254 PHILOSOPHICAL TRANSACTIONS. [aNNO 1777. 



fore, by composition, orn, the sum of the refractions orc, nrc, is to ocn the 

 sum of the angles oce, Nce, or the sun's apparent diameter, as ce to Re ; that 

 is, as the focal distance of the object-glass to the distance of the prisms from the 

 focus of the object-glass. 



Or let the prisms pr, rs, be placed with their refracting angles p, s, turned 

 from each other, as in fig. 10: the refraction of tlie prism pr will transfer the 

 • image of the sun from on to we, and the refraction of the prism rs will transfer 



the image on to '2w2e, the 2 images '2w2e, we, touching each other externally at 

 the point 2ew. Let ecn, wco, be the axes of the pencils of rays proceeding 

 from the 1 extreme limbs of the sun, and n, o, the points where the images of 

 the sun's eastern and western limbs would be formed by the object-glass, were it 

 not for the refraction of the prisms; the ray efr, which belongs to the axis ecn, 

 and is refracted by the prism rs to 2e, undergoes the refraction NR2e; and the 

 ray wgr, which belongs to the axis wco, and is refracted by the prism pr to w, 

 undergoes the refraction orw. Now Nc2e, part of the angle measured, is to 

 NR2e, the refraction of the prism rs, as rw to cw; and ocw, the other part of 

 the angle measured, is to orw, the refraction of the prism pr, in the same ratio 

 of RW to cw: therefore ocn, the whole angle measured, is to orn, the sum of 

 the refractions of the 2 prisms, as rw to cw; that is, as the distance of the 

 prisms from the focus of the object-glass to the focal distance of the object- 

 glass. 



When the prisms are placed in the manner represented in fig. Q, the point e, 

 of the image we, is illuminated only by the rays which fall on the object-glass 

 beiween a and f, and the point 2w only by the rays which fall on the ol)ject- 

 glass between b and g. Now the angles crf, crg, equal to the refractions of 

 the prisms, being constant, the spaces fc, cg, will increase in proportion as the 

 distances RF, rg, increase, and the spaces af, gb, diminish as much; and there- 

 fore the images at the point of mutual contact e2w, will be each illuminated by 

 half the rays which fall on the object-glass when the prisms are placed close to 

 the object-glass; but will be enlightened less and less the nearer the prisms are 

 brought to the focus of the object-glass. 



But when the prisms are placed in the manner shown in fig. 10, the images 

 at the point of contact, as the prisms are removed from the object-glass towards 

 the eye-glass, will be enlightened with more than half the rays that fall on the 

 object-glass, and will be most enlightened when the prisms are brought to the 

 focus itself; for the point 2e, of the image 2w2e, will be enlightened by all the 

 rays ee that fall on the object-glass between b and f, and the point w, of the 

 image we, will be enlightened by all the rays ww which fall on the object-glass 

 between a and g. But the difference of the illuminations is not very consider- 

 able in achiouiatic telescopes, on account of the great aperture of the oliject- 



