Let-the two semi-lenses have their centres at E and II, (Plate CCCLXX V. Fig. 14.) and their principal fo cus at F, and let P, Q. be two distinct objects, or the opposite limits of the same object, lying in FE, FH pro longed. The images of the two objects P, Q, formed by each semilens, will coincide at F, and therefore two images of the circular object PBQD, viz. ni z F, p x F, will be found touching one another at F. Hence the angular measure of PQ will be equal to the angle which EH or the distance of the centres of the semi lenses forms at F, and, as the angles measured are very small, they will always vary as EH. The angle, therefore, which corresponds to any one distance of the centres E, H, being known by the methods already de scribed, the angle corresponding to any other distance will be obtained by simple proportion. Mr. Dollond first adapted his micrometer to the object end of a re flecting telescope ; but his son afterwards applied it to achromatic telescopes.
The divided object-glass micrometer has a great su periority over the wire micrometer, in so far as it en ables us to measure any diameter of the sun or moon, whatever be its inclination to the direction of their mo tion ; whereas, in the wire micrometer, we can only measure that diameter which is perpendicular to the direction of the motion.
In order to apply the divided object-glass microme ter to determine differences of right ascension and de clination, Dr. Maskelyne has pointed out the following method.
" Let H C R c, Plate CCCLXXV. Fig. 15, he the field of view, HR and C c two wires bisecting the field of view at right angles to one another, and having a mo tion in their own plane, turn the wires till the western most star (which is the best, have further to move) run along ROH ; then separate the two segments, and turn about the micrometer till the two images of the same star lie in the wire C c ; and then, partly by separating the segments, and partly by raising or depressing the telescope, bring the two innermost images of the two stars to appear and run along ROH, as a, b, and the ver nier will give the difference of their declinations ; be cause, as the two images of one of the stars coincided with C c, the image of each star was brought perpendicular ly upon HR or to HR in their proper meridian. And, for the same reason, the difference of their times of pass ing the wire CO c will give their difference of right ascensions. These operations will be facilitated, if the telescope be mounted on a polar axis. if two other wires KL. MN, parallel to C c, be placed neat II and R, the observation may be made on two stars, whose difference of meridians is nearly equal to HR, the diameter of the field of view, by bringing the two images of one of the stars to coincide with one of these mireA. If two stars
be observed, whose difference of declinations is well set tled, the scale of the micrometer will be known.
It has hitherto been supposed, that the images of the two stars can be both brought into the field of view at once upon the wire HOR ; but if they cannot, set the micrometer to the difference of their declinations as nearly as you can, and make the image which comes first run along the wire IIOR, by elevating or depress ing the telescope ; and when the other star comes in, if it does not also run along HOR, alter the micrometer till it does, and half the sum of the numbers shown by the micrometer at the two separate observations of the two stars on the wire HOR will be the difference of their declination. That this should be true, it is ma nifestly necessary that the two segments should recede equally in opposite directions ; and this is effected by Mr. Dollond in his new improvement of the object-glass micrometer.
The difference of right ascensions and declinations of Venus or Mercury in the sun's disc and the sun's limb may be thus found. Turn the wires, so that the north limb n, Plate CCCLXXV. Fig. 16, of the sun's image AB, or the north limb of the image V of the planet, may run -along the wire RH, which therefore will then be parallel to the equator, and consequently C c a secondary to it ; then separate the segments, and turn about the micrometer till the two images V, v, of the planet pass C c at the same time, and then, by separating the segments, bring the north limb of the northernmost image V of the planet to touch FIR, at the time the north ernmost limb n of the southernmost image AB of the sun touches it, and the microme'er shows the difference of declinations of the northernmost limbs of the planet and sun, for the reason formerly given, we having brought the northernmost limbs of the two innermost images V and AB to HR, these two being manifestly interior to v and the northernmost limb N of the image PQ. In the same manlier, we take the difference of declinations of their southernmost limbs ; and half the difference of the two measures (taking immediately one after another) is equal to the difference of the de clinations of their centres, without any regard to the sun's or planet's diameters, or error of adjustment of the micrometer ; for as it affects both equally, the dif ference is the same as if there were no error ; and the difference of the times of the transits of the eastern or western limbs of the sun and planet over C c gives the difference of their right ascensions.