252 PHILOSOPHICAL TRANSACTIONS. [aNNO 1777- 



the sun's apparent diameter, as ae to er, or even to ar, on account of the small- 

 ness of ae with respect to ar. 



These considerations concerning the cause of a principal error that has been 

 found in the object-glass micrometer led me to inquire, whether some method 

 might not be found of producing 2 distinct representations of the sun, or any 

 other object, which should have the axes of the pencils of rays, by which they 

 are formed, diverging from one and the same point, or nearly so : and it occur- 

 red to me, that this might be done by the refraction of a prism placed to receive 

 part of the rays proceeding from the object, either before or after their refrac- 

 tion through the object-glass of a telescope. It the prism be placed without the 

 object-glass, the rays that are refracted through it will make an angle with the 

 rays that pass beside it, equal to the refraction of the prism ; and this angle will 

 not afterwards be altered by the refraction of the object-glass. Consequently 2 

 images of an object will be represented, and the prism so applied will enable us 

 to measure the apparent diameter of any object, or any other angular distance 

 which is equal to the refraction of the prism. But if the prism be placed within 

 the object-glass, that is, between the object-glass and eye-glass, the angle mea- 

 sured by the instrument will vary according to the distance of the prism from the 

 focus of the object-glass, bearing the same ratio to the refraction of the prism, 

 as the distance of the prism from the focus bears to tiie focal length of the 

 object-glass. 



Let ACB, fig. 8, represent the object-glass, and d the eye glass of a telescope, 

 and PR a prism placed to intercept part of the rays coming from an object, sup- 

 pose the sun, before they fall on the object-glass. The rays ee proceeding from 

 the eastern limb of the sun, and refracted through the object-glass acb without 

 passing through the prism, will form the corresponding point of the sun's image 

 ate; and the rays ww, proceeding in like manner from the western limb of the 

 sun will be refracted to form the correspondent point of the sun's image at w. 

 But the rays 2e, 2e, 2w, 2w, proceeding in like manner from the eastern and 

 western limbs of the sun, and falling on the prism pr, and thence refracted to 

 the object-glass acb, will, after refraction through it, form the correspondent 

 points of the sun's image at 2e, 2w. Let the refraction of the prism be equal to 

 the sun's apparent diameter : in this case, at whatever distance the prism be 

 placed beyond the object-glass, the 2 images of the sun we, 2w2e, will touch 

 each other externally at the point e2w ; for the rays 2w, 2w, proceeding from 

 the western limb of the sun, being inclined to the rays ee, proceeding from the 

 eastern limb, in the angle of the sun's apparent diameter, will, after sutii'ring a 

 refraction in passing through the prism equal to the sun's apparent diameter, 

 emerge from the prism, and fall on the object-glass parallel to the rays er, and 



