The machine must be on a steady foundation, and in a place as free from dust as possible. Though it looks complicated it is quite straight-forward to build and to operate.

It is explained in Lord Rayleigh's article on Optics in the Encyclopaedia Britannica that a very minute change in the form of the curvature of the surface of a lens will make a large difference in the spherical aberration. This is to be expected, seeing that spherical aberration is a phenomenon of a differential sort, i.e. a measure of the difference between the curvature actually attained, and the theoretical curvature at each point of the lens, for given positions of point and image. Sir H. Grubb gives an ill.u.s.tration of the minuteness of the abrasion required in pa.s.sing from a curve of one sort to a curve of another, say from a spherical to a parabolic curve, consequently the process of figuring by the slow action of a polishing tool becomes quite intelligible. In making a large mirror or lens all the processes. .h.i.therto described under grinding and polishing, etc, have to be gone through and in the manner described, and when all this is accomplished the final process of correcting to test commences.

This process is called figuring.

-- 67. Of the actual operation of this process I have no personal knowledge, and the following brief notes are drawn from the article by Sir H. Grubb, from my a.s.sistant's (Mr. Cook) experience, and from a small work On the Adjustment and Testing of Telescopic Objectives, by T. Cook and Sons, Buckingham Works, York (printed by Ben Johnson and Co, Micklegate, York). This work has excellent photographs of the interference rings of star images corresponding to various defects.

It must be understood that the following is a mere sketch. The art will probably hardly ever be required in laboratory practice, and those who wish to construct large telescopes should not be above looking up the references.

The process is naturally divided for treatment into two parts.

(1) The detection of errors, and the cause of these errors.

(2) The application of a remedy.

(1) A lens, being mounted with its final adjustments, is turned on to a star, which must not be too bright, and should be fairly overhead.

The following appearances may be noted:-

A. In focus, the star appears as a small disc with one or two rings round it; inside and outside of the focus the rings increase in number, are round, concentric with the disc, and the bright and dark rings are apparently equally wide. The appearance inside the focus exactly resembles that outside when allowance is made for chromatic effects. Conclusion: objective good, and correctly mounted.

B. The rings round the star in focus are not circular, nor is the star at the centre of the system. In bad cases the fringes are seen at one side only. Effects exaggerated outside and inside the focus.

Conclusion: the lens is astigmatic, or the objective is not adjusted to be co-axial with the eyepiece.

C. When in focus the central disc is surrounded by an intermittent diffraction pattern, i.e. for instance the system of rings may appear along, and near, three or more radii. If these shift when the points of support of the lens are shifted, flexure may be suspected.

D. On observing inside and outside the focus, the rings are not equally bright and dark. This may be due to uncorrected spherical aberration, particularly to a fault known as "zonal aberration," where different zones of the lens have different foci, but each zone has a definite focus.

E. Irregular diffraction fringes point to bad annealing of the gla.s.s.

This may be checked by an examination of the lens in polarised light.

F. If the disc appear blurred and coloured, however the focus be adjusted, incomplete correction for chromatic aberration is inferred.

If in addition the colouring is unsymmetrical (in an extreme case the star disc is drawn out to a coloured band), want of centering is to be inferred. This will also show itself by the interference fringes having the characteristics described in C.

(2) The following steps may be taken in applying a remedy:

A. The adjusting screws of the cell mounting the object gla.s.s may be worked until the best result is attained; this requires great care and patience. Any errors left over are to be attributed to other causes than the want of collinearity of the axes of object gla.s.s and eyepiece.

B. Astigmatism is detected by rotating the object gla.s.s or object gla.s.s cell. If the oval fringes still persist and the longer axis follows the lens, astigmatism may be inferred. Similarly, by rotating one lens on the other, astigmatism, or want of centering (quite a different thing) may be localised to the lens.

C. The presence of flexure may be confirmed by altering the position of the points of support with respect to the eyepiece, the lens maintaining its original position. The addition of more points of support will in general reduce the ill effects. How to get rid of them I do not know; they are only serious with large lenses.

D. Spherical aberration may be located by using stops and zonal screens, and observing the effect on the image. Sir H. Grubb determines whether any point on the lens requires to be raised or lowered, by touching the gla.s.s at that point with a warm hand or cooling it by ether. The effects so produced are the differential results of the change of figure and of refractive index. By observing the effect of the heating or cooling of any part, the operator will know whether to raise or lower that part, provided that by a suitable preliminary experiment he has determined the relation between the effect produced by the change of figure, and that due to the temperature variation of the refractive index. In general it is sufficient to consider the change of shape only and neglect the change in refractive power.

E. Marked astigmatism has never been noticed by me, but I should think that the whole lens surface would require to be repolished or perhaps reground in this case.

F. To decide in which surface faults exist is not easy. By placing a film of oil between the two surfaces nearly in contact these may be easily examined. Thus a mixture of nut and almond oil of the right proportion, to be found by trial, for the temperature, will have the same refractive index as the crown gla.s.s, and will consequently reduce any errors of figure in the interior crown surface, if properly applied between the surfaces. Similarly the interior of the flint surface may have its imperfections greatly reduced in effect by using almond oil alone, or mixed with bisulphide of carbon. The outer surfaces, I presume, must be examined by warming or cooling over suitable areas or zones.

The defects being detected, a matter requiring a great deal of skill and experience according to Sir H. Grubb, the next step is to remedy them; and the remedial measures as applied to the gla.s.s const.i.tute the process of figuring. There are two ways of correcting local defects, one by means of small paper or pitch covered tools, which according to Sir H. Grubb is dangerous, and according to the experience of Mr.

Cook, and I think of many French opticians, safe and advantageous.

Pitch polishing tools are generally used for figuring. They are made by covering a slate backing with squares of pitch. The backing is floated with pitch say one-eighth of an inch thick. This is then scored into squares by a hot iron rod. The tool, while slightly warm, is laid upon the lens surface, previously slightly smeared with dilute glycerine, until the pitch takes the figure of the gla.s.s. The polishing material is rouge and water. Small tools are applied locally, and probably can only be so applied with advantage for grave defects.

The other method is longer and probably safer. It consists in furnishing the polishing tool with squares of pitch as before. These being slightly warm, the lens is placed upon them so that they will flow to the exact figure also as before. I presume that the lens is to be slightly smeared with glycerine, or some equivalent, to keep the pitch from sticking. The squares are most thickly distributed where the abrasion is most required, i.e. less pitch is melted out by the iron rod. This may be supplemented by taking advantage of differences of hardness of pitch, making some squares out of harder, others out of softer pitch. The aim is to produce a polishing tool which will polish unequally so as to remove the gla.s.s chiefly from predetermined parts of the lens surface. The tool is worked over the surface of the lens by the polishing machine, and part of the art consists in adjusting the strokes to a.s.sist in the production of the local variations required.

A source of difficulty and danger lies in the fact that the pitch squares are rarely of the same hardness, so that some abrade the gla.s.s more rapidly than others. This is particularly likely to occur if the pitch has been overheated. [Footnote: When pitch is heated till it evolves bubbles of gas its hardness increases with the duration of the process.] The reader must be good enough to regard these remarks as of the barest possible kind, and not intended to convey more than a general idea of the nature of the process of figuring.

-- 68. A few remarks on cleaning lenses will fittingly close this part of the subject. There is no need to go beyond the following instructions given by Mr. Brashear in Popular Astronomy, 1894, which are reproduced here verbatim.

"The writer does not advise the use of either fine chamois skin, tissue paper, or an old soft silk handkerchief, nor any other such material to wipe the lenses, as is usually advised. It is not, however, these wiping materials that do the mischief, but the dust particles on the lenses, many of them perhaps of a silicious nature, which are always harder than optical gla.s.s, and as these particles attach themselves to the wiping material they cut microscopic or greater scratches on the surfaces of the objective in the process of wiping.

"I write this article with the hope of helping to solve this apparently difficult problem, but which in reality is a very simple one.

"Let us commence by taking the object gla.s.s out of its cell. Take out the screws that hold the ring in place, and lift out the ring.

Placing the fingers of both hands so as to grasp the objective on opposite sides, reverse the cell, and with the thumbs gently press the objective squarely out of the cell on to a book, block of wood, or anything a little less in diameter than the objective, which has had a cushion of muslin or any soft substance laid upon it. One person can thus handle any objective up to 12 inches in diameter.

"Before separating the lenses it should be carefully noted how they were put together with relation to the cell, and to one another, and if they art not marked they should be marked on the edges conspicuously with a hard lead pencil, so that when separated they may be put together in the same way, and placed in the same relation to the cell. With only ordinary precaution this should be an easy matter.

"Setting the objective on edge the two lenses may be readily separated.

"And now as to the cleaning of the lenses. I have, on rare occasions, found the inner surfaces of an object gla.s.s covered with a curious film, not caused directly by moisture but by the apparent oxidation of the tin-foil used to keep the lenses apart. "A year or more ago a 7-inch objective made by Mr. Clark was brought to me to clean. It had evidently been sadly neglected. The inside of the lenses were covered with such a film as I have mentioned, and I feared the gla.s.s was ruined. When taken apart it was found that the tin-foil had oxidised totally and had distributed itself all over the inner surfaces. I feared the result, but was delighted to find that nitric acid and a tuft of absorbent cotton cut all the deposit off, leaving no stains after having pa.s.sed through a subsequent washing with soap and water.

"I mention this as others may have a similar case to deal with.

"For the ordinary cleaning of an objective let a suitable sized vessel, always a wooden one, be thoroughly cleaned with soap and water, then half filled with clean water about the same temperature as the gla.s.s. Slight differences of temperature are of no moment. Great differences are dangerous in large objectives.

"I usually put a teaspoonful of ammonia in half a pail of water, and it is well to let a piece of washed 'cheese cloth' lie in the pail, as then there is no danger if the lens slips away from the hand, and, by the way, every observatory, indeed every amateur owning a telescope, should have plenty of 'cheese cloth' handy. It is cheap (about 3 cts.

per yard) and is superior for wiping purposes to any 'old soft silk handkerchief,' chamois skin, etc. Before using it have it thoroughly washed with soap and water, then rinsed in clean water, dried and laid away in a box or other place where it can be kept clean. When you use a piece to clean an objective throw it away, it is so cheap you can afford to do so.

"If the lenses are very dirty or 'dusty,' a tuft of cotton or a camel's-hair brush may be used to brush off the loose material before placing the lenses in the water, but no pressure other than the weight of the cotton or brush should be used. The writer prefers to use the palms of the hand with plenty of good soap on them to rub the surfaces, although the cheese cloth and the soap answers nicely, and there seems to be absolutely no danger of scratching when using the hands or the cheese cloth when plenty of water is used; indeed when I wish to wipe off the front surface of an objective in use, and the lens cannot well be taken out, I first dust off the gross particles and then use the cheese cloth with soap and water, and having gone over the surface gently with one piece of cloth, throw it away and take another, perhaps a third one, and then when the dirt is, as it were, all lifted up from the surface, a piece of dry cheese cloth will finish the work, leaving a clean brilliant surface, and no scratches of any kind.

"In washing large objectives in water I generally use a 'tub' and stand the lenses on their edge. When thoroughly washed they are taken out and laid on a bundle of cheese cloth and several pieces of the same used to dry them.

"I think it best not to leave them to drain dry; better take up all moisture with the cloth, and vigorous rubbing will do no harm if the surfaces have no abrading material on them. I have yet to injure a gla.s.s cleaned in this way.

"This process may seem a rather long and tedious one, but it is not so in practice, and it pays.

"In some places objectives must be frequently cleaned, not only because they become covered with an adherent dust, but because that dust produces so much diffused light in the field as to ruin some kinds of telescope work. Mr. Hale of the Kenwood Observatory tells me he cannot do any good prominence photography unless his objective has a clean surface; indeed every observer of faint objects or delicate planetary markings knows full well the value of a dark field free from diffused light. The object-gla.s.s maker uses his best efforts to produce the most perfect polish on his lenses, aside from the accuracy of the curves, both for high light value and freedom from diffused light in the field, and if the surfaces are allowed to become covered with dust, his good work counts for little.

"If only the front surface needs cleaning, the method of cleaning with cheese cloth, soap and water, as described above, answers very well, but always throw away the first and, if necessary, the second cloth, then wipe dry with a third or fourth cloth; but if the surfaces all need cleaning I know of no better method than that of taking the objective out of its cell, always using abundance of soap and water, and keep in a good humor."

-- 69. The Preparation of Flat Surfaces of Rock Salt.

The preliminary grinding is accomplished as in the case of gla.s.s, except that it goes on vastly faster. The polishing process is the only part of the operation which presents any difficulty. The following is an extract from a paper on the subject, by Mr. J. A.

Brashear, Pittsburg, Pa, U.S.A, from the Proceedings of the American a.s.sociation for the Advancement of Science, 1885. Practically the same method was shown me by Mr. Cook some years earlier, so that I can endorse all that Mr. Brashear says, with the following exceptions. We consider that for small salt surfaces the pitch is better scored into squares than provided with the holes recommended by Mr. Brashear.

Mr. Brashear's instructions are as follows. After alluding to the difficulty of drying the polished salt surface--which is of course wet--Mr. Brashear says:-

"Happily I have no trouble in this respect now, and as my method is easily carried out by any physicist who desires to work with rock salt surfaces, it gives me pleasure to explain it. For polishing a prism I make an ordinary pitch bed of about two and one-half or three times the area of the surface of the prism to be polished. While the pitch is still warm I press upon it any approximately flat surface, such as a piece of ordinary plate gla.s.s. The pitch bed is then cooled by a stream of water, and conical holes are then drilled in the pitch with an ordinary counter sink bit, say one-quarter of an inch in diameter, and at intervals of half an inch over the entire surface. This is done to relieve the atmospheric pressure in the final work. The upper surface of the pitch is now very slightly warmed and a true plane surface (usually a gla.s.s one, prepared by grinding and polishing three surfaces in the ordinary way, previously wetted) is pressed upon it until the pitch surface becomes an approximately true plane itself.

Fortunately, moderately hard pitch retains its figure quite persistently through short periods and small changes of temperature, and it always pays to spend a little time in the preparation of the pitch bed.