VOL. LXVII.] PHILOSOPHICAL TRANSACTIONS. 251 



the late Mr, John Dollond's application of it to the object-end of a reflecting 

 telescope, or the present Mr. Peter Dollond's application of it to the object-end 

 of an achromatic refracting one. But, valuable as the object-glass micrometer 

 undoubtedly is, some difficulties have been found in the use of it, owing to the 

 alterations in the focus of the eye, which are apt to cause it to give different 

 measures of the same angle at different times. For instance, in measuring the 

 sun's diameter, the axes of tlie pencils of rays, which come through the 2 seg- 

 ments of the object-glass from contrary limbs of the sun, crossing each other 

 at the focus of the telescope under an angle equal to that of the sun's diameter, 

 the union of the limbs of the 2 images of the sun cannot appear perfect, unless 

 the eye be disposed to see objects distinctly which are placed at the point of in- 

 tersection. But if the eye be disposed to see objects distinctly, which are placed 

 nearer the object-glass than the intersection is, the 2 limbs will appear separated 

 by the interval of the axes of the pencils in that place ; and if the eye be dis- 

 posed to see objects distinctly, which are placed farther from the object-glass than 

 the intersection is, the 2 limbs will appear to encroach on each other by the dis- 

 tance of the axes of the pencils, after their crossing, taken at that place. 



To explain this, let o, v, plate 2, fig. 7, represent the centres of the two 

 semi-circular glasses of the object glass micrometer, separated to the distance 

 ov from each other, subtending the angle oav, equal to the sun's diameter, at 

 the point a, which is the common focus of the 2 pencils of rays having oa and 

 va for their axes, namely, those proceeding from contrary sides of the sun, and 

 passing through the contrary semi-circles ; and let d be the eye-glass. It is evi- 

 dent, that if d be properly placed to give distinct vision of objects placed at the 

 point a, the rays oa, va, as well as all the other rays belonging to those pencils, 

 will be collected into one point on the retina of the eye ; and consequently, the 2 

 opposite limbs of the 2 images of the sun will seem to coincide, and the 2 

 images of the sun to touch one another externally. But if the state of the eye 

 should alter, the place of the eye-glass remaining the same, the eye will no 

 longer be disposed to see the image formed at the point a distinctly, but to see 

 an object placed at ef, nearer to or farther from the object-glass distinctly ; and 

 therefore an image will be formed on the retina exactly similar to the somewhat 

 confused image formed by the rays on a plane perpendicular to their course at ef. 

 Consequently, as the 2 cones of solar rays, boa, cva, formed by the 2 semi- 

 circles, are separated or encroach on each other, at this point of the axis, by the 

 distance ef, the 2 images of the sun will not seem to touch each other externally, 

 but to separate or to encroach on each other by the interval ef. The error thus 

 introduced into the measure of the sun's diameter, will be the angle erf, sub- 

 tended by ef at r, the middle point between o and v, which is to eaf or oav, 



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