Chapter II: Glass-Grinding and Opticians' Work (1)

§ 52. As no instructions of any practical value in this art have, so far as I know, appeared in any book in English, though a great deal of valuable information has been given in the English Mechanic and elsewhere, I shall deal with the matter sufficiently fully for all practical purposes. On the other hand, I do not propose to treat of all the methods which have been proposed, but only those requisite for the production of the results claimed. The student is requested to read through the chapter before commencing any particular operation.

§ 53. The simplest way will be to describe the process of manufacture of some standard optical appliance, from which a general idea of the nature of the operations will be obtained. After this preliminary account special methods may be considered in detail. I will begin with an account of the construction of an achromatic object glass for a telescope, not because a student in a physical laboratory will often require to make one, but because it illustrates the usual processes very well; and requires to be well and accurately made.

A knowledge of the ordinary principles of optics on the part of the reader is assumed, for there are plenty of books on the theory of lenses, and, in any case, it is my intention to treat of the art rather than of the science of the subject. By far the best short statement of the principles involved which I have seen is Lord Rayleigh's article on Optics in the Encyclopaedia Britannica, and this is amply sufficient.

The first question that crops up is, of course, the subject of the choice of glass. It is obvious that the glass must be uniform in refractive index throughout, and that it must be free from air bubbles or bits of opaque matter. [Footnote: The complete testing of glass for uniformity of refractive index can only be arrived at by grinding and polishing a sufficient portion of the surfaces to enable an examination to be made of every part. In the case of a small disc it is sufficient to polish two or three facets on the edge, and to examine the glass in a field of uniform illumination through the windows thus formed. Very slight irregularities will cause a "mirage" easily recognised.]

The simplest procedure is to obtain glass of the desired quality from Messrs. Chance of Birmingham, according to the following abbreviated list of names and refractive indices, which may be relied upon:-

Density. Refractive Index.

C D F G

Hard crown

2.85 1.5146 1.5172 1.5232 1.5280

Soft crown

2.55 1.5119 1.5146 1.5210 1.5263

Light flint

3.21 1.5700 1.5740 1.5839 1.5922

Dense flint

3.66 1 6175 1.6224 1.6348 1.6453

Extra dense flint

3.85 1.6450 1.6504 1.6643 1.6761

Double extra dense flint

4.45 1.7036 1.7103 1.7273 ...

The above glasses may be had in sheets from 0.25 to 1 inch thick, and 6 to 12 inches square, at a cost of, say, 7s. 6d. per pound.

Discs can also be obtained of any reasonable size. Discs 2 inches in diameter cost about £1 per dozen, discs 3 inches in diameter about 10s. each. The price of discs increases enormously with the size. A 16-inch disc will cost about £100.

For special purposes, where the desired quality of glass does not appear on the list, an application may be made to the Jena Factory of Herr Schott. In order to give a definite example, I may mention that for ordinary telescopic objectives good results may be obtained by combining the hard crown and dense flint of Chance's list, using the crown to form a double convex, and the flint to form a double concave lens. The convex lens is placed in the more outward position in the telescope, i.e. the light passes first through it.

The conditions to be fulfilled are:

(1) The glass must be achromatic;

(2) it must have a small spherical aberration for rays converging to the principal focus.

It is impossible to discuss these matters without going into a complete optical discussion. The radii of curvature of the surfaces, beginning with the first, i.e. the external face of the convex lens, are in the ratio of 1, 2, and 3; an allowance of 15 inches focal length per inch of aperture is reasonable (see Optics in Ency. Brit.), and the focal length is the same as the greatest radius of curvature. Thus, for an object glass 2 inches in diameter, the first surface of the convex lens would have a radius of curvature of 10 inches, the surface common to the convex and concave lens would have a radius of curvature of 20 inches, and the last surface a radius of curvature of 30 inches. This would also be about the focal length of the finished lens. The surfaces in contact have, of course, a common curvature, and need not be cemented together unless a slight loss of light is inadmissible.

I will assume that a lens of about 2 inches diameter is to be made by hand, i.e. without the help of a special grinding or polishing machine; this can be accomplished perfectly well, so long as the diameter of the glass is not above about 6 inches, after which the labour is rather too severe. The two glass discs having been obtained from the makers, it will be found that they are slightly larger in diameter than the quoted size, something having been left for the waste of working.

It is difficult to deal with the processes of lens manufacture without entering at every stage into rather tedious details, and, what is worse, without interrupting the main account for the purpose of describing subsidiary instruments or processes. In order that the reader may have some guide in threading the maze, it is necessary that he should commence with a clear idea of the broad principles of construction which are to be carried out. For this purpose it seems desirable to begin by roughly indicating the various steps which are to be taken.

(1) The glass is to be made circular in form and of a given diameter.

(2) Called Rough Grinding. The surfaces of the glass are to be made roughly convex, plane, or concave, as may be required; the glass is to be equally thick all round the edge. In this process the glass is abraded by the use of sand or emery rubbed over it by properly shaped pieces of iron or lead called "tools."

(3) The glass is ground with emery to the correct spherical figure as given by a spherometer.

(4) Called Fine Grinding. The state of the surface is gradually improved by grinding with finer and finer grades of emery.

(5) The glass is polished by rouge.

(6) The glass is "figured." This means that it is gradually altered in form by a polishing tool till it gives the best results as found by trial.

In processes 2 to 5 counterpart tool surfaces are required--as a rule two convex and two concave surfaces for each lens surface. These subsidiary surfaces are worked (i.e. ground) on discs of cast iron faced with glass, or on slate discs; and discs thus prepared are called "tools."

Taking these processes in the order named, the mode of manufacture is shortly as follows:-

(1) The disc of glass, obtained in a roughly circular form, is mounted on an ordinary lathe, being conveniently cemented by Regnault's mastic to a small face plate. The lathe is rotated slowly, and the glass is gradually turned down to a circular figure by means (1) of a tool with a diamond point; or (2) an ordinary hand-file moistened with kerosene, as described in § 42; or (3) a mass of brass or iron served with a mixture of emery--or sand--and water fed on to the disc, so that the disc is gradually ground circular.

The operation of making a circular disc of given diameter does not differ in any important particular from the similar operation in the case of brass or iron, and is in fact merely a matter of turning at a slow speed.

(2 and 3) Roughing or bringing the surfaces of the glass roughly to the proper convex or concave shape. This is accomplished by grinding, generally with sand in large works, or with emery in the laboratory, where the time saved is of more importance than the value of the emery.

Discs of iron or brass are cast and turned so as to have a diameter slightly less than that of the glass to be ground, and are, say, half an inch thick. These discs are turned convex or concave on one face according as they are to be employed in the production of concave or convex glass surfaces. The proper degree of convexity or concavity may be approximated to by turning with ordinary turning tools, using a circular arc cut from zinc or glass (as will be described) as a "template" or pattern. This also is a mere matter of turning.

The first approximation to the desired convex or concave surface of the glass is attained (in the case of small lenses, say up to three inches diameter) by rotating the glass on the lathe as described above (for the purpose of giving it a circular edge) and holding the tool against the rotating glass, a plentiful supply of coarse emery and water, or sand and water, being supplied between the glass and metal surfaces. The tool is held by hand against the surface of the revolving glass, and is constantly moved about, both round its own axis of figure and to and fro across the glass surface. In this way the glass gradually gets convex or concave.

The curvature is tested from time to time by a spherometer, and the tool is increased or decreased in curvature by turning it on a lathe so as to cause it to grind the glass more at the edges or in the middle according to the indications of the spherometer.

This instrument, by the way--so important for lens makers--consists essentially of a kind of three-legged stool, with an additional leg placed at the centre of the circle circumscribing the other three. This central leg is in reality a fine screw with a very large head graduated on the edge, so that it is easy to compute the fractions of a turn given to the screw. The instrument is first placed on a flat plate, and the central screw turned till its end just touches the plate, a state of affairs which is very sharply discernible by the slight rocking which it enables the instrument to undergo when pushed by the hand. See the sketch.

On a convex or concave surface the screw has to be screwed in or out, and from the amount of screwing necessary to bring all four points into equal contact, the curvature may be ascertained.

Let a be the distance between the equidistant feet, and d the distance through which the screw is protruded or retracted from its zero position on a flat surface. Then the radius of curvature rho is given by the formula 2rho = a2/3d +d.

Fig. 43.

The process of roughing is not always carried out exactly as described, and will be referred to again.

(4) The glass being approximately of the proper radius of curvature on one side, it is reversed on the chuck and the same process gone through on the other side. After this the glass is usually dismounted from the lathe and mounted by cement on a pedestal, which is merely a wooden stand with a heavy foot, so that the glass may be held conveniently for the workman. Sometimes a pedestal about four feet high is fixed in the floor of the room, so that the workman engaged in grinding the lens may walk round and round it to secure uniformity. For ordinary purposes, however, a short pedestal may be placed on a table and rotated from time to time by hand, the operator sitting down to his work.

Rough iron or brass tools do not succeed for fine grinding--i.e. grinding with fine emery, because particles of emery become embedded in the metal so tightly that they cannot be got out by any ordinary cleaning. If we have been using emery passing say a sieve with 60 threads to the inch, and then go on to some passing say 100 threads to the inch, a few of the coarser particles will adhere to the "tool", and go on cutting and scratching all the time grinding by means of the finer emery is in progress.

To get over this it is usual to use a rather different kind of grinding tool. A very good kind is made by cementing small squares of glass (say up to half an inch on the side), on to a disc of slate slightly smaller than the lens surface to be formed (Fig. 51). The glass-slate tool is then "roughed" just like the lens surface, but, of course, if the lens has been roughed "convex" the tool must be roughed "concave".

The "roughed" tool is then used to gradually improve the fineness of grinding of the glass. For this purpose grinding by hand is resorted to, the tool and lens being supplied continually with finer and finer emery. Fig. 52 gives an idea of the way in which the tool is moved across the glass surface. Very little pressure is required. The tool is carried in small circular sweeps round and round the lens, so that the centre of the tool describes a many-looped curve on the lens surface. The tool must be allowed to rotate about its own axis; and the lens and pedestal must also be rotated from time to time.

Every few minutes the circular strokes are interrupted, and simple, straight, transverse strokes taken. In no case (except to correct a, defect, as will be explained) should the tool overhang the lens surface by more than about one quarter the diameter of the latter. After grinding say for an hour with one size of emery fed in by means of a clean stick say every five minutes, the emery is washed off, and everything carefully cleaned. The process is then repeated with finer emery, and so on.

The different grades of emery are prepared by taking advantage of the fact that the smaller the particles the longer do they remain suspended in water. Some emery mud from a "roughing" operation is stirred up with plenty of water and left a few seconds to settle, the liquor is then decanted to a second jug and left say for double the time, say ten seconds; it is decanted again, and so on till four or five grades of emery have been accumulated, each jug containing finer emery than its predecessor in the process.

It is not much use using emery which takes more than half an hour to settle in an ordinary bedroom jug. What remains in the liquid to be decanted is mostly glass mud and not emery at all. The process of fine grinding is continually checked by the spherometer, and the art consists in knowing how to move the grinding tool so as to make the lens surface more or less curved. In general it may be said that if the tool is moved in small sweeps, and not allowed to overhang much, the Centre of the lens will be more abraded, while if bold free strokes are taken with much overhanging, the edges of the lens will be more ground away.

By the exercise of patience and perseverance any one will succeed in gradually fine grinding the lens surface and keeping it to the spherometer, but the skill comes in doing this rapidly by varying the shape of the strokes before any appreciable alteration of curvature has come about.

Polishing.

The most simple way of polishing is to coat the grinding tool with paper, as will be described, and then to brush some rouge into the paper. The polisher is moved over the work in much the same way as the fine grinding tool, until the glass is polished. Many operators prefer to use a tool made by squeezing a disc of slate, armed with squares of warm pitch, against the lens surface (finely ground), and then covering these squares with rouge and water instead of emery and water as in the fine grinding process.

The final process is called "figuring." It will in general be unnecessary with a small lens. With large lenses or mirrors the final touches have to be given after the optical behaviour of the lens or mirror has been tested with the telescope itself, and this process is called "figuring." A book might easily be written on the optical indications of various imperfections in a mirror or lens. Suffice it to say here that a sufficiently skilled person will be able to decide from an observation of the behaviour of a telescope whether a lens will be improved by altering the curvature of one or all of the surfaces.

A very small alteration will make a large difference in the optical properties, so that in general "figuring" is done merely by using the rouge polishing tool as an abrading tool, and causing it to alter the curves in the manner already suggested for grinding. There are other methods based on knocking squares out of the pitch-polisher so that some parts of the glass may be more abraded than others.

The "figuring" and polishing may be done by hand just like the grinding. There are machines, however, which can be made to execute the proper motions, and a polisher is set in such a machine, and the mechanical work done is by no means inconsiderable. In fact for surfaces above six inches in diameter few people are strong enough to work a polisher by hand owing to the intense adhesion between it and the exactly fitting glass surface.

Such is a general outline of the processes required to produce a lens or mirror. These processes will now be dealt with in much greater detail, and a certain amount of repetition of the above will unfortunately be necessary: the reader is asked to pardon this. It will also be advisable for the reader to begin by reading the whole account before he commences any particular operation. The reason for this is that it has been desirable to keep to the main account as far as possible without inserting special instructions for subsidiary operations, however important they may be; consequently it may not always be quite clear how the steps described are to be performed. It will be found, however, that all necessary information is really given, though perhaps not always exactly in the place the reader might at first expect.

§ 54. All the discs that I have seen, come from the makers already roughly ground on the edges to a circular figure--but occasionally the figure is very rough indeed--and in some cases, especially if small lenses have to be made, it is convenient to begin by cutting the glass discs out of glass sheet, which also may be purchased of suit-able glass. To do this, the simplest way is to begin by cutting squares and then cutting off the corners with the diamond, the approximate circular figure being obtained by grinding the edges on an ordinary grindstone.

If the pieces are larger, time and material may be saved by using a diamond compass, i.e. an ordinary drawing compass armed with a diamond to cut circles on the glass, and breaking the superfluous glass away by means of a pair of spectacle-maker's shanks (Fig. 44), or what does equally well, a pair of pliers with soft iron jaws. With these instruments glass can be chipped gradually up to any line, whether diamond-cut or not, the jaws of the pincers being worked against the edge of the glass, so as to gradually crush it away.

Fig. 44.

Assuming that the glass has been bought or made roughly circular, it must be finished on the lathe. For this purpose it is necessary to chuck it on an iron or hardwood chuck, as shown in Fig. 46. For a lens below say an inch in diameter, the centering cement may be used; but for a lens of a diameter greater than this, sufficient adhesion is easily obtained with Regnault's mastic, and its low melting point gives it a decided advantage over the shellac composition.

The glass may be heated gradually by placing it on the water bath, or actually in the water, and gradually bringing the water up to the boiling-point. The glass, being taken out, is rapidly wiped, and rubbed with a bit of waste moistened, not wet, with a little turpentine: its surface is then rubbed with a stick of mastic previously warmed so as to melt easily. The surface of the chuck being also warm, and covered with a layer of melted cement, it is applied to the glass. The lathe is turned slowly by hand, and the glass pushed gradually into the most central position; it is then pressed tight against the chuck by the back rest, a bit of wood being interposed for obvious reasons.

When all is cold the turning may be proceeded with. The quickest way is to use the method already described (i.e. actual turning by a file tool); but if the student prefers (time being no object), he may accomplish the reduction to a circular form very easily by grinding.

Fig. 45.

Fig. 46.

For this purpose he will require to make the following arrangements (Fig. 45). If the lathe has a slide rest, a piece of stout iron may be bent and cut so as to fit the tool rest, and project beneath the glass. The iron must be fairly rigid, for if it springs appreciably beneath the pressure of the glass, it will not grind the latter really round. The lathe may run rather faster than for turning cast iron of the same size. Coarse emery, passing through a sieve of 80 threads to the inch (run), may be fed in between the glass and iron, and the latter screwed up till the disc just grinds slightly as it goes round.

A beginner will generally (in this as in all cases of grinding processes) tend to feed too fast--no grinding process can be hurried. If a slide rest is not available, a hinged board, carrying a bit of iron, may (see Fig. 45) be arranged so as to turn about its hinge at the back of the lathe; and it may be screwed up readily enough by passing a long set-screw through the front edge, so that the point of the screw bears upon the lathe bed. I may add that emery behaves as if it were greasy, and it is difficult to wet it with clean water. This is easily got over by adding a little soap or alcohol to the water, or exercising a little patience.

A good supply of emery and water should be kept between the disc and the iron; a little putty may be arranged round the point of contact on the iron to form a temporary trough. In any case the resulting emery mud should on no account be thrown away, but should be carefully kept for further use. The process is complete when the glass is perfectly round and of the required diameter as tested by callipers.

§ 55. The next step is to rough out the lens, and this may easily be done by rotating it more slowly, i.e. with a surface speed of ten feet per minute, and turning the glass with a hard file, as explained in § 42. If it is desired to employ the slide rest, it is quicker and better to use a diamond tool--an instrument quite readily made, and of great service for turning emery wheels and the like,--a thing, in fact, which no workshop should be without. A bit of diamond bort, or even a clear though off-colour stone, may be employed.

An ordinary lathe tool is prepared by drawing down the tool steel to a long cone, resembling the ordinary practice in preparing a boring tool. The apex of the cone must be cut off till it is only slightly larger than the greatest transverse diameter of the diamond splinter. The latter may have almost any shape--a triangular point, one side of a three-sided prism is very convenient. A hole is drilled in the steel (which must have been well softened), only just large enough to allow the diamond to enter--if the splinter is thicker in the middle than at either end, so much the better--the diamond is fastened in position by squeezing the soft steel walls tightly down upon it. Personally I prefer to use a tool holder, and in this case generally mount the diamond in a bit of brass rod of the proper diameter; and instead of pinching in the sides of the cavity, I tin them, and set the diamond in position with a drop of soft solder.

Fig. 47.

In purchasing diamond bort, a good plan is to buy fragments that have been employed in diamond drilling, and have become too small to reset; in this case some idea as to the hardness of the bits may be obtained. Full details as to diamond tool-making are given in books on watch-making, and in Holtzapffell's great work on Mechanical Manipulation; but the above notes are all that are really necessary--it is, in fact, a very simple matter. The only advantage of using a diamond tool for glass turning is that one does not need to be always taking it out of the rest to sharpen it, which generally happens with hard steel, especially if the work is turned a little too fast.

I recommend, therefore, that the student should boldly go to work "free hand" with a hard file; but if he prefer the more formal method, or distrust his skill (which he should not do), then let him use a diamond point, even if he has the trouble of making it. When using a diamond it is not necessary to employ a lubricant, but there is some advantage in doing so.

The surface of the lens can be roughly shaped by turning to a template or pattern made by cutting a circular arc (of the same radius as the required surface) out of a bit of sheet zinc. Another very handy way of making templates of great accuracy is to use a beam compass (constructed from a light wooden bar) with a glazier's diamond instead of a pencil. A bit of thin sheet glass is cut across with this compass to the proper curvature--which can be done with considerable accuracy and the two halves of the plate, after breaking along the cut, are ground together with a view to avoiding slight local irregularities, by means of a little fine emery and water laid between the edges. In this process the glass is conveniently supported on a clean board or slate, and the bits are rubbed backwards and forwards against each other.

§ 56. It is not very easy for a beginner to turn a bit of anything--iron, wood, or glass--with great accuracy to fit a template, and consequently time may be saved by the following procedure, applied as soon as the figure of the template is roughly obtained. A disc of lead or iron, of the same diameter as the glass, and of approximately the proper curvature, is prepared by turning, and is armed with a handle projecting coaxially from the back of the disc. The glass revolving with moderate speed on the lathe, the lead tool, supplied with coarse emery and water, is held against it, care being taken to rotate the tool by the handle, and also to move it backwards and forwards across the disc, through a distance, say, up to half an inch; if it is allowed to overhang too much the edges of the glass disc will be overground. By the use of such a tool the glass can readily be brought up to the template.

The only thing that remains, so far as the description of this part of the process goes, is to give a note or two as to the best way of making the lead tools, and for this purpose the main narrative of processes must be interrupted. The easiest way is to make a set of discs to begin with. For this purpose take the mandrel out of the lathe, and place it nose downwards in the centre of an iron ring of proper diameter on a flat and level iron plate.

The discs are made by pouring lead round the screw-nose of the mandrel. This method, of course, leaves them with a hole in the centre; but this can be stopped up by placing the hot disc (from which the mandrel has been unscrewed) on a hot plate, and pouring in a sufficiency of very hot lead; or, better still, the mandrel can be supported vertically at any desired distance above the plate while the casting is being poured. Lead discs prepared in this way are easily turned so as to form very convenient chucks for brass work, and for use in the case now being treated, they are easily turned to a template, using woodturners' tools, which work better if oiled, and must be set to cut, not scrape.

If the operator does not mind the trouble of cutting a screw, or if he has a jaw chuck, the lead may be replaced by iron with some advantage.

The following is a neat way of making concave tools. It is an application of the principle of having the cutting tool as long as the radius of curvature, and allowing it to move about the centre of curvature. Place the disc of iron or lead on the lathe mandrel or in the chuck, and set the slide rest so that it is free to slide up or down the lathe bed. Take a bar of tool steel and cut it a little longer than the radius of curvature required. Forge and finish one end of the bar into a pointed turning tool of the ordinary kind. Measure the radius of curvature from the point of the tool along the bar, and bore a hole, whose centre is at this point, through the bar from the upper to the lower face. I regard the upper face as the one whose horizontal plane contains the cutting point when the tool is in use. Clamp a temporary back centre to the lathe bed, and let it carry a pin in the vertical plane through the lathe centres, and let this pin exactly fit the hole in the bar.

Fig. 48.

Place the "radius" tool in position for cutting, and let it be lightly held in the slide rest nearly at the cutting point, the centre of rotation of the pedestal (or its equivalent) passing through the central line of the bar. Then adjust the temporary back rest, so that the tool will take a cut. In the sketch the tool is shown swinging about the back centre instead of about a pin--there is little to choose between the methods unless economy of tool steel is an object. The tool must now be fed across the work. The pedestal must of course be free to rotate, and the slide rest to slip up and down the bed. In this way a better concave grinding tool can be made than would be made by a beginner by turning to a template--though an expert turner would probably carry out the latter operation so as to obtain an' accuracy of the same order, and would certainly do it in much less time than would be required in setting up the special arrangements here described.

On the other hand, if several surfaces have to be prepared, as in the making of an achromatic lens, the quickest way would be by the use of the radius tool, bored of course to work at the several radii required. I have tried both methods, and my choice would depend partly on the lathe at my disposal, and partly on the number of grinding tools that had to be prepared.

Having obtained a concave tool of any given radius, it is easily copied--negatively, so as to make a convex tool in the following manner. Adjust the concave tool already made on the back rest, so that if it rotated about the line of centres, it would rotate about its axis of figure.

Arrangements for this can easily be made, but of course they will depend on the detailed structure of the lathe. Use the slide rest as before, i.e. let it grasp an ordinary turning tool lightly, the pedestal being fixed, but the rest free to slide up or down the lathe bed. Push the back rest up till the butt of the turning tool (ground to a rounded point) rests against the concave grinding tool. If the diameter of the convex tool required be very small compared with the radius of curvature of the surface (the most usual case), it is only necessary to feed the cutting tool across to "copy" the concave surface sufficiently nearly.

Fig. 49.

There seems no reason, however, why these methods should not be applied at once to the glass disc by means of a diamond point, and the rough grinding thus entirely avoided. I am informed that this has been done by Sir Henry Bessemer, but that the method was found to present no great advantage in practice. A reader with a taste for mechanical experimenting might try radius bar tools with small carborundum wheels rapidly driven instead of a diamond.

Enough has now been said to enable any one to prepare rough convex or concave grinding tools of iron or lead, and of the same diameter as the glass to be ground.

The general effect of the process of roughing the rotating lens surface is to alter the radius of curvature of both tool and glass; hence it is necessary to have for each grinding tool another to fit it, and enable it to be kept (by working the two together) at a constant figure. After a little practice it will be found possible to bring the glass exactly up to the required curvature as tested by template or spherometer. The art of the process consists in altering the shape of the grinding tool so as to take off the glass where required, as described in § 53, and from this point of view lead has some advantages; (opinions vary as to the relative advantages of lead and iron tools for this purpose, however). The subsidiary grinding tool is not actually needed for this preliminary operation, but it has to be made some time with a view to further procedure, and occasionally is of service here.

§ 57. 'The glass disc must be ground approximately to the proper curvature on each side before any fine grinding is commenced. It is precisely for this purpose that the previous turning of the disc is recommended, for it is easy to unmount and recentre a round object, but not so easy if the object have an indefinite shape. Using a cement which is plastic before it sets, the disc may be easily taken off the chuck and centred by a little handicraft, i.e. by rotating the lathe slowly and pushing the disc into such a position that it rotates about its axis. The grinding of the second surface is accomplished exactly as in the former case; of course on reversing the glass the chuck has to be slightly turned up to fit the convex or concave surface.

§ 58. There is, however, one point of interest and importance--attention to which will save a good deal of useless labour afterwards. The glass must be ground in such a manner that the thickness at the edge is the same all round. In other words, the axes of figure of the two surfaces must coincide. This will be the case if the recentering has been accurately performed, and therefore no pains should be spared to see that it is exactly carried out. Any simple form of vernier gauge (such as Brown and Sharpe's vernier callipers) will serve to allow of a sufficiently accurate measurement of the edge thickness of the lens. If any difference of thickness is observed as the gauge moves round the edge, one or other of the surfaces must be reground. Of course the latitude of error which may be permitted depends so much on the final arrangements for a special finishing process called the "centering of the lens"--which will be described--that it is difficult to fix a limit, but perhaps one-thousandth of an inch may be mentioned as a suitable amount for a 2-inch disc. For rough work, of course; more margin may be admitted.

§ 59. In a large shop I imagine that lenses of only two inches diameter would be ground in nests; or, in other words, a number would be worked at a time, and centering, even of a rough kind, would be left to the last; but this process will be treated hereafter. At present I shall assume that only one lens will be made at a time. Consequently we now enter on the stage of fine grinding by hand. A leaden pedestal, for the sake of stability, must be provided on which to mount the lens, so that the surface to be operated on may be nearly horizontal (Fig. 50). Before this can be done, however, fresh grinding tools (two for each surface) must be properly prepared. After trying several plans I unhesitatingly recommend that all fine-grinding surfaces should be made of glass. This is easily done by taking two discs of lead, or iron, or slate, cut to a one-tenth inch smaller radius of curvature (in the case of a convex tool, and the opposite in the other case) than the lens surface (Fig. 51, A). On these, square bits of sheet glass, one-tenth of an inch thick, are to be cemented, so as to leave channels of about one-eighth of an inch between each bit of glass (Fig. 52, B). The "mastic" cement formerly described may be employed for this purpose.

Fig. 50.

The bits of glass ought first to have their edges dressed smooth on the grind-stone. A convex and concave glass surface having been thus roughly prepared, they must be mounted in turn in the lathe, and brought to the proper curvature by grinding with the tools formerly employed and tested by the template or spherometer. It is well to control this process by means of a spherometer, so that the desired radius may be approximately reached. The two glass-grinding tools are then ground together by hand (see § 53 and § 61), the spherometer being employed from time to time to check the progress of the work. In general, if large circular sweeps are taken, greatly overhanging the side of the glass surface to be figured, both the upper and lower surfaces will be more ground at the edges, while in the opposite event the centre will be chiefly affected.

Fig. 51.

A spherometer capable of measuring a 2-inch surface may be procured, having a screw of, say, 50 threads to the inch, and a micrometer surface divided into 200 parts, each part easily capable of subdivision--into tenths or even twentieths. To get the full advantage of the spherometer it must screw exceedingly freely (i.e. must be well oiled with clock oil), and must not be fingered except at the milled head. If one of the legs is held by the fingers the expansion is sufficient to throw the instrument quite out of adjustment. The glass-grinding tools being brought to the proper figure, the next process is to transfer the same to the lens, and this is done by similar means, the fellow tool being used to correct the one employed in grinding the lens surface. Before the grade of emery is changed all three surfaces must agree, as nearly, at least, as the spherometer will show.

In order to prevent confusion the following summary of the steps already taken may be given. The discs of glass are first ground or turned so as to be truly circular. Four "tools" are made for each surface--a rough pair of iron or lead, and a finishing pair of iron, lead, or slate faced by glass squares. For a small lens the iron or lead backing may be used, for a large one the slate. The rough tools are used to give an approximate figure both to the lens and to the finishing tools.

The final adjustment is attained by grinding one of the glass-faced tools alternately upon the lens and upon the fellow glass-faced tool. The spherometer is accepted at all stages of the process as the final arbiter as to curvature. Some hints on the form of strokes used in grinding will be given later on (see § 61). It suffices to state here that the object throughout is to secure uniformity by allowing both the work and the tool to rotate, and exercising no pressure by the fingers. The tool backing may weigh from one to two pounds for a 2-inch lens.

§ 60. The tools and lens being all of the same curvature, the state of the surface is gradually improved by grinding with finer and finer emery. The best way of grading the emery is by washing it with clean water, and allowing the emery (at first stirred up with the water) to settle out. The longer the time required for this part of the process the finer will be the emery deposited. An ordinary bedroom jug is a very good utensil to employ during this process; a large glass jug is even better. The following grades will be found sufficient, though I daresay every operative's practice differs a little on this point.

1st grade: Flour emery, with the grit washed out, i.e. allowed to stand for 2" (sec.) before being poured off.

2nd grade: Stand 5" (secs.), settle in 1' (min.)

3rd grade: Stand 1', settle in 10'.

4th grade: Stand 10', settle in 60'.

It is generally advisable to repeat the washing process with each grade. Thus, selecting grade 2 for illustration, the liquor for grade 3 must be poured off without allowing any of the sediment to pass over with it. If any sediment at all passes, one has no security against its containing perhaps the largest particle in the jug. As soon as the liquor for No. 3 has been decanted, jug No. 2 is filled up again with clean water (filtered if necessary), and after standing 5" is decanted into jug No. 2b, the sediment is returned to jug No. 1, and the liquor, after standing 1', is transferred to jug No. 3.

The greatest care is necessary at each step of the operation to prevent "sediment" passing over with liquor. There is a little danger from the tendency which even comparatively large particles of emery have to float, in consequence of their refusing to get wet, and the emery worked up on the side of the jug is also a source of danger, therefore wipe the jug round inside before decanting.

In order to get a uniform grade stop the currents of water in the jug, which may work up coarse particles, by holding a thin bit of wood in the rotating liquid for a moment, and then gently withdrawing it in its own plane. These precautions are particularly necessary in the case of grades Nos. 2, 3, and 4, especially No. 4, for if a single coarse particle gets on the tool when the work has progressed up to this point it will probably necessitate a return to grinding by means of No. 2, and involve many hours' work.

The surface of the lens will require to be ground continuously with each grade till it has the uniform state of roughness corresponding to the grade in question. Two hours for each grade is about the usual time required in working such a lens as is here contemplated.

The coarser grades of emery may be obtained by washing ordinary flour of emery, but the finer ones have to be got from emery which has been used in the previous processes. It is not a good plan to wash the finer grades of emery out of the proceeds of very rough grinding say with anything coarser than flour of emery--as there is a danger of thereby contaminating the finer grades with comparatively coarse glass particles (owing to their lightness) and this may lead to scratching. If the finer grades are very light in colour, it may be inferred that a considerable portion of the dust is composed of glass, and this does no good. Consequently time may be saved by stirring up the light-coloured mass with a little hydrofluoric acid in a platinum capsule; this dissolves the finely divided glass almost instantaneously. The emery and excess of hydrofluoric acid may then be thrown into a large beaker of clean water and washed several times. Fine emery thus treated has much the same dark chocolate colour as the coarser varieties.

The operator should not wear a coat, and should have his arms bare while working with fine emery, for a workshop coat is sure to have gathered a good deal of dust, and increases the chances of coarse particles getting between the surfaces.

§ 61. Details of the Process of Fine Grinding.

A lens of the size selected for description is mounted as before mentioned on a leaden pedestal, and the operator places the latter on a table of convenient height in a room as free from dust as possible. Everything should be as clean as a pin, and no splashes of emery mud should be allowed to lie about. I have found it convenient to spread clean newspapers on the table and floor, and to wear clean linen clothes, which do not pick up dust. I have an idea that in large workshops some simpler means of avoiding scratches must have been discovered, but I can only give the results of my own experience. I never successfully avoided scratches till I adopted the precautions mentioned.

Fig. 52.

The left hand should be employed in rotating the pedestal either continuously (though slowly) or at intervals of, say, one minute. This point is rather important. Some operators require two hands to work the grinding tool, and in any case this is the safer practice. Under these circumstances the pedestal may be rotated through one-eighth or tenth of a revolution every three minutes, or thereabouts. The general motion given to the grinding tool should be a series of circular sweeps of about one-fourth the diameter of the glass disc, and gradually carried round an imaginary circle drawn on the surface of the lens and concentric with it (Fig. 52).

The tool may overhang the lens by a quarter of the diameter of the latter as a maximum. The circuit may be completed in from twelve to thirty sweeps. The grinding tool should be lightly held by the fingers and the necessary force applied parallel to the surface. The tool itself must be slowly rotated about its axis of figure. If the tool be lightly held, it will be found that it tends to rotate by itself. I say "tends to rotate," for if the tool be touching evenly all over the surface it will rotate in a direction opposite to the direction of the circular sweep. For instance, if the tool be carried round its looped path clockwise, it will tend to rotate about its own axis of figure counter-clockwise. If it touch more in the middle, this rotation will be increased, while if it touches more along the edge, the rotation will be diminished, or even reversed in an extreme case.

Every fifty sweeps or so the tool should be simply ground backwards and forwards along a diameter of the lens surface. This grinding should consist of three or four journeys to and fro along, say, eight different diameters. About one-quarter of the whole grinding should be accomplished by short straight strokes, during which the tool should only overhang about one-quarter of an inch. The object of the straight strokes is to counteract the tendency to a gradual accumulation of the emery in the centre, which results from the circular grinding.

A great deal of the art of the process consists in knowing how to work the tool to produce any given effect. For instance, if the lens requires to be ground down near the centre, the epicycloidal strokes must be nearly central; the tool must never overhang very much. If, on the other hand, it is the edges which require attention, these must be dealt with by wider overhanging strokes. The tool must be frequently tested on its fellow, and, indeed, ground upon it if any marked unevenness of action (such as that just described) is required for the lens. A check by spherometer will be applied at intervals according to the judgment of the operator, but, in any case, the fellow tool and lens should be kept at very nearly the same figure.

The emery should never be allowed to become anything like dry between the tool and the lens, for in some way (probably by capillary action increasing the pressure of the tool) this seems to lead to scratching and "rolling" of the emery. The channels in the glass tool between the squares are of the greatest importance in enabling the emery to distribute itself. Perhaps the best guide in enabling one to judge as to when it is time to wash off the emery and apply fresh is the "feel" of the tool; also when the mud gets light in colour we know that it is full of glass dust, and proportionately inoperative.

New emery may be put on, say, every five minutes, but no absolute rule can be given, for much depends on the pressure of the tool upon the lens. In the case considered a brass or lead, or even slate tool, of an inch, or even less, in thickness, will press quite heavily enough. In washing the lens and tool before new emery is introduced, a large enamelled iron bucket is very handy; the whole of the tool should be immersed and scrubbed with a nail-brush. The lens surface may be wiped with a bit of clean sponge, free from grit, or even a clean damp cloth.

When the time comes to alter the grade of emery, a fresh lot of newspapers should be put down, and tools, lens, and pedestal well washed and brushed by the nail-brush. The surfaces should be wiped dry by a fresh piece of rag, and examined for scratches and also for uniformity of appearance; a good opinion can be formed as to the fit of the surfaces by noting whether--and if so, to what degree--they differ in appearance from point to point when held so that the light falls on them obliquely.

It is necessary to exercise the greatest care in the washing between the application of successive grades of emery, and this will be facilitated if the edges of the glass squares were dressed on a grindstone before they were mounted. An additional precaution which may be of immense advantage is to allow the tool to dry between the application of successive grades of emery (of course, after it has been scrubbed), and then to brush it vigorously with a hat-brush. It sometimes happens that particles of mud which have resisted the wet scrubbing with the nail-brush may be removed by this method.

As my friend Mr. Cook informs me that his present practice differs slightly from the above, I will depart from the rule I laid down, and add a note on an alternative method.

Consider a single lens surface. This is roughed out as before by an iron tool, a rough fellow tool being made at the same time. The squares of glass are cemented to the roughing tool, and this is ground to the spherometer by means of the counterpart tool. The glass-coated tool is then applied to the lens surface and grinding with the first grade of emery commenced. The curvature is checked by the spherometer. Two auxiliary tools of, say, half the diameter of the lens, are prepared from slate, or glass backed with iron, and applied to grind down either the central part of the lens surface or tool surface, according to the indications of the spherometer. Any changes that may occur during grinding are corrected by these tools. The spherometer is accepted as the sole guide in obtaining the proper curvature. A slate backing is preferred for tools of any diameter over, say, 2 inches.

§ 62. Polishing.