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JANUARY 12, 1883.J TSE PHOTOGRAPHIC NEWS. Again, or nearly 2'8 HE_BH II C AH sliding aiungatneiu. Tins oar carries the gratug u a one end, and the plate P at the other, the centre of the plate P occupying the centre of the circle of which the grating G is an arc. The slit S is fixed. It will be seen that this fulfils the requirements of the theorem just given. By keeping the centre of the grating at P a true normal spectrum is always thrown, and, however the angle S G P is altered so as to get different parts of the spectrum, the scale of the photographs remains unchanged, since the dis tance from G to P is fixed. I would also ask you to remark, that as the angle is increased so is the slit placed nearer to the grating, which means that a larger cone of light, and consequently greater brilliancy of spec trum, is given than would otherwise be obtained ; this is, how ever, at the expense of the fineness of the lines, since the breadth of a line is the disc of confusion of a point - breadth of c1; v distance of plate from grating , , snt X — _i— 2—2, This is, however, more distance ot slit from grating than compensated for by the fact that if you largely increase the angle S G P, Fig. 2, you work in higher orders of the spec trum, which give increased dispersion, and do not get a pro portionate shortening of the distance of the slit from the grating. Thus we have already taken an angle of 30° as an example, and found that the total shortening of the slit is 124'7 inches. If we take 60°, which will give us the same rays of the 2nd order we find that the focal distance is reduced 144. cos. 60 = 72 inches. In this last case the image of the line will be 124'7 ~ broader, for which the dispersion is doubled ; there will also be a slight increase in the disc of confusion. 124-7% 2 72 - ) ’ times that which would be the case supposing the focal distance of the slit remained at 72 inches. A certain diminution in this amount must be made, owing to the height of the slit being magnified as well as the breadth; but, owing to the grating being spherical, the edges of the spectrum are less intense than the central portion, which is the part of importance, most of the light being collected there. Another property 1 would call your attention to. C and E are conjugate foci, as are C and E*. .. E and E 1 are also conjugate foci. If, therefore, the slit and the photographic plate are pivoted about 0, with arms of length 0 B, they may occupy any posi tion and still will remain in focus. The photographic plate A sin e cos A= 144 sin 30 cos 36‘=-754 inch. 2 A further calculation will show that the disc of confusion or breadth of a point would be = '754 tan ) = '015. The confusion of this disc would be almost inappreciable at the edges ; in fact, we may take it to begin to be appreciable at 1 that diameter. The breadth of a point may therefore be taken at about r. of an inch, which is well within the limits admitted to give a sharp focus, and is better than that which can be got from a lens under similar circumstances. The same problem may be solved geometrically. Using the same notation as before, and assuming B to be very close to A, it follows that A B is very small compared with CDorCKi and it will be seen that D K — A B, taking A B as parallel to C D ; therefore, for all intents, C D may be taken = C K. Now the triangle A H C and B H E are similar, as are the triangles B H A and H C K. ,BH_AB BH+HC_AB+CD "HCCD r HO CD .BH+HC_BC AC AB+CD_CK CD , But Ho HCHcaoD CDTCD1 (i.) ..AC=lorAC=HC; that is, H is very close to A and B. II E_A E HCFAC since H if very close to A, A B being small. .... AE_BH (“•)•• ACAH now B H and A H are both small; and BII • V! V ’ ' A H might be very large, and therefore cannot be reflecte Now, ah_bh A HKXBH s . HK re HO Substituting this value of A H in (ii.)— (iii.)AE_ BH X H 0 _H C AC HKXBH HK how both H C and H K are large quantities. . HC_AC "HKAK since H is indefinitely near A. Substituting in iii. we get— A E XAK=AC. If a circle be described about C E K, it follows, since this rela tion holds good, that A C must be a tangent to the circle ; and hs, by hypothesis, C K is at right angles to A C, therefore the arc 0 E K. is a semicircle; since arc 0 E K is a semicircle O E K ... A E = asin = a cos Where • is very small, i. = a = 12 feet and A B of focus, we will take the P and Q as the external Lsine. tan 2 2 = 3 inches = } width of grating. Suppose 0-30°. Then a cos 0= 144 X cos 309=1217 inches. cos • absolute size of the grating, taking edges of the grating. In this case, tan 0=1. since A C 48 , , , c-, when B is indefinitely close to A, A E = a cos 0, which shows that C E A is a right angle. To calculate the disc of confusion cos • 2 cos(2 + e) cos • 2 s: = a.— AB = AC sin sin (90° — 2) cos (•+e sin • must be a right angle. That is, the focus for the rays is found by letting fall a perpendicular from the centre of curvature on to the reflected ray ; or if the focus of the reflected rays be at the centre of curvature, the focus for the incident ray must be found in the same way. -This last is what Professor Rowland carries out in practice the reflected ray is also reflected towards the centre of the sphere of which G is a segment; the distance between the grating and the plate or focussing screen remains unchanged, and the dis tance between the slit and the grating is altered. To effect this he has two bars at right angles to one another, with a third bar