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for all practical purposes. The work has the spectrum, the outer border being been accomplished by giving to the two red. sides of the lenses different curvatures, so To refract light, and still keep the adapted that the aberration produced by colors united, it is necessary, after the

rays are refracted, and thus separated, to use a substance of greater dispersive

power, which brings the rays together Fig. 19.

again by refracting them only a part of the distance back to their original direction.

The problem is : can we make two lenses of different kinds of glass, with equal dispersive, but unequal refractive, powers ? The researches of Euler and Dolland answer in the affirmative, by showing that the dispersive power of dense flint glass is about double that of crown glass, while the refractive power is nearly the same. Hence, a doubleconvex lens of crown glass AA (Fig. 21) is united with a plano-convex lens of

flint glass BB, having a focus about one shall be more or less counteracted by double that of AA. BB corrects the the aberration produced by the other.

chromatic aberration of AA, leaving (2.) Chromatic aberration. White' about } of the refractive power of AA light, when refracted by a lens of any as the effective refracting power of the

a

Fig. 20.

R

single transparent substance, like glass, compound lens. No exact rule respectis acted upon as by a prism, and dis- ing ihe ratio of the curvature can be persed into all the colors of the solar given, because the refractive powers of spectrum. This effect is shown in (Fig. different specimens of glass differ, and 20), where V is the focus of the violet the proper ratio in each case is found by rays, which are most refracted, and R is trial. Having found it, the two lenses the focus of the red rays, which are have equal aberrations, but in opposite least refracted. A violet image is directions, while AA refracting more formed at V, and a red image at R, and powerfully than BB, the rays are the space VR is occupied by images of brought to a focus at a distance a little intermediate colors. “An image of a more than double the focal distance of point formed at V is violet, but sur- AA. rounded by fringes of all the colors of Having explained the general princi

Fig. 21.

А

B

(re"-1)(0,--,); (m" – 1)(r,-",)

RR,

B

R,R,

ples upon which achromatic lenses are parallel rays, r and r', the radii of the produced, it will be satisfactory in a surfaces, and n the index of refraction question of such importance to supply of any lens, we have, by a formula of the mathematical details of its solution. optics :

rr! F=

(n-1)(r—p')
By this formula:

1 (n'-1)(R,-R.) 1
F
R,R,

1,2
1 (m-1)(R, -R) 1
fi

fi rir,
But since

1 1 1 1 F+F"

+

ff" we have,

1 1 1 1
F

IF" F.
Therefore,

n'-m') (R-R) The problem is : to find what form must

(n" —m") (", —r.), be given to two lenses of different refractive powers, to render the focal and consequently, length of the compound lens, for light of

n! -m'

(r, —r,)R,R, any one refrangibility, equal to that for light of any other refrangibility. Let F'

n'' - m"

(R,-R,)r, and F" be the focal lengths of the two (n') and (n"-m") are the difference belenses for light, of which the indices of tween the indices of the two lights havrefraction are n' and n' for the media ing different refrangibilities, or the discomposing the lenses respectfully. Let persive powers of the media composing f' and" be the focal lengths for light of the lenses for each of the two lights. If, which the indices of refraction are m' then, the radii of the two lenses be so and m". Let F be the focal length of

("; -r.)-R,R, the compound lens.

selected as to render The converging

equal

(R-R,)r, power

of the compound lens, on each to the ratio of the dispersive powers of kind of light, is equal to the sum of the the materials of the two lenses for the converging powers of the two lenses, two kinds of light, the latter are separately, on the same kind of light. brought to the same focus by the comThe converging power of the compound pound lens. lens, therefore, on the light whose indices

Suppose the first a double-convex lens

1 1 of refraction are n' and n", is

L (Fig. 22), with equal radii, and the

FF' second a double-concave lens L', the and its converging power on the light surface of which, in contact with the whose indices of refraction are m' and first, has the same curvature with it, and, 1

consequently, the same radius. Obserym", is +

But since these two conof

ing that when the convexities are turned verging powers must be rendered equal, in contrary directions, the radii have 1 1 1

n'-m' (r, -r,)R,R, +

,
FTF
"!

n" - m"

(R, -R,)r,r, then, to assign such magnitudes to the

n'-m' 1,-R, is

reduced radii of the surfaces of the lenses as will

n' fulfill this condition. Let R, and R, be the Let us suppose that the double-convex radii of the surfaces of the first, and r, lens is composed of crown glass, for and r, those of the surfaces of the sec- which n=1.546566, and m'=1.525832 ; ond lens. When F equals the focus of and the double-concave of flint glass,

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for which n"=1.671062 and m"= reference to the correction of spherical

n'-m' aberration, and for a long time object1.627749. We then have

n'' - m"

glasses of this form were claimed by the .020734_1,-R,

most competent judges to exhibit a more Hencer,=23.47XR complete achromatism, and in other re.043313 The radius of the second surface of L' found with object-glasses of other forms.*

spects more perfect definition, than was

The problem presented to the mathematician, as to what shall be the form

and disposition of the surfaces of two or Fig. 22.

more lenses composed of materials of different dispersive powers, which shall most effectually destroy the aberration of color and figure, is an indeterminate one ; so that, for every lens of crown glass of positive focus, whatever the radii of its surfaces may be, a lens of

Fig. 24,

must in this case, therefore, be 23.47 times the radius of L.

Some of the earlier achromatic objec. tives were made of three lenses, as in (Fig. 23), a double concave lens of flint glass being fitted between two double convex lenses of crown glass. In June,

Croun

Flint

Fig. 23.

Crown

Flint

Crown

fint glass can be constructed which will form, when united with it, an achromatic and aplanatic object-glass. This allows a great range in the choice of curves, and a variety of conditions have been proposed by different authorities for determining the selection. The theory of telescope objectives is at this time being discussed by many able mathematicians, among whom, in our own country, are

Professors Newcomb and Harkness, of 1860, Professor Steinheil communicated Washington, and Professor Chas. Hastto the Royal Academy of Sciences at ings, of the Johns Hopkins University. Munich, a notice of an object-glass of In regard to the form of objectives, the form shown in (Fig. 24), executed Messrs. Alvan Clark and Sons, of Camaccording to the system of curves pro. bridgeport, Mass., whose reputation as posed by Gauss. The curves in this com

* Paper published by G. P. Bond in 1863 on "The bination bear a considerable resemblance New Form of the Achromatic object-Glass introduced to the systems designed with express Academy of Arts and Sciences.” Vol. vi.

telescope makers is known throughout of such curves that the red and violet the world, in a letter to me, dated March are combined, the green remains slightly 10, 1879, say: “Many forms may be outstanding. If the second prism disused, but from our experience we have perses the violet as much as the first one found that to make the crown glass lens does, when they are reversed they exof equal curvature, and the flint glass actly compensate red and violet. But lens nearly flat on the side next the eye, is the second acts more strongly than the the most convenient, and gives as good first on the green, which is overcompen. results as any other form; of course, the sated; and if we weaken the second curves must differ with different glass prism, so that the green and red are corused; but the difference will be small." rected, then the violet will be slightly This is the form shown in (Fig. 21). If outstanding. The defect is hardly nothe dispersive power of the fint were ticeable in small telescopes, but in the just double that of the crown, the outer immense refractors of two feet aperture, face of the former would have to be a or upwards, this secondary aberration plane surface to produce achromatism, constitutes the most serious optical debut this is not generally the case. As fect-a defect which, arising from the no two specimens of glass made at dif-properties of glass itself, no art can dim

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ferent meltings have exactly the same inish. It has bcen suggested that this refractive and dispersive powers, the difficulty may be lessened by increasing optician must find the ratio of the dis- the length of the instrument. But in persion of the two glasses, and then give doing this with glasses of such large size, the outer face of the fint such a degree engineering difficulties will be encounof curvature as to neutralize the disper-tered which soon become insurmountasion of the crown. Usually, this face ble, and it is the opinion of many opti. will have to be slightly concave.

cians and astronomers that “the limit of (3.) Secondary Spectrum.—The image optical power for such instruments has formed at the focus of a so-called achro- been very nearly attained." matic lens is not absolutely colorless. A difficulty arises from the fact that flint glass, as compared with crown, disperses the violet end of the spectrum In boring for water in the Wimmera more than the red end. If R, G, and V, district, Victoria, recently, a tree was (Fig. 25), are the centers of the red, passed through for 6 feet, at a depth of green and violet in the spectrum given 250 feet, and the cup brought up several by a prism of the glass of which one lens fruit stones similar to the nuts of plums; is made, and R', G', and V', are those some were smashed, but the kernels of the other; and if the lenses are placed were recognizable. It seemed evident 60 as to counteract each other, and are that there was a grove of trees there.

THE CYCLICAL USE OF STEAM.

From “The Engineer.” By the cyclical use of steam, we meanstruction of this steam in a condenser or to imply the use of a given weight of its waste in the atmosphere. To make steam over and over again in a cycle. this proposition quite clear, we will asIn the development of motive power air sume that one pound of water at 212 may be thus used. A given weight may deg. is introduced into a boiler. It will be heated, expanded, made to drive à then be converted into steam having a piston in expanding, withdrawn from the pressure of 100 lbs. During the process cylinder, cooled down, and reheated and of conversion 1001 units—omitting fracexpanded, over and over again. In some tions-of heat will be taken up or ab. forms of hot-air engine the initial air in sorbed by the water. The resulting the apparatus might be nsed for ever pound' of steam, occupying a space of without addition of any kind, were it 4.33 cubic feet, being admitted to a cynot for imperfections in the apparatus linder and worked in the ordinary way which permit the air to leak away. Can -and by assumption without loss by exsteam be thus employed ? That it can ternal cooling-will part with 206.5 take the place of air, and that a hot. units of heat which will be converted steam engine might be constructed as into work. The remaining 794.5 units well as a hot-air engine, no one doubts; will pass into the condenser, or will but whether it can or cannot be used escape into the air, as the case may be. over and over again in quite another If it were possible to rescue even a way, is a question of very great import-fourth part of this 794.5 units, and conance, and to the consideration of this vert them into useful work, it is evident question we wish to direct the attention that the economy of the steam engine of our readers. What we are about to would be enormously augmented. say may correct some misconceptions, It will be seen that the loss of 794.5 and prove specially useful to many of units, out of a total of 1001 units, our younger readers.

is entirely due to the throwing away In the steam engine as usually made of the steam which has been used, there is an inherent defect which is pre- and the consequent necessity for obtainjudicial to economy. This defect is that ing a fresh supply from the boiler. Any before steam can be used it must be attempt to prevent the loss in question made, and that after it is used it is must therefore be directed to devising thrown away. Under this system the means for using the same steam over and greatest amount of work which it is pos- over again in a cycle. In order to do sible in theory to get out of one ponnd this we must work—with 100 lbs. steam of steam expanded, say eight times, in a our engine between 328 deg. as the cylinder with 7 per cent. clearance at maximum limit, and 212 deg. as the each end of the stroke, the absolute in minimum limit of temperature; that is itial pressure being 100 lbs. on the square to say, the engine must receive steam at inch, is 159,433 foot-pounds, and the 328 deg., the temperature corresponding heat converted into work will amount to to 100 lbs. pressure, and reject it at 212 206.5 units, or 20.7 per cent. of all the deg., the temperature corresponding to a heat communicated io the water in the pressure of 14.7 lbs. It is not necessary boiler, assuming that the feed-water is that the fall in temperature should be introduced at 212 deg. Thus 79.3 per brought about wholly in the cylinder. cent. of the fuel consumed is wasted

100 even in theory, to say nothing of prac

To do this would involve = 6.8-fold

14.7 tical losses by cylinder condensation, 'expansion; but for the attainment of radiation, and so on. As we have shown, the best result this ought to be the this Joss is a result of the system of ratio of expansion. If it is less, then working which involves first the manu. the steam would have to be reduced in

cam, and secondly the de pressure and temperature by external

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