The larger ships in the navy, and some of the more recent small ones, such as the new cruisers of the Phaeton class, are fitted with powerful steam winches of a type made by Messrs. Belliss and Co. These are used for lifting the pinnaces and torpedo boats.
We give an illustration of one of these winches. The cylinders are 6 in. in diameter and 10 in. stroke. The barrel is grooved for wire rope, and is safe to raise the second class steel torpedo boats, weighing nearly 12 tons as lifted. The worm gearing is very carefully cut, so that the work can be done quietly and safely. With machinery of this kind a boat is soon put into the water, and as an arrangement is fitted for filling the boat's boilers with hot water from the ship's boilers, the small craft can be under way in a very short time from the order being given.
Mr. White is fitting compound engines with outside condensers to boats as small as 21 ft. long, and we give a view of a pair of compound engines of a new design, which Messrs. Belliss are making for the boats of this class. The cylinders are 4 in. and 7 in. in diameter by 5 in. stroke. The general arrangement is well shown in the engraving. On a trial recently made, a 25 ft. cutter with this type of engines reached a speed of 7.4 knots.
About three years ago the late Controller of the Navy, Admiral Sir W. Houston Stewart, wished to ascertain the relative consumption of fuel in various classes of small vessels. An order was accordingly sent to Portsmouth, and a series of trials were made. From the official reports of these we extract the information contained in tables F and G, and we think the details cannot fail to be of interest to our readers. The run around the island was made in company with other boats, without stopping, and observations were taken every half hour. The power given out by the engines was fairly constant throughout. The distance covered was 56 knots, and the total amount of fuel consumed, including that required for raising steam, was 1,218 lb. of coal and 84 lb. of wood. The time taken in raising steam to 60 lb. pressure was forty-three minutes. The rate of consumption of fuel is of course not the lowest that could be obtained, as a speed of over 10 knots is higher than that at which the machinery could be worked most economically.
STEAM WINCH FOR HOISTING AND LOWERING PINNACLES AND TORPEDO BOATS.
STEAM WINCH FOR HOISTING AND LOWERING PINNACLES AND TORPEDO BOATS.
The trials afterward made to find the best results that could be obtained in fuel consumption were rather spoiled by the roughness of the weather on the day they were made. The same boat was run for 10 miles around the measured mile buoys in Stokes Bay. The following are some of the results recorded:
In connection with this subject it may perhaps be of interest to give particulars of a French and American steam launch; these we extract from the United States official report before mentioned.
The boat is built of wood, and coppered. The engine consists of one non-condensing cylinder, 7½ in. in diameter and 5.9 in. stroke. The boiler has 4.3 square feet of grate surface. The screw is 21⅔ in. in diameter by 43.3 in, pitch. The speed is 7 knots per hour obtained with 245 revolutions per minute, the slip being 19.7 per cent. of the speed.
The United States navy steam cutters built at the Philadelphia navy yard are of the following dimensions:
The engine has a single cylinder 8 in. in diameter and 8 in. stroke of piston. The screw is four bladed, 4 in. long and 31 in. in diameter by 45 in. pitch. The following is the performance at draught of water 2 feet above rabbet of keel:
These boats are of 1870 type, but may be taken as typical of a large number of steam cutters in the United States navy. The naval authorities have, however, been lately engaged in extensive experiments with compound condensing engines in small boats, and the results have proved so conclusively the advantages of the latter system that it will doubtless be largely adopted in future.—Engineer.
[2]
In consequence of the seas breaking over the boat, a large number of diagrams were destroyed, and, on account of the roughness of the weather, cards were only taken with the greatest difficulty. The records of power developed are therefore not put forward as authoritative.
The illustrations we give represent an expansion trap by Mr. Hyde, and made by Mr. S. Farron, Ashton-under-Lyne. The general appearance of this arrangement is as in Fig. 1 or Fig. 3, the center view, Fig. 2, showing what is the cardinal feature of the trap, viz., that it contains a collector for silt, sand, or sediment which is not, as in most other traps, carried out through the valve with the efflux of water. The escape valve also is made very large, so that while the trap may be made short, or, in other words, the expansion pipe may not be long, a tolerably large area of outlet is obtained with the short lift due to the small movement of the expansion pipe.
IMPROVED STEAM TRAP.
IMPROVED STEAM TRAP.
The object of a steam trap is for the removal of water of condensation without allowing the escape of steam from drying apparatus and steam pipes used for heating, power, or other purposes. One of the plans employed is by an expansion pipe having a valve fixed to its end, so that when the pipe shortens from being cooler, due to the presence of the water, the valve opens and allows the escape of the water until the steam comes to the trap, which, being hotter, lengthens the pipe and closes the valve. Now with this kind of trap, and, in fact, with any variety of trap, we understand that it has been frequently the experience of the user to find his contrivance inoperative because the silt or sand that may be present in the pipes has been carried to the valve and lodged there by the water, causing it to stick, and with expansion traps not to close properly or to work abnormally some way or other. The putting of these contrivances to rights involves a certain amount of trouble, which is completely obviated by the arrangement shown in the annexed engravings, which is certainly a simple, strong, and substantial article. The foot of the trap is made of cast iron, the seat of the valve being of gun metal, let into the diaphragm, cast inside the hollow cylinder. The valve, D, is also of gun metal, and passing to outside through a stuffing box is connected to the central expansion pipe by a nut at E. The valve is set by two brass nuts at the top, so as to be just tight when steam hot; if, then, from the presence of water the trap is cooled, the pipe contracts and the water escapes. A mud door is provided, by which the mud can be removed as required. The silt or dirt that may be in the pipes is carried to the trap by the water, and is deposited in the cavity, as shown, the water rises, and when the valve, D, opens escapes at the pipe, F, and may be allowed to run to waste. A pipe is not shown attached to F, but needless to say one may be connected and led anywhere, provided the steam pressure is sufficient. For this purpose the stuffing-box is provided; it is really not required if the water runs to waste, as is represented in the engraving. To give our readers some idea of the dimensions of the valve, we may say that the smallest size of trap has 1 in. expansion pipe and a valve 3 in. diameter, the next size 1¼ in. expansion pipe and a valve 4½ in. diameter, and the largest size has a pipe 1½ in. and a valve 6 in. diameter. Altogether, the contrivance has some important practical advantages to recommend it.—Mech. World.
In our study of the exact methods of measurement in use to-day, in the various branches of scientific investigation, we should not forget that it has been a plant of very slow growth, and it is interesting indeed to glance along the pathway of the past to see how step by step our micron of to-day has been evolved from the cubit, the hand's breadth, the span, and, if you please, the barleycorn of our schoolboy days. It would also be a pleasant task to investigate the properties of the gnomon of the Chinese, Egyptians, and Peruvians, the scarphie of Eratosthenes, the astrolabe of Hipparchus, the parallactic rules of Ptolemy, Regimontanus Purbach, and Walther, the sextants and quadrants of Tycho Brahe, and the modifications of these various instruments, the invention and use of which, from century to century, bringing us at last to the telescopic age, or the days of Lippershay, Jannsen, and Galileo.
FIG. 1.
FIG. 1.
It would also be a most pleasant task to follow the evolution of our subject in the new era of investigation ushered in by the invention of that marvelous instrument, the telescope, followed closely by the work of Kepler, Scheiner, Cassini, Huyghens, Newton, Digges, Nonius, Vernier, Hall, Dollond, Herschel, Short, Bird, Ramsden, Troughton, Smeaton, Fraunhofer, and a host of others, each of whom has contributed a noble share in the elimination of sources of error, until to-day we are satisfied only with units of measurement of the most exact and refined nature. Although it would be pleasant to review the work of these past masters, it is beyond the scope of the present paper, and even now I can only hope to call your attention to one phase of this important subject. For a number of years I have been practically interested in the subject of the production of plane and curved surfaces particularly for optical purposes,i.e., in the production of such surfaces free if possible from all traces of error, and it will be pleasant to me if I shall be able to add to the interest of this association by giving you some of my own practical experience; and may I trust that it will be an incentive to all engaged in kindred workto do that work well?
FIG. 2.
FIG. 2.
In the production of a perfectly plane surface, there are many difficulties to contend with, and it will not be possible in the limits of this paper to discuss the methods of eliminating errors when found; but I must content myself with giving a description of various methods of detecting existing errors in the surfaces that are being worked, whether, for instance, it be an error of concavity, convexity, periodic or local error.
FIG. 3
FIG. 3
A very excellent method was devised by the celebrated Rosse, which is frequently used at the present time; and those eminent workers, the Clarks of Cambridge, use a modification of the Rosse method which in their hands is productive of the very highest results. The device is very simple, consisting of a telescope (a, Fig. 1) in which aberrations have been well corrected, so that the focal plane of the objective is as sharp as possible. This telescope is first directed to a distant object, preferably a celestial one, and focused for parallel rays. The surface,b, to be tested is now placed so that the reflected image of the same object, whatever it may be, can be observed by the same telescope. It is evident that if the surface be a true plane, its action upon the beam of light that comes from the object will be simply to change its direction, but not disturb or change it any other way, hence the reflected image of the object should be seen by the telescope,a, without in any way changing the original focus. If, however, the supposed plane surface proves to beconvex, the image will not be sharply defined in the telescope until the eyepiece is movedawayfrom the object glass; while if the converse is the case, and the supposed plane is concave, the eyepiece must now be movedtowardthe objective in order to obtain a sharp image, and the amount of convexity or concavity may be known by the change in the focal plane. If the surface has periodic or irregular errors, no sharp image can be obtained, no matter how much the eyepiece may be moved in or out.
FIG. 4
FIG. 4
This test may be made still more delicate by using the observing telescope,a, at as low an angle as possible, thereby bringing out with still greater effect any error that may exist in the surface under examination, and is the plan generally used by Alvan Clark & Sons. Another and very excellent method is that illustrated in Fig. 2, in which a second telescope,b, is introduced. In place of the eyepiece of this second telescope, a diaphragm is introduced in which a number of small holes are drilled, as in Fig. 2,x, or a slit is cut similar to the slit used in a spectroscope as shown aty, same figure. The telescope,a, is now focused very accurately on a celestial or other very distant object, and the focus marked. The object glass of the telescope,b, is now placed against and "square" with the object glass of telescopea, and on looking through telescope a an image of the diaphragm with its holes or the slit is seen. This diaphragm must now be moved until a sharp image is seen in telescopea. The two telescopes are now mounted as in Fig. 2, and the plate to be tested placed in front of the two telescopes as atc. It is evident, as in the former case, that if the surface is a true plane, the reflected image of the holes or slit thrown upon it by the telescope,b, will be seen sharply defined in the telescope,a.
FIG. 5.
FIG. 5.
If any error of convexity exists in the plate, the focal plane is disturbed, and the eyepiece must be movedout. If the plate is concave, it must be movedinto obtain a sharp image. Irregular errors in the plate or surface will produce a blurred or indistinct image, and, as in the first instance, no amount of focusing will help matters. These methods are both good, but are not satisfactory in the highest degree, and two or three important factors bar the way to the very best results. One is that the aberrations of the telescopes must be perfectly corrected, a very difficult matter of itself, and requiring the highest skill of the optician. Another, the fact that the human eye will accommodate itself to small distances when setting the focus of the observing telescope. I have frequently made experiments to find out how much this accommodation was in my own case, and found it to amount to as much as 1/40 of an inch. This is no doubt partly the fault of the telescopes themselves, but unless the eye is rigorously educated in this work, it is apt to accommodate itself to a small amount, and will invariably do so if there is a preconceived notion or biasin the direction of the accommodation.
FIG. 6.
FIG. 6.
Talking with Prof. C.A. Young a few months since on this subject, he remarked that he noticed that the eye grew more exact in its demands as it grew older, in regard to the focal point. A third and very serious objection to the second method is caused by diffraction from the edges of the holes or the slit. Let me explain this briefly. When light falls upon a slit, such as we have here, it is turned out of its course; as the slit has two edges, and the light that falls on either side is deflected both right and left, the rays that cross from the right side of the slit toward the left, and from the left side of the slit toward the right, produce interference of the wave lengths, and when perfect interference occurs, dark lines are seen. You can have a very pretty illustration of this by cutting a fine slit in a card and holding it several inches from the eye, when the dark lines caused by a total extinction of the light by interference may be seen.
FIG. 7.
FIG. 7.
If now you look toward the edge of a gas or lamp flame; you will see a series of colored bands, that bring out the phenomenon of partial interference. This experiment shows the difficulty in obtaining a perfect focus of the holes or the slit in the diaphragm, as the interference fringes are always more or less annoying. Notwithstanding these defects of the two systems I have mentioned, in the hands of the practical workman they are productive of very good results, and very many excellent surfaces have been made by their use, and we are not justified in ignoring them, because they are the stepping stones to lead us on to better ones. In my early work Dr. Draper suggested a very excellent plan for testing a flat surface, which I briefly describe. It is a well known truth that, if an artificial star is placed in the exact center of curvature of a truly spherical mirror, and an eyepiece be used to examine the image close beside the source of light, the star will be sharply defined, and will bear very high magnification. If the eyepiece is now drawn toward the observer, the star disk begins to expand; and if the mirror be a truly spherical one, the expanded disk will be equally illuminated, except the outer edge, which usually shows two or more light and dark rings, due to diffraction, as already explained.
FIG. 8.
FIG. 8.
Now if we push the eyepiece toward the mirror the same distance on the opposite side of the true focal plane, precisely the same appearance will be noted in the expanded star disk. If we now place our plane surface any where in the path of the rays from the great mirror, we should have identically the same phenomena repeated. Of course it is presumed, and is necessary, that the plane mirror shall be much less in area than the spherical mirror, else the beam of light from the artificial star will be shut off, yet I may here say that any one part of a truly spherical mirror will act just as well as the whole surface, there being of course a loss of light according to the area of the mirror shut off.
This principle is illustrated in Fig. 3, whereais the spherical mirror,bthe source of light,cthe eyepiece as used when the plane is not interposed,dthe plane introduced into the path at an angle of 45° to the central beam, andethe position of eyepiece when used the with the plane. When the plane is not in the way, the converging beam goes back to the eyepiece,c. When the plane,d, is introduced, the beam is turned at a right angle, and if it is a perfect surface, not only does the focal plane remain exactly of the same length, but the expanded star disks, are similar on either side of the focal plane.
FIG. 9.
FIG. 9.
I might go on to elaborate this method, to show how it may be made still more exact, but as it will come under the discussion of spherical surfaces, I will leave it for the present. Unfortunately for this process, it demands a large truly spherical surface, which is just as difficult of attainment as any form of regular surface. We come now to an instrument that does not depend upon optical means for detecting errors of surface, namely, the spherometer, which as the name would indicate means sphere measure, but it is about as well adapted for plane as it is for spherical work, and Prof. Harkness has been, using one for some time past in determining the errors of the plane mirrors used in the transit of Venus photographic instruments. At the meeting of the American Association of Science in Philadelphia, there was quite a discussion as to the relative merits of the spherometer test and another form which I shall presently mention, Prof. Harkness claiming that he could, by the use of the spherometer, detect errors bordering closely on one five-hundred-thousandth of an inch. Some physicists express doubt on this, but Prof. Harkness has no doubt worked with very sensitive instruments, and over very small areas at one time.
I have not had occasion to use this instrument in my own work, as a more simple, delicate, and efficient method was at my command, but for one measurement of convex surfaces I know of nothing that can take its place. I will briefly describe the method of using it.
FIG. 10.
FIG. 10.
The usual form of the instrument is shown in Fig. 4;ais a steel screw working in the nut of the stout tripod frame,b;c c care three legs with carefully prepared points;dis a divided standard to read the whole number of revolutions of the screw,a, the edge of which also serves the purpose of a pointer to read off the division on the top of the milled head,e. Still further refinement may be had by placing a vernier here. To measure a plane or curved surface with this instrument, a perfect plane or perfect spherical surface of known radius must be used to determine the zero point of the division. Taking for granted that we have this standard plate, the spherometer is placed upon it, and the readings of the divided head and indicator,d, noted when the point of the screw,a, just touches the surface,f. Herein, however, lies the great difficulty in using this instrument,i.e., to know the exact instant of contact of the point of screw,a, on the surface,f. Many devices have been added to the spherometer to make it as sensitive as possible, such as the contact level, the electric contact, and the compound lever contact. The latter is probably the best, and is made essentially as in Fig. 5.
FIG. 11.
FIG. 11.
I am indebted for this plan to Dr. Alfred Mayer. As in the previous figure,ais the screw; this screw is bored out, and a central steel pin turned to fit resting on a shoulder atc. The end ofdprojects below the screw,a, and the end,e, projects above the milled head, and the knife edge or pivot point rests against the lever,f, which in turn rests against the long lever,g, the point,h, of which moves along the division atj. It is evident that if the point of the pin just touches the plate, no movement of the index lever,g, will be seen; but if any pressure be applied, the lever will move through a multiplied arc, owing to the short fulcri of the two levers. Notwithstanding all these precautions, we must also take into account the flexure of the material, the elasticity of the points of contact, and other idiosyncrasies, and you can readily see that practice alone in an instrument so delicate will bring about the very best results. Dr. Alfred Mayer's method of getting over the great difficulty of knowing when all four points are in contact is quite simple. The standard plate is set on the box,g, Fig. 4, which acts as a resonater. The screw,a, is brought down until it touches the plate. When the pressure of the screw is enough to lift off either or all of the legs, and the plate is gently tapped with the finger, arattleis heard, which is the tell-tale of imperfect contact of all the points. The screw is now reversed gently and slowly until themomentthe rattle ceases, and then the reading is taken. Here the sense of hearing is brought into play. This is also the case when the electric contact is used. This is so arranged that the instant of touching of the point of screw,a, completes the electric circuit, in which an electromagnet of short thick wire is placed. At the moment of contact, or perhaps a little before contact, the bell rings, and the turning of the screw must be instantly stopped. Here are several elements that must be remembered. First, it takes time to set the bell ringing, time for the sound to pass to the ear, time for the sensation to be carried to the brain, time for the brain to send word to the hand to cease turning the screw, and, if you please, it takes time for the hand to stop. You may say, of what use are such refinements? I may reply, what use is there in trying to do anything the very best it can be done? If our investigation of nature's profound mysteries can be partially solved with good instrumental means, what is the result if we have better ones placed in our hands, and what, we ask, if thebestare given to the physicist? We have only to compare the telescope of Galileo, the prism of Newton, the pile of Volta, and what was done with them, to the marvelous work of the telescope, spectroscope, and dynamo of to-day. But I must proceed. It will be recognized that in working with the spherometer, only the points in actual contact can be measured at one time, for you may see by Fig. 6 that the four points,a a a a, may all be normal to a true plane, and yet errors of depression, as ate, or elevation, as atb, exist between them, so that the instrument must be used over every available part of the surface if it is to be tested rigorously. As to how exact this method is I cannot say from actual experience, as in my work I have had recourse to other methods that I shall describe. I have already quoted you the words of Prof. Harkness. Dr. Hastings, whose practical as well as theoretical knowledge is of the most critical character, tells me that he considers it quite easy to measure to 1/80000 of an inch with the ordinary form of instrument. Here is a very fine spherometer that Dr. Hastings works with from time to time, and which he calls his standard spherometer. It is delicately made, its screw being 50 to the inch, or more exactly 0.01998 inch, or within 2/100000 of being 1/50 of an inch pitch. The principal screw has a point which is itself an independent screw, that was put in to investigate the errors of the main screw, but it was found that the error of this screw was not as much as the 0.00001 of an inch. The head is divided into two hundred parts, and by estimation can be read to 1/100000 of an inch. Its constants are known, and it may be understood that it would not do to handle it very roughly. I could dwell here longer on this fascinating subject, but must haste. I may add that if this spherometer is placed on a plate of glass and exact contact obtained, and then removed, and the hand held over the plate without touching it, the difference in the temperature of the glass and that of the hand would be sufficient to distort the surface enough to be readily recognized by the spherometer when replaced. Any one desiring to investigate this subject further will find it fully discussed in that splendid series of papers by Dr. Alfred Mayer on the minute measurements of modern science published in SCIENTIFIC AMERICAN SUPPLEMENTS, to which I was indebted years ago for most valuable information, as well as to most encouraging words from Prof. Thurston, whom you all so well and favorably know. I now invite your attention to the method for testing the flat surfaces on which Prof. Rowland rules the beautiful diffraction gratings now so well known over the scientific world, as also other plane surfaces for heliostats, etc., etc. I am now approaching the border land of what may be called the abstruse in science, in which I humbly acknowledge it would take a vast volume to contain all I don't know; yet I hope to make plain to you this most beautiful and accurate method, and for fear I may forget to give due credit, I will say that I am indebted to Dr. Hastings for it, with whom it was an original discovery, though he told me he afterward found it had been in use by Steinheil, the celebrated optician of Munich. The principle was discovered by the immortal Newton, and it shows how much can be made of the ordinary phenomena seen in our every-day life when placed in the hands of the investigator. We have all seen the beautiful play of colors on the soap bubble, or when the drop of oil spreads over the surface of the water. Place a lens of long curvature on a piece of plane polished glass, and, looking at it obliquely, a black central spot is seen with rings of various width and color surrounding it. If the lens is a true curve, and the glass beneath it a true plane, these rings of color will be perfectly concentric and arranged in regular decreasing intervals. This apparatus is known as Newton's color glass, because he not only measured the phenomena, but established the laws of the appearances presented. I will now endeavor to explain the general principle by which this phenomenon is utilized in the testing of plane surfaces. Suppose that we place on the lower plate, lenses of constantly increasing curvature until that curvature becomes nil, or in other words a true plane. The rings of color will constantly increase in width as the curvature of the lens increases, until at last one color alone is seen over the whole surface, provided, however, the same angle of observation be maintained, and provided further that the film of air between the glasses is of absolutely the same relative thickness throughout. I say the film of air, for I presume that it would be utterly impossible to exclude particles of dust so that absolute contact could take place. Early physicists maintained that absolute molecular contact was impossible, and that the central separation of the glasses in Newton's experiment was 1/250,000 of an inch, but Sir Wm. Thomson has shown that the separation is caused by shreds or particles of dust. However, if this separation is equal throughout, we have the phenomena as described; but if the dust particles are thicker under one side than the other, our phenomena will change to broad parallel bands as in Fig. 8, the broader the bands the nearer the absolute parallelism of the plates. In Fig. 7 letaandbrepresent the two plates we are testing. Rays of white light,c, falling upon the upper surface of platea, are partially reflected off in the direction of raysd, but as these rays do not concern us now, I have not sketched them. Part of the light passes on through the upper plate, where it is bent out of its course somewhat, and, falling upon thelowersurface of the upper plate, some of this light is again reflected toward the eye atd. As some of the light passes through the upper plate, and, passing through the film of air between the plates, falling on the upper surface of thelowerone, this in turn is reflected; but as the light that falls on this surface has had to traverse the film of airtwice, it is retarded by a certain number of half or whole wave-lengths, and the beautiful phenomena of interference take place, some of the colors of white light being obliterated, while others come to the eye. When the position of the eye changes, the color is seen to change. I have not time to dwell further on this part of my subject, which is discussed in most advanced works on physics, and especially well described in Dr. Eugene Lommel's work on "The Nature of Light." I remarked that if the two surfaces were perfectlyplane, there would be one color seen, or else colors of the first or second order would arrange themselves in broad parallel bands, but this would also take place in plates of slight curvature, for the requirement is, as I said, a film of air of equal thickness throughout. You can see at once that this condition could be obtained in a perfect convex surface fitting a perfect concave of the same radius. Fortunately we have a check to guard against this error. To produce a perfect plane,three surfaces mustbe worked together, unless we have a true plane to commence with; but to make this true plane by this method wemustwork three together, and if each one comes up to the demands of this most rigorous test, we may rest assured that we have attained a degree of accuracy almost beyond human conception. Let me illustrate. Suppose we have plates 1, 2, and 3, Fig. 11. Suppose 1 and 2 to be accurately convex and 3 accurately concave, of the same radius. Now it is evident that 3 will exactly fit 1 and 2, and that 1 and 2 will separately fit No. 3,butwhen 1 and 2 are placed together, they will only touch in the center, and there is no possible way to make three plates coincide when they are alternately tested upon one another than to makeperfect planesout of them. As it is difficult to see the colors well on metal surfaces, a one-colored light is used, such as the sodium flame, which gives to the eye in our test, dark and bright bands instead of colored ones. When these plates are worked and tested upon one another until they all present the same appearance, one may be reserved for a test plate for future use. Here is a small test plate made by the celebrated Steinheil, and here two made by myself, and I may be pardoned in saying that I was much gratified to find the coincidence so nearly perfect that the limiting error is much less than 0.00001 of an inch. My assistant, with but a few months' experience, has made quite as accurate plates. It is necessary of course to have a glass plate to test the metal plates, as the upper platemustbe transparent. So far we have been dealing with perfect surfaces. Let us now see what shall occur in surfaces that are not plane. Suppose we now have our perfect test plate, and it is laid on a plate that has a compound error, say depressed at center and edge and high between these points. If this error is regular, the central bands arrange themselves as in Fig. 9. You may now ask, how are we to know what sort of surface we have? A ready solution is at hand. The bandsalways travel in the direction of the thickest film of air, hence on lowering the eye, if the convex edge of the bands travel in the direction of the arrow, we are absolutely certain that that part of the surface being tested is convex, while if, as in the central part of the bands, the concave edges advance, we know that part is hollow or too low. Furthermore, any small error will be rigorously detected, with astonishing clearness, and one of the grandest qualities of this test is the absence of "personal equation;" for, given a perfect test plate,it won't lie, neither will it exaggerate. I say, won't lie, but I must guard this by saying that the plates must coincide absolutely in temperature, and the touch of the finger, the heat of the hand, or any disturbance whatever will vitiate the results of this lovely process; but more of that at a future time. If our surface is plane to within a short distance of the edge, and is there overcorrected, or convex, the test shows it, as in Fig. 10. If the whole surface is regularly convex, then concentric rings of a breadth determined by the approach to a perfect plane are seen. If concave, a similar phenomenon is exhibited, except in the case of the convex, the broader rings are near the center, while in the concave they are nearer the edge. In lowering the eye while observing the plates, the rings of the convex plate will advance outward, those of the concave inward. It may be asked by the mechanician, Can this method be used for testing our surface plates? I answer that I have found the scraped surface of iron bright enough to test by sodium light. My assistant in the machine work scraped three 8 inch plates that were tested by this method and found to be very excellent, though it must be evident that a single cut of the scraper would change the spot over which it passed so much as to entirely change the appearance there, but I found I could use the test to get the general outline of the surface under process of correction. These iron plates, I would say, are simply used for preliminary formation of polishers. I may have something to say on the question of surface plates in the future, as I have made some interesting studies on the subject. I must now bring this paper to a close, although I had intended including some interesting studies of curved surfaces. There is, however, matter enough in that subject of itself, especially when we connect it with the idiosyncrasies of the material we have to deal with, a vital part of the subject that I have not touched upon in the present paper. You may now inquire, How critical is this "color test"? To answer this I fear I shall trench upon forbidden grounds, but I call to my help the words of one of our best American physicists, and I quote from a letter in which he says by combined calculation and experiment I have found the limiting error for white light to be 1/50000000 of an inch, and for Na or sodium light about fifty times greater, or less than 1/800000 of an inch. Dr. Alfred Mayer estimated and demonstrated by actual experiment that the smallest black spot on a white ground visible to the naked eye is about 1/800 of an inch at the distance of normal vision, namely, 10 inches, and that a line, which of course has the element of extension, 1/5000 of an inch in thickness could be seen. In our delicate "color test" we may decrease the diameter of our black spot a thousand times and still its perception is possible by the aid of our monochromatic light, and we may diminish our line ten thousand times, yet find it just perceivable on the border land of our test by white light. Do not presume I am so foolish as to even think that the human hand, directed by the human brain, can ever work the material at his command to such a high standard of exactness. No; from the very nature of the material we have to work with, we are forbidden even to hope for such an achievement; and could it be possible that, through some stroke of good fortune, we could attain this high ideal, it would be but for a moment, as from the very nature of our environment it would be but an ignis fatuus. There is, however, to the earnest mind a delight in having a high model of excellence, for as our model is so will our work approximate; and although we may go on approximatingourideal forever, we can never hope to reach that which has been set for us by the great Master Workman.