face, and R the required radius of curvature.

F2 + d(F

2.

d cos zv

a)

Then R = , or as d is generally very small compared with

F, it is often sufficiently accurate, if v = 90°, to take R2.83

F2 d

If the surface is concave, the eye-piece has to be pushed in, if convex, out. Test in the same way the other plane surfaces, also the two sides of the lens. Any distortion of the image is due to irregularity of the surfaces, as is well shown by trying a piece of window glass.

The parallelism of two plane surfaces, like those of the sextantglass, is well tested in the same way. If both surfaces are perfectly plane and parallel, only a single image is formed, otherwise there are two, one from each face. The angle A, between them, may be determined from the divergence of the images, by the D cos v in which n is the index of refraction, D 2n cos r

formula A= the angle between the images, and r the angle of refraction of the light in the glass. The latter is known from the equation sin vn sin r, in which v is the angle between the telescopes. If v = 90°, A .267 D, and if v = = 0°, A = .33 D. If the surfaces are curved, it is also possible to determine the curvature of both, from the two images, but the problem is then much more complex.

D

n

י1

or if n =

1.5, A

Another method is to place the telescopes opposite each other, and cover half their object-glasses with the plate to be tested. If the two surfaces are plane and parallel, no effect will be produced. If they are inclined, they form a prism, and cause a second image. If D is the angular interval between the two images, and A the angle between the two faces, A 2D. Comparing this formula with that given above, it is evident this method possesses only about one-seventh the delicacy of the other, since for a given value of A, the divergence of the two images is only a seventh part as great. The delicacy of the method by reflection may also be increased indefinitely by increasing v. If the surfaces are curved they act like a lens, and throw the image out of focus. The problem now becomes indeterminate,

as there is only one equation to determine the curvature of both faces. The focus of the equivalent lens may, however, be found by measuring, as before, the change in position of the eye-piece, F2+d(F- a) when the focus ƒ will equal If d is very small, F2

d

f=, which is the best method of measuring the focus of a

=

very flat lens. Thus, if F 24 inches, and done inch, f will equal nearly fifty feet. As in the case of reflection, any irregularity of the surfaces produces a distortion of the image. Test in this way the plates of glass, and the lens.

Still another method of testing the flatness of a glass plate is to form Newton's rings, using the monochromatic light of a soda flame. Very slight irregularities in the surface will then appear covered with yellow and black rings, like contour lines.

As it is often desirable to increase the reflecting power of a plane surface of glass when it is to be used as a mirror, the most common methods of silvering are here appended. A looking-glass is made by covering the back of the glass with an amalgam of mercury and tin, as follows. Lay a sheet of tinfoil the size of the glass to be silvered on a level surface, and pour some mercury upon it, making it spread over the whole surface with a hare's foot. Lay a sheet of paper on it, and the glass over all. Then draw the paper slowly out, when the mercury, as it is exposed, will unite with the glass, and the paper will remove any adhering dust. Special care is needed that the tin, mercury, paper and glass, should be perfectly clean, and that no bubbles remain under the glass. Sometimes the paper is dispensed with, and the glass slid on over the mercury, bringing it first in contact at one corner. It is then subjected to pressure, and set up on edge to drain. It is best to keep this mercury by itself, as if used for other purposes, it is difficult to remove the tin, which gives much trouble by adhering to any glass surfaces with which it is brought in contact. When a bright light is viewed in such a mirror, holding it very obliquely, a large number of images is seen. The first, reflected from the front surface is faint, the second from the mercury is strongly marked, and these are succeeded by many others, caused by successive reflections, and growing fainter and fainter until they finally become invisible.

12

To obtain a single image only, sometimes a plate of black glass is used, or the lower surface is covered with black paint, or better, since much light is lost in this way, the front surface is covered with a deposit of metallic silver. One method of doing this is by dissolving 10 grms. of pure nitrate of silver in 20 grms. of water, and adding 5 grms. of ammonia. Filter, add 35 grms. of alcohol of specific gravity .842, and 10 drops of oil of cassia. Cover the plate with this mixture to a depth of quarter or half an inch, and add 6 to 12 drops at a time of a mixture of 1 part of oil of cloves to 3 of alcohol, until the whole surface is covered with the precipitated silver. The plate is then dried, cleaned and polished. Various other receipts are recommended, some using starch, sugar, or tartaric acid, instead of oil of cloves to precipitate the silver. Probably much more depends on the practice and skill of the experimenter than on the details of the different formulas. Liebig employs a liquid formed by adding soda-ley of sp. gr. 1.035 to 45 cm.3 of an ammoniacal solution of fused nitrate of silver, and dissolving the precipitate formed by adding ammonia until the volume equals 145 cm.3. Add 5 cm.3 of water, and shortly before using it, mix with one sixth to one eighth of its volume of a solution of sugar of milk, containing 1 part of sugar, to 10 of water. Flood the glass to a depth of half an inch, and it will soon become covered with a thick coating of silver.

Another method of making reflectors, is by platinizing glass, or covering it with a layer of metallic platinum. This is accomplished by covering the surface with chloride of platinum with a brush, reducing it to a metallic state by oil of lavender, and heating it in a muffle.

84. TESTING TELESCOPES.

Apparatus. A long darkened chamber with a small aperture at the farther end, through which the light of the sky, or of a lamp, shines. A long empty water-pipe, or unused flue, answers very well for this purpose, but if this cannot be obtained, a large black screen with a small hole in it may be placed at the farther end of the room, and a short tube blackened on the interior, used to cut off the stray light. A double length may be obtained by placing a plane mirror at the farther end of the room, and the screen close to the observer. A telescope to be tested, which should have an

object-glass at least three inches in diameter, is also needed. It is composed of two lenses, one concave, of flint, the other convex, of crown glass. The focus of the latter will be about three-fifths that of the two together. Suppose this is three feet, then the focal length of the crown glass will be about 22 inches. Procure two similar lenses of 20 and 24 inches focus, respectively. Combining the first with the flint gives an under-corrected, while the other gives an over-corrected lens.

Experiment. The principal defects to be sought for, are striæ or irregularity of the glass, spherical aberration or incorrect form, chromatic aberration or imperfect correction for color, imperfect annealing of the lenses, and wrong centering or want of coincidence of their axes with that of the telescope.

First, to test for striæ, direct the telescope towards the artificial star or minute point of light at the farther end of the room. Then remove the eye-piece, and placing the eye in the axis of the instrument a bright circle of light will be seen, which will cover the whole object-glass when the eye is exactly at the principal focus. If now the glass is free from veins, striæ, or other imperfections, this circle will appear perfectly uniform, otherwise the striæ are shown in a very marked manner. To determine whether they are caused by the crown or flint lens, remove the latter, and see if they still remain. Test in the same way the other two convex lenses, and sketch any striæ that may be present. Some cheap cosmorama lenses are made of common plate-glass, in which case they are often full of parallel striæ, running in the direction in which the glass was rolled.

To test for spherical aberration, place the eye a little beyond the focus, and pass a card through the latter. Since all the rays would intersect at the focus if there were no spherical aberration, the light would be instantly extinguished when the card covered this point. In practice, however, the bright circle of light assumes the appearance of a curiously shaped surface of revolution, from which the form of the lens is readily determined.

To test for chromatic aberration, examine the image of the artificial star with an eye-piece, precisely as when looking through the telescope at a real star. If the lens was perfectly achromatic, a very minute circle of light would be obtained, which would enlarge on pushing the eye-piece in or out, remaining all the time

perfectly colorless. The change in size is due to the fact, that the rays of light form a cone of which the object-glass is the base, and the focus the apex. The field of view is really a section of this cone at right angles to its axis. If an uncorrected lens is used, since the violet rays are more bent than the red, they form a cone with vertex nearer the object-glass; accordingly, if the eye-piece is pushed in, the centre of the circle will be violet, and the exterior red. Owing to the unequal dispersion of different parts of the spectrum by the two glasses, it is impossible ever to obtain entire freedom from color, but the best correction is obtained when the eyepiece being pushed in, the circle has a bluish purple exterior, and · when pulled out, a lemon green exterior. In the same way an under corrected lens should give inside the focus a pure purple, and outside a yellowish margin; an over-corrected lens will give a blue or violet color inside, and outside an orange margin. Use the three convex lenses in turn, and note the colors in each instance. Many other things may be learnt from the appearance of the artificial star. Thus if part of the object-glass is covered, the circle assumes the shape of the uncovered portion. Spherical aberration also shows itself by the formation of rings in the image of unequal brilliancy, and imperfect centering or obliquity of the lenses, by converting the circle into an ellipse, or throwing out a ray of light on one side. This effect is greatly increased by using the monochromatic light of a soda flame.

One other test remains to be applied, that for imperfect annealing of the glass. Lay a plate of glass horizontally in front of the window, so that the light reflected from it shall be polarized. Interpose the lens between it and the eye, and examine the transmitted light by a Nicol's prism, as will be described more in detail in Experiment 88. Any inequality in density of the glass will at once show itself by dark patches, which change their position as the prism is turned. Of course all these tests must be regarded as secondary to the real test of every large telescope by trying it on various celestial objects of known difficulty, and comparing the results with those obtained with other instruments of the same size.

Next measure the magnifying power of the different eye-pieces furnished with the telescope. The power of a small telescope or