[8]See his "Martyrs of Science."[9]This portion of the subject was illustrated by means of a Diagram exhibiting the Diameters and Magnitudes of Planets, thus:—Table of diameters of planets with drawings.The Moon's diameter is 2,160 miles; and its distance from the Earth is 237,000 miles.[Text alternative to image:]Miles.The Sun882,000Jupiter91,522Saturn76,018Uranus35,100Neptune33,600Earth7,916Venus7,702Mars4,398Mercury3,123[10]See the Table,Plate I.Fig. 2, for distinguished names of their angels, spirits, or demons.[11]See Translation, by Admiral W. H. Smith, and Robert Grant, M.A., in 2 vols. 8vo. 1855, Vol. I., page 10.
[8]See his "Martyrs of Science."
[9]This portion of the subject was illustrated by means of a Diagram exhibiting the Diameters and Magnitudes of Planets, thus:—
Table of diameters of planets with drawings.
The Moon's diameter is 2,160 miles; and its distance from the Earth is 237,000 miles.
[Text alternative to image:]
[10]See the Table,Plate I.Fig. 2, for distinguished names of their angels, spirits, or demons.
[11]See Translation, by Admiral W. H. Smith, and Robert Grant, M.A., in 2 vols. 8vo. 1855, Vol. I., page 10.
Of the Twelve Houses.—The 1st, 4th, 7th, and 10th houses—angular.—These are of more durable signification than the others, denoting the wife or husband—a situation under Government, &c. &c.
The twelve houses have signification of all the various concerns of human life, and of nature at large.
For Example.—When the cusp of the first house is well aspected by, or has the presence of Jupiter or Venus, and these are not afflicted by the aspects of evil planets, they preserve life in infancy, and give health, and often an agreeable person.
But if their rays or presence (says Varley) should be thrown on the cusp of the second house, then the native will have success in concerns of property. The Sun in this house helps to disperse property; and if he be peregrine, that is, in the sign of a contrary nature to his own, where he has no dignities, and is without reception, then the native's property is dispersed in vainglorious expenses; but if the Sun be in Leo, his property in general will be ample enough to admit of instant acts of bounty and benevolence.
In a similar strain, Astronomers particularize the remaining eleven houses. It would be impossible, in any reasonable space, to describe further the operations of the planets in the several houses thus assigned to them.
As to when the Planets are most powerful.—Barrett says:—The planets are powerful when they are ruling in a house, or in exaltation, or triplicity, or term, or face, without combustion of what is direct in the figure of the heavens; but we must take care that they are not in the bounds or under the dominion of Saturn or Mars. The angles of the ascendant, and 10th and 7th are fortunate; as also the lord of the ascendant, and place of the Sun and Moon.
The Moon is powerful if she be in her house, in exaltation, in triplicity, in face, or in degree convenient for the desired work, &c. &c.
Varley's Table of Signs, Houses, Exaltation, and Triplicity.
The falls of the Planets are opposite to their Exaltations, and their Detriments opposite to their Houses.
Aries and Scorpio are the house of Mars♂Taurus and Libra are the house of Venus♀Gemini and Virgo are under the dominion of Mercury☿Cancer is the house of the Moon☽Leo is the house of the Sun☉Sagittarius and Pisces are the houses of Jupiter♃Capricorn is the house of Saturn♄And Aquarius is governed by the Herschel Planet♅
This table gives the usual symbols employed for indicating the several planets, and which are still retained in Astronomy for simplicity of expression, but which Astrologers venerate as possessing a cabalistic character.
Associated with these symbols are the names of certain principal angels, spirits, or demons, forming, however, but a small proportion of such airy nothings.
The Astrological Symbols were also employed by the Alchemists to indicate the seven metals then known.
Mr. James Smith, of Liverpool, the most laborious among recent workers in this field of enquiry, claiming to have propounded several simple and exact methods, offers the following as sufficiently demonstrative:—
I construct my diagrams in the following way:—I draw two straight lines at right angles, making O the right angle. From the point O, in the direction OA, I mark off four equal parts together equal to OA, and from O, in the direction of OB, I mark off three of such equal parts together, equal to OB, and join AB. It is obvious, or rather self-evident, that AOB is a right-angled triangle, of which the sides that contain the right angle are in the ratio of 4 to 3, by construction. With A as centre and AB as interval, I describe the circle X, produce AO and BO to meet and terminate in the circumference of the circle at the points G and C, and join AC, CG, and BG, producing the quadrilateral ACGB. I bisect AG at F, and with O as centre, and OF as interval, describe the circle Z. The line OF is the line that joins the middle points of the diagonals in the quadrilateral ACGB; and it follows that,
{AG2+ CB2+ 4(OF2)} = {AC2+ CG2+ BG2+ AB2.}
When AO = 4, we get the following equation:—
{52+ 62+ (4 × 1'52)} = {52+ sqrt(102) + sqrt(102) + 52,} or, {25 + 36 +9}={25 + 10 + 10 + 25} = 70. From the points B and C, I draw straight lines at right angles to AB and AC, and therefore tangential to the circle X, to meet AG produced at D, and join BD and CD, producing the quadrilateral ACDB. I bisect AD at E, and with O as centre, and EO as interval describe the circle XY, and with E as centre, and EA or ED as interval describe the circle Y.
Now, to square the circle, or, in other words, to get exactly equal in superficial area to the circle X, I will show how to find it. From the point G draw a straight line—say Gm—perpendicular to ED, making Gmequal GD. Produce GA to a pointn, making Gnequal to 2AG - GD, and joinn m. The square onn mwill be the required square. (I have indicated this square by dotted lines.) For example:—If AO = 4, then AG = 5, and GD = 1'25; therefore {2 AG - GD} = {10 - 1'25} = 8'75 = Gn: and Gm = 1'25; therefore, Gn2+ Gm2= 3-1/8 (AB2); that is, {8'752+ 1'252} = 3-1/8 (52), or, {76'5625 + 1'5625} = {3'125 × 25}; and this equation=Area of the Circle X; and area of the square onn m:: and it follows, that the area of every circle, is equal to the area of a square on the hypotenuse of a right-angled triangle, of which the sides that contain the right angle are in the ratio of 7 to 1, and the sum of these two sides equal to the diameter of the circle. In many ways I have proved this fact, by practical or constructive geometry.
Duplication of the Cube.—In his "Young Geometrician; or, Practical Geometry without Compasses," 1865, Mr. Oliver Byrne's 40th Problem is as follows:—
Let AB be the side of a given cube BD. It is required to find AC, the side of another cube CE, so that the solid contents of the cube CE are double the solid contents of the cube BD.
Ancient and modern mathematicians (says Mr. Byrne) have in vain attempted to solve this problem geometrically, that is, by the ruler and compasses only.
Let AB = BG = GR = RQ = QP = QO = OR = VZ. The length of the shortest side of the lesser set square; a line of any other given length may be applied. Draw OP and VR parallel to it; then apply the set squares in close contact, the edge OV of OVT passing through the point O, while the points of V and Z of ZSV fall exactly on the lines RV, RZ. Then draw the line ZBC, cutting FA produced in C; then the cube on AC is double the cube on AB.
Trisection of an Angle.—In his work entitledYoung Geometrician, 1865, Mr. Oliver Byrne gives as the 39th Problem: To divide a given angle BAC into three equal angles:—
The line Amis made =p q, the least side of the lesser triangular ruler; by (II)p mis drawn parallel, andm nperpendicular to AB. Then both rulers are kept in motion, and at the same time in close contact, as represented in the figure, untilpfalls on the linep m, andnon the linem n;r nA passing through the angular point A.
Then the angle DAB is one-third of the angle CAB. Mr. Byrne asserts that this problem is not capable of solution by the straight line and circle. Mathematicianshave in vain attempted to solve it geometrically, that is, by the ruler and compasses only.
Perpetuum Mobile.Desaguliers demonstrated the absurdity of attempting to raise weights enclosed in a cellular wheel, simply by providing for their approach in succession nearer to the centre on the ascending side, while they should be projected further from the centre on the descending side. He remarks:—
Those who think the velocity of the weight is the line it describes, expect that that weight shall be overpoised, which describes the shortest line, and therefore contrive machines to cause the ascending weight to describe a shorter line than the descending weight.
For example, in the circle A B Da, the weights A and B being supposed equal, it is imagined that, if by any contrivance whatever, whilst the weight A describes the arc Aa, the weight B is carried in any arc, as Bb, so as to come nearer the centre in its rising, than if it went up the arc B D; the said weight shall be overpoised, and consequently, by a number of such weights, a perpetual motion produced.
Now the velocity of any weight isnotthe line which it describes in general, but the height that it rises up to, or falls from, with respect to its distance from the centre of the earth. So that when the weight describes the arc Aa, its velocity is the line A C, which shows the perpendicular descent, and likewise the line B C denotes the velocity of the weight B, or the height that it rises to, when it ascends in any of the arcs Bb, instead of the arc B D: so that, in this case, whether the weight B, in its ascent be broughtnearer the centre or not, it loses no velocity, which it ought to do, in order to be raised up by the weight A.
Indeed, if the weight at B, could by any means spring as it were, or be lifted up tox, and move in the arcx b, the end would be answered, because then the velocity would be diminished, and becomexC.
In "The Life, Times, and Scientific Labours of the Marquis of Worcester," 1865, page 454, will be found a full account of the present diagram, which is intended to illustrate as far as possible, an approach to the probable construction of the wheel by the Marquis in the 56th article of his memorable "Century of Inventions."
If any likely-looking method, could, more than another, render hopelessness more hopeless, surely this mechanical demonstration must prove most efficient for that purpose. For here, we actually produce a wheel agreeing to the terms with which Desaguliers closes his demonstration, when he suggests the only likely method to effect the end proposed, namely, perpetual motion. We find the fallen weight is absolutely "lifted up" as he desires, and "moves in the arc" he describes, and yet although he declares that then "the end would be answered"—it absolutely isnotanswered in this instance.
It is not requisite to calculate throughout the effect of the Marquis's entire number of 40 weights; four will suffice, taking the vertical and horizontal spokesa a a a, showing two ringsaandb; one,b, 12 inches within the other, so that the wheel being, as the Marquis says, 14 feet diameter, the inner ring will be 12 feet diameter. Now let eachweight D be attached in the centre of a cord or chaina´, D, b´, 2 feet long, and then secure one end, asa´, so the extreme end of each spokea´, and the other end of the cord, as b´, to place on one lesser ring, as atb, or 12 inches from each spoke.
We shall then find by admeasurement that the upper weight on the vertical spoke is 7 feet from the centre, and the lower weight 6 feet; while at the same time there appears to be a preponderance due to the superior length of the horizontal arm A´; but against this latter we have the rising weightb´D, 1 foot from the centre, which, added to the 6 feet on the horizontal spoke, neutralizes the hoped-for effect, and the wheel remains instatu quo.
THE END.
Plate 1.LONDON. E. & F. N. SPON. 48, CHARING CROSS.[Link to explanation of Plate 1.]
Plate 2.LONDON. E. & F. N. SPON. 48, CHARING CROSS.[Link to explanation of Plate 2.]
Plate 3.LONDON. E. & F. N. SPON. 48, CHARING CROSS.[Link to explanation of Plate 3.]
Plate 4.LONDON. E. & F. N. SPON. 48, CHARING CROSS.[Link to explanation of Plate 4.]
Plate 5.LONDON. E. & F. N. SPON. 48, CHARING CROSS.[Link to explanation of Plate 5.]
Plate 6.LONDON. E. & F. N. SPON. 48, CHARING CROSS.[Link to explanation of Plate 6.]
One Volume 8vo., of 650 pages, illustrated with Steel Engravings of two unpublished Portraits and 45 Wood Engravings, price 24s,
THE LIFE, TIMES, AND SCIENTIFIC LABOURS OFEDWARD SOMERSET,sixth earl and secondMARQUIS OF WORCESTER,
To which is added,
A REPRINT OF HIS CENTURY OF INVENTIONS (1663),with a commentary thereon.
⁂ Thirty copies are printed on Large Paper, 1 vol. 4to. withIndia Proofsbefore the Letters of the Portraits, price £3. 3s.
"A monument raised late, it is true, but not too late, to a great and modest genius. A national biography which illustrates and elevates our ideas of the past, and a contribution which the world will recognize to the European history of Science."—Dublin University Magazine, September, 1865.
"A work which displays a high order of literary ability, careful antiquarian research, much ingenuity, and withal thorough honesty of purpose.
"[Lord Worcester], his life, told as Mr. Dircks has told it, is one of much interest.
"Here we have an elaborate—although of course not a completely exhaustive—account of his life; at any rate the most complete account of him ever likely to be written—a work filled with abundant evidence of the most painstaking research, a work written in a generous and sympathising spirit, and with every attribute of conscientiousness."—Engineering, 5th January, 1866.
"The production of this volume is no common achievement; Mr. Dircks has undertaken to write the life of a man about whom the public know very little.
"He has, we think, collected some curious information, and established the claim of the Marquis to be the first constructor of a steam-engine. The reprint of the celebratedCentury of Inventionsadds greatly to the interest of the volume."—The Spectator, 14th September, 1867.
One Volume, 8vo., price 21s, only 100 copies printed,
WORCESTERIANA;
A COLLECTION OF
BIOGRAPHICAL AND OTHER NOTICES, ALPHABETICALLY ARRANGED, RELATING TO EDWARD SOMERSET, SECOND
MARQUIS OF WORCESTER,
AND HIS IMMEDIATE FAMILY CONNECTIONS; WITH OCCASIONAL NOTES.
"The present volume is, as it were, a supplement. [To. Mr. Dircks'sLife of the Marquis of Worcester.] It contains what the French call 'pièces justificatives,' on which that biography was founded; and such other materials connected with the history of Lord Worcester's family and his invention of the steam-engine as will prevent, as far as possible, a repetition of the gross errors hitherto promulgated on these subjects."—Notes and Queries, February 3, 1866.
One Volume, post 8vo., with 130 wood engravings, price 10s6d,
PERPETUUM MOBILE;
OR,
HISTORY OF THE SEARCH FOR SELF-MOTIVE POWER DURING THE17TH, 18TH, AND 19THCENTURIES,
With an Introductory Essay.
"The literature of this subject [Perpetual Motion] is very extensive, but scattered mainly through Patent Records and ephemeral pamphlets. We would especially refer the curious reader to a recent work by Mr. Dircks, entitledPerpetuum Mobile, to which we have been indebted for historical notices. It is extremely complete and interesting as a history."—Chambers's Encyclopædia, Part 15, 1865.
"A very useful collection on the history of the attempts at perpetual motion, that is, of obtaining the consequences of power without any power to produce them."—Professor De Morgan'sBudget of Paradoxes, No. 28.—Athenæum, July 15, 1865.
One Volume, post 8vo., with portrait, price 3s6d,
CONTRIBUTION TOWARDS A HISTORY OFELECTRO-METALLURGY,ESTABLISHING THE ORIGIN OF THE ART.
"In his Introduction, Mr. Dircks has clearly stated the claims of invention, and fairly discussed the only just grounds that can give claim to priority of invention."—The Mining Journal, February 7, 1863.
"In the collection of chronological and other data for the history of various branches and application of science, Mr. Dircks appears to be indefatigable."—The Electrician, February 27.
"It is a useful and clear digest of evidence, and apparently impartially put together."—The Practical Mechanics' Journal(Glasgow), July.
One Volume, post 8vo., with two portraits, price 4s,
INVENTORS AND INVENTIONS,
IN THREE PARTS.
I.The Philosophy of Invention, considered strictly in relation to Ingenious Contrivances tending to facilitate Scientific Operations, to extend Manufacturing Skill, or to originate New Sources of Industry.—II.The Rights and Wrongs of Inventors, Legally and Politically Examined.—III.Early Inventors' Inventories of Secret Inventions, employed from the 13th to the 17th Century, in substitution of Letters Patent.
"The author enters fully and effectually into the claims and grievances of the inventor. He discusses the arguments for and against the concession of patent right, and examines very ably leaders in theTimeson patent monopoly; very clearly dissipating the sophism of the opponents of patent right; also Sir William Armstrong's evidence regarding 'patent monopoly,' &c., affording an interesting and useful publication from its many excellences."—The Scientific Review, September 2, 1867.
"The second part of the volume discusses the right of inventors to a property in their inventions, and thus raises the question of the patent laws, and the twofold issue, whether it will be better to retain them and reform them, or to sweep them away altogether. We are bound to admit that he treats this topic in a fair spirit, and without any taint of bigotry. Mr. Dircks is a man whose opinions are entitled to a hearing."—The London Review, September 21.
"Mr. Dircks treats the real problem and discusses the comparative merits of the existing system, and the advantages which he, together with many others, hopes would follow on the establishment of some judicial council of inventions. The difficulties of the question are enormous, and no one will think the less of them after having gone through this volume.
"The third part, or the lists of their inventions left by many great and some ingenious persons, is interesting and curious."—The Westminster Review, October.
One Volume, post 8vo., price 3s6d,
A BIOGRAPHICAL MEMOIR OFSAMUEL HARTLIB,MILTON'S FAMILIAR FRIEND,
With Bibliographical Notices of Works published by him; and a reprint of his Pamphlet entitled
"AN INVENTION OF ENGINES OF MOTION."
"Mr. Dircks's is the first careful attempt to make posterity his (Hartlib's) friend."—The Examiner, 18th February, 1865.
"A scholar-like little monograph, giving all the information that can be given about a man whose name occurs in the correspondence of almost every eminent literary or scientific person of the time of the Commonwealth."—The Spectator, 20th May.
One Volume, post 8vo., with engravings, price 2s,
THE GHOST!
AS PRODUCED IN THE SPECTRE DRAMA,
POPULARLY ILLUSTRATING THE MARVELLOUS OPTICAL ILLUSIONS OBTAINED BY THE APPARATUS CALLED THE DIRCKSIAN PHANTASMAGORIA.
"Mr. Dircks gives us the benefit of all his progressive discoveries in the matter, from the paper first read at the British Association Meeting at Leeds, in 1858, to the more recent improvements, with full explanations of the machinery, apparatus, and processes adopted in these ghost dramas, and further favours the public with a number of new adaptations. As a curious description of these spectral illustrations, the book is most interesting."—The Technologist, January, 1864.
"A volume explanatory of the uncommonly clever and scientific "spectral illusion" which has of late fairly turned the public head."—The Dublin Builder, January 1.
"A few months ago all London was rushing off to see Professor Pepper's Ghost, as it was called, but which it now appears was the property of Mr. Dircks, and from which his good name was filched in a very unhandsome manner. Here then he tells us all about it, how the spectre was raised, and how we may ourselves at pleasure call spirits from the vasty deep."—The Bookseller, February 29.
Transcriber's NotesPage36: changed "Sorbiere" to "Sorbière" (15. Samuel Sorbière visited the works at Vauxhall)Page61: changed "Jupiper" to "Jupiter" (of cloves, &c. to Jupiter;)Page83: changed "BD2" to "BG2" ({AG2+ CB2+ 4(OF2)} = {AC2+ CG2+ BG2+ AB2.})Page83: changed "sqrt(10252)" to "sqrt(102) + 52" ( ... = {52+ sqrt(102) + sqrt(102) + 52,})Page84: changed closing parenthesis to closing braces ( ... 9}={25 + 10 + 10 + 25} = 70)Page84: changed "tangental" to "tangential" (tangential to the circle X)Page84: changed "Q" to "2" (making Gnequal to 2AG - GD)Page84: added missing opening parenthesis in "(I have indicated this square by dotted lines.)"Page84: changed "+ 1'25}" to "× 25" ({76'5625 + 1'5625} = {3'125 × 25})Page84: changed "hypothenuse" to "hypotenuse" (the area of a square on the hypotenuse)
Page36: changed "Sorbiere" to "Sorbière" (15. Samuel Sorbière visited the works at Vauxhall)
Page61: changed "Jupiper" to "Jupiter" (of cloves, &c. to Jupiter;)
Page83: changed "BD2" to "BG2" ({AG2+ CB2+ 4(OF2)} = {AC2+ CG2+ BG2+ AB2.})
Page83: changed "sqrt(10252)" to "sqrt(102) + 52" ( ... = {52+ sqrt(102) + sqrt(102) + 52,})
Page84: changed closing parenthesis to closing braces ( ... 9}={25 + 10 + 10 + 25} = 70)
Page84: changed "tangental" to "tangential" (tangential to the circle X)
Page84: changed "Q" to "2" (making Gnequal to 2AG - GD)
Page84: added missing opening parenthesis in "(I have indicated this square by dotted lines.)"
Page84: changed "+ 1'25}" to "× 25" ({76'5625 + 1'5625} = {3'125 × 25})
Page84: changed "hypothenuse" to "hypotenuse" (the area of a square on the hypotenuse)