal office concerned, with the parcels.In some cases the passengers themselves may be so transmitted.The omnibuses passing between the principal offices to carry passengers and parcels from each for the other. Thus every coach will practically start from both principal offices.Coaches to depart from each principal office all at the same time. Say, for all principal places, once every hour, from —— in the morning till —— at night.Coaches to arrive at each principal office all at the same time, say a few minutes before the time of departure, the interval being sufficient to transfer passengers and parcels.The periods of departure and arrival at one office to differ by half-an-hour from the corresponding periods at the other, so as to allow just time enough (calculated at half-an-hour), for a transfer by the omnibuses from one office to the other. Thus the coaches from one office will start at the beginning and from the other in the middle of each hour.Horses to be kept and changed at the country offices, or at stations about the middle of each route. The latter arrangement will make the stage shorter, and will bring the horse stations more immediately under central revision. It will also require a less number of horse stations, as in many cases one station will serve for two or more roads branching out from each other. (At least one pair of horses must be kept at the extreme station).Supernumerary coaches and horses to be kept at the central offices for use on any road on which there may be a temporary demand.Each coachman to pay a certain rent, and with certain deductions to receive the payments for passengers and parcels, but to have no control as to the sum to be charged, the hour of starting, &c.The masters of the stations to be remunerated by a certain sum (to be paid by the coachman) for each passenger booked, and for each parcel received or distributed.Contracts to be made in all possible cases. Thus the coachmaker may supply coaches at —— each per annum, or at —— per mile travelled.The keepers of the horse stations may contract each for the supply of horses required at his station at —— per mile.In disposing of the shares, a preference to be given to those who would make frequent use of the coaches, especially to those who travel to London daily, as their influence would materially promote the interests of the concern.A personal right to go to or from town daily, by the same coach, to be sold for a period, say a week, at a considerably reduced rate, or a month at a still lower rate.Proprietors to be entitled to similar privileges at five per cent. less than others.Transferable tickets, giving the holder a right to travel by any coach in either direction on a particular road, to be sold (say twenty at a time) at a slightly reduced rate.All the carriages to be painted alike, and so as readily to distinguish them from those not belonging to the Company.An establishment on an extensive scale, such as is described in the foregoing sketch, would possess many decided advantages over the little independent establishments now existing. It would be more economically managed; the necessary publicity would be more easily given to its arrangements; the responsibility of the servants would be more efficient; and the extent and permanence of the undertaking would justify the most watchful attention to exact punctuality, to a proper speed, to the safety and comfort of the passengers, and, in short, to all circumstances conducive to a high reputation with the public.Economy.—This would manifestly result from the great division of labour, and the wholesale demand for every article of expenditure. Also from the power of transferring coaches from any road on which there was less to one on which there was more travelling than usual.The system of contracts and sub-contracts could not be introduced with advantage into a small concern.Publicity.—The readiness with which the arrangements could be described would tend greatly to their publicity. Thus, it would be easily said and easily remembered, that from a certain office coaches depart every hour, and from a certain other office at the half-hour, to all the principal places within the limits of the threepenny post. This statement, with a list of the places, fares, &c., would be placarded at every station, and on every coach and omnibus.Responsibility.—An active and intelligent superintendent, well acquainted with the means of holding others to responsibility, should devote his whole time to the undertaking, visiting the various stations periodically to see that all arrangements are observed, to settle the accounts, &c.He should require accurate reports to be made, showing at all times the actual state of affairs, and the improvement or deterioration in each department The most exact rules should be laid down and enforced for the conduct of each class of servants. These rules should be placarded in the coaches, at the stations, &c.Enquiries as to the conduct of all concerned should be made frequently of the proprietors who use the coaches daily, and everypossible attention paid to the well-founded complaints of passengers generally. A till might be placed in each carriage, with an inscription requesting passengers having cause to complain to put a statement of such complaint, withname and address, into the till, which should be opened at the central office at least once in each day.Punctuality and Speed.—The proper time of starting and that of passing each station should be inscribed conspicuously on each coach, as well as at each station. The actual time kept should be recorded at each extreme station and at the horse station, and fines levied on the coachman for deviation beyond certain limits. The allowance of time for the journey should be such as to require the coachman to drive steadily but rapidly, with no stoppage beyond a very short one (say a minute) at each station, and a little more for taking up and putting down passengers on the road.The coach should never wait nor turn out of the direct road between the extreme stations. To save time, the passengers, in the omnibuses at least, should be requested to pay as they go on. At the inferior stations a signal might be established to show whether the coach need stop or not.Safety of Passengers.—Coaches of the safest construction, steady horses, and temperate coachmen, only should be employed; and whenever an accident occurs from whatever cause, a heavy fine should be levied on the coachman, allowing him the right to recover the whole or part of the penalty of the coach-contractor or horse-contractor, according to circumstances. No galloping should be allowed.The coach-contractor should be required to station a man at each central office to examine each coach every time it comes in.Comfort of Passengers.—Some protection from wet and cold to be provided for the outside passengers. Means of ascending and descending to be improved. A convenient room at each station for those waiting. The stations shouldnotbe taverns; but coffee and some other refreshments may be provided—there being no obligation, however, to call for anything. The room should contain a map of London, directory, &c.The arrangements of the Company would be capable of gradual and almost indefinite extension. Thus they might take in towns more and more distant, or they might comprehend hackney-coaches, cabriolets, and omnibuses to all parts of London. The machinery required for the distribution of parcels might be applied to that of the periodic publications; and a contract might be entered into, advantageous to the public as well as to the Company, for thecollection, carriage, and distribution of the twopenny and threepenny post letters.This distribution might easily take placeeach hour, the letters being carried by the coaches. No guards would be required, as the bags might be put into a boot, of which keys should be kept at the post-offices only.APPENDIX F.[See p. 230.][The following letter toThe Scotsmanwas written by Mr. John Forster, late Member for Berwick. In a marginal note Sir R. Hill has written, “I vouch for its accuracy.”]
“My dear Admiral,—I have just completed the perusal of your very interesting volume on ‘The Colours of Double Stars,’ kindly presented to me by Dr. Lee in your name and his; and I thank you for the gratification it has afforded me.“What you say on the subject of variable stars has called to my recollection an idea which first occurred to me shortly after the discovery of the periodicity of the increase and decrease in the number and frequency of solar spots. I am aware that such increase and decrease is not continuous, and that the variation is not such as materially to affect the Sun’s brightness. Still, in point of fact, is not our own Sun a variable star—however slightly—with a period, tolerably well defined, of about eleven years? And may not the more marked character of other variable stars be owing to similar causes to those which produce the spots in our sun, acting with greater regularity and intensity?“If you think it deserving attention, pray favour me with youropinion of my theory. Possibly it may have been suggested previously, but if so, I am not aware of the fact.“I remain, my dear Admiral, yours faithfully,“Rowland Hill.“Admiral Smyth, F.R.S., &c., &c., &c.”
“My dear Admiral,—I have just completed the perusal of your very interesting volume on ‘The Colours of Double Stars,’ kindly presented to me by Dr. Lee in your name and his; and I thank you for the gratification it has afforded me.
“What you say on the subject of variable stars has called to my recollection an idea which first occurred to me shortly after the discovery of the periodicity of the increase and decrease in the number and frequency of solar spots. I am aware that such increase and decrease is not continuous, and that the variation is not such as materially to affect the Sun’s brightness. Still, in point of fact, is not our own Sun a variable star—however slightly—with a period, tolerably well defined, of about eleven years? And may not the more marked character of other variable stars be owing to similar causes to those which produce the spots in our sun, acting with greater regularity and intensity?
“If you think it deserving attention, pray favour me with youropinion of my theory. Possibly it may have been suggested previously, but if so, I am not aware of the fact.
“I remain, my dear Admiral, yours faithfully,
“Rowland Hill.
“Admiral Smyth, F.R.S., &c., &c., &c.”
Shortly afterwards I received a very friendly letter from Mrs. Smyth, the tenor of which will be sufficiently understood from what follows:—
“Hampstead, 20th January, 1865.“Dear Mrs. Smyth,—Many thanks for your letter. Pray don’t let the Admiral withdraw himself from his present work. My theory can wait, or I may find an opportunity of consulting some other authority.“Our kindest regards.“Very truly yours,“Rowland Hill.”
“Hampstead, 20th January, 1865.
“Dear Mrs. Smyth,—Many thanks for your letter. Pray don’t let the Admiral withdraw himself from his present work. My theory can wait, or I may find an opportunity of consulting some other authority.
“Our kindest regards.
“Very truly yours,
“Rowland Hill.”
I accordingly, on the 14th February following, addressed a letter—similar to the one to Admiral Smyth—to my friend, Mr. Warren De La Rue, then President—as Admiral Smyth had once been—of the Astronomical Society; but although Mr. De La Rue took much trouble to ascertain whether my theory had, as he thought, been suggested before, it was not till long afterwards that he was able to give any definite information on the subject.
In a letter of July 9th, 1866, Mr. De La Rue drew my attention to a paper by Mr. Balfour Stewart in the Transactions of the Royal Society of Edinburgh, which, in the opinion of Mr. De La Rue, “gives a very explicit enunciation” of the theory.
On referring to the paper in question (Vol.XXIII, part iii.), I found that it was read on the 18th April, 1864, and the following is an extract from a memorandum which I made on the subject:—“Indirectly, by showing a probable connexion between the maxima and minima of Sun-spots and the rotation of Jupiter about the Sun, and by suggesting that the periodic variations of the stars is caused by the rotation of large planets about them, Mr. Balfour Stewart has, I think, forestalled me.” Perhaps, however, I may be justified in doubting whether the enunciation here given is very explicit.
Before proceeding, it is necessary to digress for a moment. When a boy I was fond of reading books of elementary science. Ioccasionally met with statements which puzzled me—which appeared to me to be wrong—but assuming, as children do, the infallibility of the author—or perhaps I should say of a printed book—I naturally came to the conclusion that my own understanding was in fault, and became greatly disheartened. After awhile—I forget on what occasion—I applied for solution of the puzzle to my father, who, possessing a large amount of general information, was well qualified to advise. To my great delight, he assured me that I was right and the author wrong. My unqualified faith in printed statements was now, of course, at an end; and a habit was gradually formed of mentally criticising almost everything I read—a habit which, however useful in early life, is, as I have found in old age, a cause of much waste of thinking power when the amount is so reduced as to render economy of essential importance.
Still, through the greater part of my life this habit of reading critically, combined as it was with the power of rapid calculation, has been of great use to me, especially in my contests with the Post Office, and, after I had joined the Department, in the revision of the thousands of Reports, Returns, and Minutes prepared by other officers.
In general literature, if the author attempt to deal with science, the chance of a blunder appears to be great. Even Lord Macaulay could not always do so with safety, as appears from the following passage:—“In America the Spanish territories [in 1698] spread from the equator northward and southwardthrough all the signs of the Zodiacfar into the temperate zone.”[367]What can be the meaning of the words which I have marked for Italics?
Mrs. Oliphant, too, whose admirable stories I never miss reading, says, in one of her latest, “there was a new moon making her wayupwardsin the pale sky.”[368]
There is no writer to whom I feel more grateful than to Miss Edgeworth. When a boy I read her delightful stories with the greatest possible interest, and I feel sure that they had considerable influence in the formation of my character. Unfortunately, however, they are frequently disfigured by scientific errors. Thus, in her admirable story of “The Good Aunt,” the following passage occurs: “My dearest Aunt,” cried he [Charles], stopping her hand, as she was giving her diamond ear-rings to Mr. Carat—“stay, my dearest aunt, one instant, till I have seen whether this is a good day for selling diamonds.”
“O, my dear young gentleman, no day in the Jewish calendar more proper for de purchase,” said the Jew.
“For the purchase! yes,” said Charles, “but for the sale?”
“My love,” said his aunt, “surely you are not so foolish as to think there are lucky and unlucky days.”
“No, I don’t mean anything about lucky and unlucky days,” said Charles, running up to consult the barometer; “but what I mean is not foolish indeed; in some book I’ve read that the dealers in diamonds buy them when the air is light, and sell them when it is heavy, if they can, because their scales are so nice that they vary with the change in the atmosphere.”
Now, as the metallic weights are of greater specific gravity than the diamonds, the interests of the dealers—so far as they are affected by change of atmosphere—must be to buy when the air isheavyand sell when it islight. An increase of density in the air would, of course, reduce the gravity of both diamonds and weights, but not equally: the diamonds, being the more bulky, would lose gravity more than the weights, and consequently would weigh less. If it were possible that the air should increase in density till it became as heavy, bulk for bulk, as the diamonds, they would float therein, or, in other words, weigh nothing at all.
I well remember when, as a boy, I first read this admirable story, how much I was puzzled by the mistake in question.
An error, occasionally met with in novels, is as follows. A wonderful marksman has to exhibit his powers, which he does thus:—He throws into the air two birds—or perhaps inanimate objects—as two apples; then,waiting till both are in a line with himself, sends his arrow or bullet through both. A slight consideration will show that, in a vast majority of cases, no amount of waiting would suffice.
Another prevailing error is, that a person simply standing by the side of a pool can see his own reflection from the surface—Narcissus must have found some support which enabled him to lean over the fountain.
But it is in books especially intended to teach elementary science that such errors are most to be regretted.
A few years since I purchased for some of my grandchildren the eighth edition of “The Seasons,” by Mrs. Marcet. It is an admirable work, highly interesting and useful; but before placing it in the hands of my grandchildren, I thought it necessary to read it myself—a very pleasing task, by-the-by—and to correct any errors I might find. As examples, I may mention that in Volume I.snow is described as frozen rain; that in Volume IV.bothstones in a flour-mill are said to revolve; and that the description in the same volume of a marine steam engine is very incorrect.
Again, few books are better calculated to interest boys than Dr. Parris’s “Philosophy in Sport,” but when, in the year 1829, I bought a copy for the School-Library at Bruce Castle, I found it necessary, before placing it there, to make numerous corrections to which I drew the attention of the author, who, in a letter dated March 18th, 1829, still in my possession, thanks me for my communication, and admits some of the errors, though not all.
As a specimen of the admitted errors, I give the following:—“Mr. Seymour now informed his young pupils that he had an experiment to exhibit, which would further illustrate, in a very pleasing manner, the truth of the doctrine ofvis inertiæ. He accordingly inverted a wine-glass, and placed a shilling on its foot; and having pushed it suddenly along the table,the coin flew off towards the operator, or in a direction opposite to that in which the glass was moving.”[369]
My correction is as follows: “The coin would fall nearly in a perpendicular direction, but inclined a littletowardsthe direction in which the glass was moving, owing to the friction between the glass and coin.”
As a specimen of the non-admitted errors, I give the following: “He had ignorantly fired a quantity of oxygen and hydrogen gases in a tin vessel; the consequence of the combustion was the immediate formation of avacuum; and what happened? Why, the pressure of the external air, not being any longer balanced by elastic matter in the interior of the apparatus, crushed it with violence, as any other enormous weight might have done; and so ended the accident, which report magnified into a most awful catastrophe.”[370]
My correction is as follows: “The first effect of the combustion was toexpandthe air in the vessel, and thisexpansionit was that caused the accident.”
On which the author, after quoting my correction, replies, “Now you will allow me to say that here you have fallen into an error; I am perfectly correct in saying that the accident arose from the external pressure of the atmosphere; for remember that the vessel contained a mixture of oxygen and hydrogen gases, which, bycombustion, immediately combined and formed water, leaving an almost perfect vacuum in the interior.”
If any one entertain a doubt as to which of us is correct, I would suggest his filling a small bladder with the proper mixture of oxygen and hydrogen, and exploding it by electrical means; as I did nearly sixty years ago. The bladder will be destroyed; but, according to Dr. Parris’s view, it should simply collapse.
But even men of unquestionable scientific knowledge are not always correct. The late Professor Phillips, in his able and interesting Address as President of the British Association in 1865, after noticing Foucault’s recent admeasurement of the velocity of light, proceeded as follows:—“By this experiment the velocity of light appears to be less, sensibly less, than was previously admitted; and this conclusion is of the highest interest. For, as by assuming too long a radius for the orbit of Jupiter, the calculated rate of light-movement was too great; so now, by employing the more exact rate and the same measures of time, we can correct the estimated distance of Jupiter and all the other planets from the Sun.”[371]
Professor Phillips’s great forte was geology, not astronomy. To any one familiar with the means by which Römer determined the velocity of light, it is unnecessary to point out that, although his observations were made on the satellites of Jupiter, the radius of Jupiter’s orbit has nothing to do with the problem. The only material facts are, first, thedifferencebetween the maximum and minimum distance of Jupiter from the earth,—that is to say (disregarding eccentricity) the diameter of the earth’s orbit; and, secondly, the effect which this varying distance has on the times at which the eclipses apparently take place. This effect Römer found to extend to about 16 minutes—and he thence concluded that light occupied 16 minutes in travelling across the earth’s orbit.
With the view of rendering the above intelligible to those not familiar with the subject, I offer the following illustration:—Suppose it to be known that about a certain hour a gun will be fired at a remote spot, the direction of which, but not the distance, is known, and that two persons (A. and B.) arrange to avail themselves of the opportunity for ascertaining, approximately, the velocity of sound; then, each being furnished with a good watch marking seconds, A. places himself at a certain spot, and B. at a known distance—say a mile—from A., and in a direction opposite to that of the gun, so that B.’s distance from the gun shall be a mile greater than A.’s—the actual distance in either case is unimportant.
Each now records the exact moment at which he hears the report; and if the gun be fired repeatedly, several such records are made, in order to give a more accurate result.
A. and B. then meet and compare notes. They, of course, find that A.’s time is in each instance earlier than B.’s. The average of the several differences would be about 4¾ seconds—showing that sound travels a mile in that time.[372]
The mode of procedure here described is, of course, not that actually adopted for determining the velocity of sound, but it is a practicable mode, and is selected because it is analogous to that adopted by Römer for determining the velocity of light.
A copy of Professor Phillips’s Address was sent to me immediately after its delivery, and, on my detecting the error, I endeavoured to induce a friend of his, deservedly eminent as a practical astronomer, to draw the Professor’s attention thereto, with a view to its correction before the publication of the permanent report of the Society’s proceedings; but, unfortunately, the attempt did not succeed.
In another similar case, however, as appears by the following correspondence between the Astronomer Royal and myself, I was more successful:—
“Hampstead, N.W.“1868—June 17.[373]“My dear Sir,—Pray accept my thanks for the copy of your Report. It came while I was at Brighton; but, since my return home, I have read it with great interest. I felt it a great privation not to be able to attend the Visitation.“Will you allow me to request your attention to what appear to me to be serious errors in the recent annual Address of the President of the Astronomical Society? They will be found in the last paragraph of page 119 of the ‘Monthly Notices’ for February. To save you trouble, I have extracted the part in question, and have underlined the words which I think erroneous. ‘At the present time the Earth is about three millions of miles nearer to the Sun in our northerly winter than in our summer; our coldest month is about 60° Fh. colder than our hottest, and our winter lasts for about eight dayslongerthan our summer. M. Leverrier has calculatedthat 200,000 years ago the Earth approached the Sun by upwards of ten millions of miles nearer in winter than in summer: the winters were then nearly a monthlongerthan the summers, and in the latitude of London there was a difference of about 112° Fh. between the hottest and the coldest periods of the year.’“If you find that I am right, perhaps you will have the kindness to draw Mr. Pritchard’s attention to the errors, with a view to their correction before the Address is printed in the ‘Transactions.’ I would write to Mr. Pritchard myself, but that, as I could not speak with authority, I might give offence.“I have watched the subsequent monthly numbers in the expectation of finding a correction, but none has appeared.“Faithfully yours,“Rowland Hill.“The Astronomer Royal, &c., &c., &c.”
“Hampstead, N.W.“1868—June 17.[373]
“My dear Sir,—Pray accept my thanks for the copy of your Report. It came while I was at Brighton; but, since my return home, I have read it with great interest. I felt it a great privation not to be able to attend the Visitation.
“Will you allow me to request your attention to what appear to me to be serious errors in the recent annual Address of the President of the Astronomical Society? They will be found in the last paragraph of page 119 of the ‘Monthly Notices’ for February. To save you trouble, I have extracted the part in question, and have underlined the words which I think erroneous. ‘At the present time the Earth is about three millions of miles nearer to the Sun in our northerly winter than in our summer; our coldest month is about 60° Fh. colder than our hottest, and our winter lasts for about eight dayslongerthan our summer. M. Leverrier has calculatedthat 200,000 years ago the Earth approached the Sun by upwards of ten millions of miles nearer in winter than in summer: the winters were then nearly a monthlongerthan the summers, and in the latitude of London there was a difference of about 112° Fh. between the hottest and the coldest periods of the year.’
“If you find that I am right, perhaps you will have the kindness to draw Mr. Pritchard’s attention to the errors, with a view to their correction before the Address is printed in the ‘Transactions.’ I would write to Mr. Pritchard myself, but that, as I could not speak with authority, I might give offence.
“I have watched the subsequent monthly numbers in the expectation of finding a correction, but none has appeared.
“Faithfully yours,
“Rowland Hill.
“The Astronomer Royal, &c., &c., &c.”
The Astronomer Royal promptly replied as follows:—
“Royal Observatory, Greenwich, London, S.E.“1868—June 18.“My dear Sir,—I will duly bring before Mr. Pritchard the substance of your note of yesterday.“The two clauses which you have cited are, on the face of them, erroneous; and in the first the fault clearly is in the wordlonger. In the second, the fault may be in the wordnearer. For, during the period through which the great eccentricity prevails, the semi-revolution in the precession of the equinoxes may have reversed the seasons.“It would seem that Mr. Pritchard has had in view the table in ‘Lyell’s Principles of Geology,’ Vol.I., p. 293. In the notes continued on p. 294, the references are to the case of winter in aphelion.“The subject is a thorny one, but well worth your attention.“I am, my dear Sir, yours very truly,“G. B. Airy“Sir Rowland Hill, K.C.B., &c., &c., &c.”
“Royal Observatory, Greenwich, London, S.E.“1868—June 18.
“My dear Sir,—I will duly bring before Mr. Pritchard the substance of your note of yesterday.
“The two clauses which you have cited are, on the face of them, erroneous; and in the first the fault clearly is in the wordlonger. In the second, the fault may be in the wordnearer. For, during the period through which the great eccentricity prevails, the semi-revolution in the precession of the equinoxes may have reversed the seasons.
“It would seem that Mr. Pritchard has had in view the table in ‘Lyell’s Principles of Geology,’ Vol.I., p. 293. In the notes continued on p. 294, the references are to the case of winter in aphelion.
“The subject is a thorny one, but well worth your attention.
“I am, my dear Sir, yours very truly,
“G. B. Airy
“Sir Rowland Hill, K.C.B., &c., &c., &c.”
I am not aware how the passage in question stands in the Society’s Transactions.[374]
The following narrative seems to show that in a progressive science like Astronomy even the highest authority is not infallible.
Some sixty years ago, my attention having been accidentally drawn to a tide-mill for grinding corn, I began to consider what was the source of the power employed, and came to the conclusion that it was the momentum of the earth’s revolution on its axis. The next question I asked myself was—could such power be diverted, in however slight a degree, without drawing, as it were, on the stock? Further consideration showed me that the draught required for grinding the corn was trifling in comparison with that employed in grinding the pebbles on every seashore upon the earth’s surface; and, consequently, that the drain on the earth’s momentum might suffice in the course of ages to effect an appreciable retardation in the earth’s diurnal revolution.
I now, as usual in case of difficulty, applied to my father. He could detect no fault in my reasoning, but informed me that Laplace had demonstrated in his great work (“La Mécanique Céleste”) that the time occupied in the earth’s diurnal revolution is absolutely invariable. Of course both my father and I accepted the authority as unquestionable; but I never could fully satisfy my mind on the subject, and for the greater part of my life it was a standing puzzle.
It may be stated briefly that Laplace’s demonstration appears to have rested mainly on the fact that his Lunar Tables, if employed in calculating backwards certain eclipses of the Sun which happened about 2,000 years ago, give results agreeing so nearly with the ancient records as altogether to exclude the possibility of any appreciable increase in the length of the sidereal day during that long period.
But in the year 1866 Professor Adams (really the first discoverer of the planet Neptune) received the Gold Medal of the Astronomical Society for, among other recent claims, the discovery of an error in the data on which Laplace constructed his Lunar Tables which vitiates the above demonstration.
The details of this important discovery—and the co-operation therein of M. Delaunay—were fully and ably stated by Mr. Warren De La Rue, then President of the Society, on the presentation of the Medal.[375]And the position of the question two years later is concisely stated as follows by the Rev. Charles Pritchard, in an Addendum to his address as President in 1868:—“At present, then, the case stands thus,—the Lunar Tables, if calculated on the principles of gravitation alone, as expounded by Messrs. Adams andDelaunay, and as confirmed by other mathematicians, will not exactly represent the moon’s true place at intervals separated by 2,000 years, provided the length of the day is assumed to be uniform and unaltered during the whole of the intervening period. There are grounds, however, for at least suspecting that, owing to the effects of tidal action, the diurnal rotation is, and has been, in a state of extremely minute retardation; but the mathematical difficulties of the case, owing greatly to the interposition of terrestrial continents, are so great that no definite quantitative results have hitherto been attainable. The solution of the difficulty is one of those questions which are reserved for the Astronomy of the future.”[376]
I need not say that this confirmation of the truth of my early conjecture proved highly gratifying. I have only to add that the increase during the last 2,000 years in the length of the sidereal day is generally estimated at about the eightieth part of a second; but the estimate has, I apprehend, no better foundation than this—namely, that since the recent correction in the Lunar Tables an assumed increase to the extent in question has become necessary in order to make the backward calculation of the ancient eclipses agree with the records as to time.
I have found it very difficult at my age (little less than fourscore), and with my mental powers seriously impaired, to deal, however imperfectly, with a subject so abstruse as that now under consideration; and I think it by no means improbable that there may be some error in my statement of facts or in my argument thereon.
All that I can say is that I have done my best to render intelligible to ordinary readers an important advance in modern Astronomy—interesting in itself, irrespective of its remote and accidental connection with my own biography.
The following very gratifying letter from the Astronomer Royal may perhaps be appropriately given here. It is in reply to my congratulations when, in recognition of his great public services, he was made a K.C.B.:—
“Flamsteed House, Greenwich Park, London, S.E.“1872—June 22.“My dear Sir,—I could scarcely have had a more gratifying letter in reference to the public compliment just paid to me from any one than that from yourself. I can truly say that it has been my secretpride to do what can be done by a person in my position for public service; and whose recognition of this can be more grateful than that of one who—by efforts in a similar strain, but on an infinitely larger scale—has almost changed the face of the civilized world?“My wife (I am hesitating between two titles, not knowing which is at the present moment correct, but being quite sure of that which I have written) begs me to convey to you her acknowledgment of your kind message.“I am, my dear Sir, very truly yours,“G. B. Airy.”
“Flamsteed House, Greenwich Park, London, S.E.“1872—June 22.
“My dear Sir,—I could scarcely have had a more gratifying letter in reference to the public compliment just paid to me from any one than that from yourself. I can truly say that it has been my secretpride to do what can be done by a person in my position for public service; and whose recognition of this can be more grateful than that of one who—by efforts in a similar strain, but on an infinitely larger scale—has almost changed the face of the civilized world?
“My wife (I am hesitating between two titles, not knowing which is at the present moment correct, but being quite sure of that which I have written) begs me to convey to you her acknowledgment of your kind message.
“I am, my dear Sir, very truly yours,
“G. B. Airy.”
[See p. 71.]
“In presenting to the public ‘The Laws and Regulations of the Society for Literary and Scientific Improvement,’ its members feel it their duty briefly to state the motives which influenced them in the formation of such an establishment, and to explain their reasons for occasionally deviating in the construction of their Laws from the systems which are generally adopted for the governance of similar bodies.
“The experience of almost every one who has passed the time usually devoted to education, but who still feels desirous of improvement, must have convinced him of the difficulty of regularly devoting his leisure hours to the object he has in view, from the want of constantly acting motives, and the absence of regulations which can enforce the observance of stated times. However strong the resolutions he has made, and whatever may be his conviction of the necessity of adhering to them, trivial engagements which might easily be avoided, will furnish him, from time to time, with excuses to himself for his neglect of study: thus may he spend year after year, constantly wishing for improvement, but as constantly neglecting the means of it, and old age may come upon him before he has accomplished the object of his desires; then will he look back with regret on the many opportunities he has lost, and acknowledge in despair that the time is gone by.
“Under these impressions, a few individuals who are desirous of extending their literary and scientific knowledge, have endeavoured to establish a society for that purpose; convinced that by so doing they have provided most powerful motives for mental improvement.
“It has been thought highly desirable, that every member of the society should be, as nearly as possible, upon an equality, that all may feel alike interested in the success of the whole. In order to accomplish this important object, every regular auditor is expected, according to the rules of the society, to deliver a lecture in his turn. Thus, instead of the society being divided into two parties, one consisting of lecturers, the other of critics, every member feels himself called upon to listen to the others with candour and attention, as he is aware that the time will come when he shall require the same consideration from them. It will be observed also, on a perusal of the laws, that each lecture is followed by a discussion. Thus care is insured on the part of the lecturer that he shall not attempt a subject which he has not well studied; and an opportunity is given to every member to obtain an explanation of anything advanced, which he may not have understood, or to express his opinions on the questions that may arise, and, by these means, correct or confirm his own ideas. But the principal advantage of a discussion is, that it calls forth the individual exertion of every member, by inviting each to take a part in the general instruction, and thus affording constant inducements to private reading and study.
“In a town so populous as Birmingham, and which for superiority in art is dependent on the discoveries of science, it cannot be doubted that many individuals may be found who are desirous of intellectual advancement. For such persons ‘The Society for Literary and Scientific Improvement’ was established; and they are respectfully and earnestly invited to lend their assistance towards the promotion of its objects. The society cannot promise that they shall meet with any considerable talent or learning among its members; but in mixing with their equals, with young men of similar tastes and similar pursuits, they may hope to find in a generous emulation most powerful motives for application and perseverance.
“The details of management of a society like this, may, on a superficial view, appear of little importance; those, however, who have had opportunities of closer examination, will, it is presumed, agree with the members of this Institution, in considering an attention to such particulars as necessary, not only to the well-being, but to the permanent existence of an association, for whatever purpose it may be formed.
“With views like these, the ‘Society for Literary and Scientific Improvement’ have been anxious to establish a mode of electingthe Committee, that should secure (as nearly as possible), an accurate representation of the whole body; not only because it appeared reasonable that the members would feel interested in the welfare of the Institution, in proportion as the arrangements and regulations met their own views and wishes, but because experience proves that, owing to imperfect methods of choosing those who are to direct the affairs of a society, the whole sway sometimes gets into the hands of a small party, and is exercised, perhaps unconsciously, in a way that renders many persons indifferent, and alienates others, until all becomes listlessness, decay, and dissolution.
“Men of worth and talent, of every denomination in religion and politics, will be welcome members of the society; and to prevent any unpleasant collision of opinions, it has been thought advisable to exclude altogether the discussion of subjects which have reference to peculiarities in religious belief, or to the political speculations of the day; the important questions which respect the wealth of nations, however, as they have no connexion with passing politics, are considered as among the proper objects for the society’s attention.
“Such gentlemen as may feel desirous of improving their minds by engaging in establishments of a nature similar to this, but who, on account of their residing at a distance from any large town, have not hitherto had the opportunity, will, it is hoped, be induced by the regulations respecting corresponding members, to join the society; and they may depend upon meeting with every attention, whenever the Committee shall be favoured with their communications.”
[See p. 93.]
The mode of extracting the roots ofexact cubeswhich I taught the boys, and which was probably that adopted by Zerah Colbourn, will be best shown by an example. Suppose the question to be, What is the cube root of 596,947,688? This looks like a formidable array of figures, and a schoolboy, resorting to the usual mode of extracting the root, would fill his slate with figures, and perhaps occupy an hour in the process. Zerah Colbourn or my class would have solved the question in a minute, and without making any figures at all. My class would have proceeded as follows: They would first fix in their memories the number of millions (596) and the last figure of the cube (8), disregarding all other figures. Then, knowing the cubes of all numbers from 1 to 12 inclusive, they would at once see that the first or left-hand figure of the root must be 8; and deducting the cube of 8 (512) from 596, they would obtain a remainder of 84. This they would compare with the difference between the cube of 8 (512) and the cube of 9 (729), that is to say, with 217; and seeing that it was nearly four-tenths of such difference, they would conclude that the second figure of the root was 4. The third or last figure of the root would require no calculation, the terminal figure of anexactcube always indicating the terminal figure of its root—thus 8 gives 2. The cube root, therefore, is 842. In this process there is some risk of error as regards the second figure of the root, especially when the third figure is large; but with practice an expert calculator is able to pay due regard to that and certain other qualifications which I could not explain without making this note unduly long. As already stated, Zerah Colbourn did occasionally blunder in the second figure; and this circumstance assisted me in discovering the above process, which I have little doubt is the one he followed. If, instead of an exactcube, another number of nine figures be taken, the determination of the third figure of the root, instead of being the easiest, becomes by far the most difficult part of the calculation.
[This part of the explanation was written by Sir Rowland Hill, as a note to the Prefatory Memoir, before the year 1871. What follows was added in 1875.]
Rule for extracting the roots of imperfect cubes divisible into three periods:—
1. Find first and second figures as described above.
2. Deduct cube of first figure from the first period (of the number whose root is to be extracted), modified, if necessary, as hereafter described.
3. Then multiply the number (expressed by both figures) by each figure in succession, and by 3.
4. Deduct the product (or the significant figures thereof—see example), from the remainder obtained as above. (See 2).
5. Divide the remaindernowobtained by the square of the number expressed by both figures (see 3), multiplied by 3—dropping insignificant figures (see example),—and the quotient will be the last figure (or 3rd figure) of the root.
I can confidently affirm from experience that there is nothing in the above calculations too difficult for those who, possessing a natural aptitude, are thoroughly well practised in mental arithmetic. I doubt, however, whether the mode just described be exactly that which we followed; our actual mode, looking at the results as described above (which is in exact accordance with my Journal), must, I think, have been more facile; but as it is fully fifty years since I gave any thought to the subject, and as, in the eightieth year of my age, I find my brain unequal to further investigation, I must be contented with the result at which I have arrived.
It must be remarked, however, that cases will arise when some modification of the process will be necessary. As, for instance, when the first period of the cube is comparatively light, it may be necessary to include therein one or more figures of the second period treated as decimals; indeed, if the first period consist of a single figure, it will be better to incorporate it with the second period, and treat both together as one period,[377]relative magnitude in the first period dealt with being important as a means of securing accuracy in the last figure of the root. But expert calculators soon learn toadopt necessary modifications, and by the “give-and-take” process to bring out the correct result. Indeed, I find it recorded in my Journal that “small errors will sometimes arise which, under unfavourable circumstances, will occasionally amount to a unit.” These observations it must be understood to apply only to the extraction of the roots of imperfect cubes, which Zerah Colbourn invariably refused to attempt. When the cube is perfect, the last figure of the root, as shown in the text, requires no calculation at all.
Example.What is the cube root of 596,947,687?[Note.—This is the number treated above, except that in the unit’s place 7 is substituted for 8, in order to render the number an imperfect cube; so slight a change, however—though rendering it necessary tocalculatethe last figure of the root,—will still leave the root as before.]Following the rule, we find the first and second figures of the root in the manner described above. They are 8 and 4.We next calculate the third or last figure of the root.As the first figure of the second period of the cube is so large, it will be unsafe to disregard it. Call the first period, therefore, 596·9; all other figures may be neglected.596·9mill.(2)8³ =512”84·9”(3) deduct 84 x 8 x 4 x 3 = (roughly)80·6”(5) divide by 84² x 3 = (88 x 80 x 3)[378]= 2·14·32Quotient—2, which is the third or last figure of the root.[Note.—I have not encumbered the above figures with the ciphers which should accompany them, as, to the expert calculator, this will be needless.]The root, therefore, is 842.
Example.
What is the cube root of 596,947,687?
[Note.—This is the number treated above, except that in the unit’s place 7 is substituted for 8, in order to render the number an imperfect cube; so slight a change, however—though rendering it necessary tocalculatethe last figure of the root,—will still leave the root as before.]
Following the rule, we find the first and second figures of the root in the manner described above. They are 8 and 4.
We next calculate the third or last figure of the root.
As the first figure of the second period of the cube is so large, it will be unsafe to disregard it. Call the first period, therefore, 596·9; all other figures may be neglected.
[Note.—I have not encumbered the above figures with the ciphers which should accompany them, as, to the expert calculator, this will be needless.]
The root, therefore, is 842.
It is stated in the text that my pupils could extract the cube roots of numbers ranging as high as 2,000,000,000. In the ordinary mode this number would be divided, as above, into four periods; but my pupils treated the 2,000 as one period, the approximate root of which is of course 12, the cube of 12 being 1,728.
[See p. 202.]
Bruce Castle, Tottenham,June 7th, 1832.
To the Council of the Royal Astronomical Society.
Gentlemen,—In troubling you with the following sketch of an improvement in astronomical clocks, I have a two-fold object. First, to obtain the loan of the necessary instruments, should you consider the plan worth prosecuting; and, secondly, to avail myself of the suggestions of such members of the Society as are more experienced than myself in the minute details of practical astronomy. The objects of the proposed improvement are: To supply an apparatus capable of measuring time to a small fraction of a second, and to make the determination of the exact time a matter of calm and deliberate inquiry, and thus to avoid the errors which must frequently arise from the hurry attending the present method.
In order to accomplish these objects, I propose to make use of the principle of the Vernier, by suspending in front of the clock an additional pendulum somewhat shorter than that of the clock, and so placed that the coincidence of the two when vertical may be determined by means similar to those used by Captain Kater; this additional or Vernier pendulum to be put in motion at the instant of observation by means of a trigger under the command of the observer at the telescope, and its vibrations reckoned till a coincidence takes place between it and the clock pendulum. This pendulum may have a maintaining power and an index to save the trouble of counting. When at rest, the Vernier pendulum must of course be raised to the extent of its oscillation.
The results of experiments commenced with very imperfect instruments about two years and a-half ago, and continued at intervals to the present time, appear to be as follows:—
When a Vernier pendulum, vibrating once in ·9 second, or 10 times in 9 seconds, is employed, its coincidences with the seconds pendulum of the clock may be determined to a single vibration with the greatest ease by the unassisted eye, and thus, of course, tenths of a second are readily estimated.
When a Vernier pendulum vibrating once in ·99 second, or 100 times in 99 seconds, is employed, its coincidences with the seconds pendulum of the clock may also be determined to a single vibration, but not without the aid of a telescope. By these means hundredths of a second are measured without much difficulty.
In order to avoid the inconvenience of having to suspend sometimes one pendulum and sometimes the other, and also to escape the loss of time which, if the hundredths pendulum were constantly used, would arise when the observer wished to estimate tenths of a second only, I propose to adopt the following arrangement:—To employ a single Vernier pendulum of such a length as to vibrate once in 8·99 second, or a thousand times in 899 seconds. This pendulum differs so slightly from the tenths pendulum (making ten vibrations in 8·99 seconds, instead of 9 seconds), that for estimating tenths of a second it is practically the same, while it affords the means of measuring hundredths of a second also. Its operation will be best understood by an example:—Suppose the interval to be measured by means of the Vernier to be ·24 second. At the second and third vibrations of the Vernier pendulum after its release there would be approximate coincidences between it and the clock pendulum, showing the fraction of time to be between two-tenths and three-tenths of a second. The coincidence at the second vibration would, however, be somewhat nearer than that at the third. At the twelfth vibration there would be another approximate coincidence somewhat closer than the first. At the twenty-second vibration there would be a yet closer coincidence. At the thirty-second one closer still, and at the forty-second vibration the coincidence would be the most accurate of the series. Thus it appears that the tenths of a second may be known by counting single vibrations of the Vernier pendulum till a coincidence of some kind occurs, and that the hundredths of a second may be determined by counting the decades of vibrations, or all the coincidences after the first, until the most exact coincidence arises.
By the use of the Vernier pendulum, when connected with anindex, all chance of error in reading the clock will, it is conceived, be avoided. Having touched the trigger at the moment of observation, the observer has, as it were, registered the time, and he may examine the clock at his leisure, for it is manifest that a comparison of the index of the Vernier pendulum with that of the clock will at any time determine the moment of observation. It will also be seen that, should the observer omit to notice the first coincidence of the pendulums, no inconvenience except delay will arise, because the same coincidences will occur in a regular series as long as the pendulums continue in motion.
There are a few provisions necessary for extreme accuracy which, in this hasty sketch, it would be out of place to notice. I will just mention, however, that the apparatus contains within itself the means of measuring what may be calledthe mean error of the observer, or the average interval which, as regards the particular individual, elapses between the instant of observation and the release of the Vernier pendulum.
To subject the plan which I have here attempted hastily to describe to a rigid trial will require instruments of much greater accuracy than those which I can command, and if the Society possess a good clock not now in use, I shall feel extremely obliged if I can obtain the loan of it. An additional pendulum the requisite length, is not, I presume, to be found among the Society’s instruments.
I have the honour to be, Gentlemen,
Your obedient servant,
Rowland Hill.
[See p. 205.]
Two (or more) principal offices to be established in convenient places for business—say,one near the Bank, and one near the Regent Circus, Piccadilly; these offices to communicate with each other by means of omnibuses.
Coaches and omnibuses to radiate from these offices to all parts of the environs of London.
A country office to be established at the extremity of each route.
The town to be divided into small districts, and the country into larger, each with a house for the receipt and distribution ofparcels. (Shopkeepers who have goods to distribute in the neighbourhood may undertake this). These stations to be, as far as practicable, on the routes of the coaches.
The principal and the country offices to be receiving and distributing houses, each for its own district.
Each coach in coming from the country to collect parcels from the stations on its route, bringing them to its principal office. On going out, to carry parcels for distribution from the principal office to the same stations. Thus every parcel will pass through one or other of the principal offices. (Exceptions can be made, if desirable, with respect to parcels which would otherwise pass twice over the ground, viz., those received at stations between the principal office and the place of their destination; but the first arrangement would be by far the most simple).
Stations not on a coach route must transfer parcels to the nearest stations which are on a route, and receive parcels from the same. [Qy. A small extra charge].
Places to be booked at any station for any coach; a memorandum being transmitted to the principal office concerned, with the parcels.
In some cases the passengers themselves may be so transmitted.
The omnibuses passing between the principal offices to carry passengers and parcels from each for the other. Thus every coach will practically start from both principal offices.
Coaches to depart from each principal office all at the same time. Say, for all principal places, once every hour, from —— in the morning till —— at night.
Coaches to arrive at each principal office all at the same time, say a few minutes before the time of departure, the interval being sufficient to transfer passengers and parcels.
The periods of departure and arrival at one office to differ by half-an-hour from the corresponding periods at the other, so as to allow just time enough (calculated at half-an-hour), for a transfer by the omnibuses from one office to the other. Thus the coaches from one office will start at the beginning and from the other in the middle of each hour.
Horses to be kept and changed at the country offices, or at stations about the middle of each route. The latter arrangement will make the stage shorter, and will bring the horse stations more immediately under central revision. It will also require a less number of horse stations, as in many cases one station will serve for two or more roads branching out from each other. (At least one pair of horses must be kept at the extreme station).
Supernumerary coaches and horses to be kept at the central offices for use on any road on which there may be a temporary demand.
Each coachman to pay a certain rent, and with certain deductions to receive the payments for passengers and parcels, but to have no control as to the sum to be charged, the hour of starting, &c.
The masters of the stations to be remunerated by a certain sum (to be paid by the coachman) for each passenger booked, and for each parcel received or distributed.
Contracts to be made in all possible cases. Thus the coachmaker may supply coaches at —— each per annum, or at —— per mile travelled.
The keepers of the horse stations may contract each for the supply of horses required at his station at —— per mile.
In disposing of the shares, a preference to be given to those who would make frequent use of the coaches, especially to those who travel to London daily, as their influence would materially promote the interests of the concern.
A personal right to go to or from town daily, by the same coach, to be sold for a period, say a week, at a considerably reduced rate, or a month at a still lower rate.
Proprietors to be entitled to similar privileges at five per cent. less than others.
Transferable tickets, giving the holder a right to travel by any coach in either direction on a particular road, to be sold (say twenty at a time) at a slightly reduced rate.
All the carriages to be painted alike, and so as readily to distinguish them from those not belonging to the Company.
An establishment on an extensive scale, such as is described in the foregoing sketch, would possess many decided advantages over the little independent establishments now existing. It would be more economically managed; the necessary publicity would be more easily given to its arrangements; the responsibility of the servants would be more efficient; and the extent and permanence of the undertaking would justify the most watchful attention to exact punctuality, to a proper speed, to the safety and comfort of the passengers, and, in short, to all circumstances conducive to a high reputation with the public.
Economy.—This would manifestly result from the great division of labour, and the wholesale demand for every article of expenditure. Also from the power of transferring coaches from any road on which there was less to one on which there was more travelling than usual.
The system of contracts and sub-contracts could not be introduced with advantage into a small concern.
Publicity.—The readiness with which the arrangements could be described would tend greatly to their publicity. Thus, it would be easily said and easily remembered, that from a certain office coaches depart every hour, and from a certain other office at the half-hour, to all the principal places within the limits of the threepenny post. This statement, with a list of the places, fares, &c., would be placarded at every station, and on every coach and omnibus.
Responsibility.—An active and intelligent superintendent, well acquainted with the means of holding others to responsibility, should devote his whole time to the undertaking, visiting the various stations periodically to see that all arrangements are observed, to settle the accounts, &c.
He should require accurate reports to be made, showing at all times the actual state of affairs, and the improvement or deterioration in each department The most exact rules should be laid down and enforced for the conduct of each class of servants. These rules should be placarded in the coaches, at the stations, &c.
Enquiries as to the conduct of all concerned should be made frequently of the proprietors who use the coaches daily, and everypossible attention paid to the well-founded complaints of passengers generally. A till might be placed in each carriage, with an inscription requesting passengers having cause to complain to put a statement of such complaint, withname and address, into the till, which should be opened at the central office at least once in each day.
Punctuality and Speed.—The proper time of starting and that of passing each station should be inscribed conspicuously on each coach, as well as at each station. The actual time kept should be recorded at each extreme station and at the horse station, and fines levied on the coachman for deviation beyond certain limits. The allowance of time for the journey should be such as to require the coachman to drive steadily but rapidly, with no stoppage beyond a very short one (say a minute) at each station, and a little more for taking up and putting down passengers on the road.
The coach should never wait nor turn out of the direct road between the extreme stations. To save time, the passengers, in the omnibuses at least, should be requested to pay as they go on. At the inferior stations a signal might be established to show whether the coach need stop or not.
Safety of Passengers.—Coaches of the safest construction, steady horses, and temperate coachmen, only should be employed; and whenever an accident occurs from whatever cause, a heavy fine should be levied on the coachman, allowing him the right to recover the whole or part of the penalty of the coach-contractor or horse-contractor, according to circumstances. No galloping should be allowed.
The coach-contractor should be required to station a man at each central office to examine each coach every time it comes in.
Comfort of Passengers.—Some protection from wet and cold to be provided for the outside passengers. Means of ascending and descending to be improved. A convenient room at each station for those waiting. The stations shouldnotbe taverns; but coffee and some other refreshments may be provided—there being no obligation, however, to call for anything. The room should contain a map of London, directory, &c.
The arrangements of the Company would be capable of gradual and almost indefinite extension. Thus they might take in towns more and more distant, or they might comprehend hackney-coaches, cabriolets, and omnibuses to all parts of London. The machinery required for the distribution of parcels might be applied to that of the periodic publications; and a contract might be entered into, advantageous to the public as well as to the Company, for thecollection, carriage, and distribution of the twopenny and threepenny post letters.
This distribution might easily take placeeach hour, the letters being carried by the coaches. No guards would be required, as the bags might be put into a boot, of which keys should be kept at the post-offices only.
[See p. 230.]
[The following letter toThe Scotsmanwas written by Mr. John Forster, late Member for Berwick. In a marginal note Sir R. Hill has written, “I vouch for its accuracy.”]