VOL. LXVII.] PHILOSOPHICAL TRANSACTIONS. 253 



consequently will have their focus "Zw coincident with the focus e of the rays ee, 

 and therefore the 2 images of the sun we, 'iw'ie, will touch each other exter- 

 nally at the point e2w, and the instrument will measure the angle ecZw, and 

 that only. 



But if the prism be placed within the telescope, the angle measured by the 

 instrument, will be to the refraction of the prism, as the distance of the prism 

 from the focus of the object-glass, is to the focal distance of the object-glass : 

 or if 2 prisms be used to form the 2 images, witli their refracting angles placed 

 contrary ways, as represented in fig. g and 10, the angle measured, will be to 

 the sum of the refractions of the prisms, as the distance of the prisms from the 

 focus of the object-glass, is to the focal distance of the object-glass. For let 

 ACB (fig. 9) represent the object-glass, and d the eye-glass of a telescope, and 

 PR, RS, 2 prisms interposed between them, with their refracting angles turned 

 contrary ways, and the common sections of their refracting planes touching each 

 other at r. The rays proceeding from an object, suppose the sun, will be dis- 

 posed, by the refraction of the object-glass, to form an image of the sun at the 

 focus ; but part of them falling on one prism, and part on the other, will be 

 thus refracted contrary ways, so as to form 2 equal images we, 2w2e, which, if 

 the refractions of the prisms be of proper quantities, will touch each other ex- 

 ternally at the point e2w. Let ecn be the axis of the pencil of rays ee pro- 

 ceeding from the sun's eastern limb ; and woo the axis of the pencil of rays ww 

 proceeding from the sun's western limb ; and the point n the place where the 

 image of the sun's eastern limb would be formed, and the point o where that of 

 the western limb would be formed, were not the rays diverted from their course 

 by the refractions of the prisms. But by this means part of the rays ee, which 

 were proceeding to n, falling on the prism pb, will be refracted to form an 

 image of the sun's eastern limb at e, while other rays ee, which fall on the 

 prism RS, will be refracted to form an image of the sun's eastern limb at 2e. In 

 like manner, part of the rays ww, which were proceeding to form an image of 

 the sun's western limb at o, falling on the prism rs, will be refracted to form an 

 image of the sun's western limb at 2w coincident with e, the point of the image 

 correspondent to the sun's eastern limb ; while other rays ww, which fall on the 

 prism PR, will be refracted to form the image of the sun's western limb at w. 

 The two images we, 2w2e, are supposed to touch each other externally at the 

 point e2w. The ray epr, which belongs to the axis ecn, and is refracted by the 

 prism PR to e, undergoes tlie refraction nrc, which (because small angles are 

 proportional to their sines, and the sine of nrc is equal to the sine of its supple- 

 ment nrc) is to NCR, as nc or ce is to nr or Re. In like manner the ray wgr, 

 which belongs to the axis woo, and is refi-acted by the prism rs to 2w or e, un- 

 dergoes the refraction orc, which is to oce, as oc or ce is to ro or Re ; there- 



