466 PHILOSOPHICAL TRANSACTIONS. [aNNO 1754. 



known, be set up at some known distance ; the angle it will subtend from the 

 glass may then be found by trigonometry : then let it be measured by this mi- 

 crometer, and the distance between the centres of the segments, found on the 

 scale already mentioned, will be the constant measure of the same angle, in all 

 other cases ; because the distance of the object makes no alteration in the mea- 

 sure of the angle, as has been demonstrated : and thus having obtained the dis- 

 tance between the centres of the segments, which answers to any one angle, all 

 other distances may be computed by the rule of three. 



All that has been hitherto said relates to the first method of using this micro- 

 meter ; that is, by fitting it to the end of a tube suited to its focal length, and 

 by viewing the images with a proper eye-glass, in the manner of an astronomi- 

 cal telescope. But the length of the tube, in this way, would be very trouble- 

 some ; and therefore it will be proper to consider other methods for an easier 

 management. He therefore proceeds to the 2d method, mentioned in Obs. 10, 

 which is, by using another object-glass to shorten the focus of that which serves 

 for the micrometer. To facilitate the understanding of this method, it will be 

 necessary to premise the following observation. 



Obs. 1 1. — Rays of light, which are brought to such convergency as to form 

 the image of an object, proceed, after that, diverging in the manner they did 

 when they issued from the object before they were transmitted through the glass , 

 and therefore they may be again collected by another spherical glass, so as to 

 form a 2d representation of the same object ; which may again be repeated by a 

 3d glass, &c. So that the first image may be considered as an object to the 2d 

 glass, and the 2d image will be an object to the 3d, and so on. Though these 

 images may be very different in respect to their magnitudes, yet they will be all 

 similar; being true representations of the same object: this will hold good, 

 though the 2d glass should be put so near the first, as to receive the rays before 

 the image is formed : for as the rays are tending to meet at a certain distance, the 

 2d will receive them in that degree of convergency, and, by an additional refrac- 

 tion, bring them to a nearer focus ; but the image will still be similar to that 

 which would have been made by the first glass, if the 2d had not been there. 



On this principle all refracting telescopes are made ; some of which are a com- 

 bination of 4, 3, or 6 glasses. The first glass forms an image of the object ; 

 the 2d repeats the image, which it receives from the first ; and so on, till the last 

 glass brings a true representation of the object to the eye. The same may be 

 said of reflecting telescopes : for a spherical mirror acts in the same manner, in 

 that respect, as a spherical glass. 



Now let this be applied to the subject in hand. Suppose the focal distance of 

 the divided object-glass to be about 40 feet ; and suppose the segments to be 

 opened wide enough to bring the opposite edges of an object in contact : then 



