VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 233 



by the handle p, which commands the position of the arm, I raise or depress it 

 so as to bring the 2 lucid points to a similar situation with the 2 stars ; and, by 

 the handle d, I approach or remove the moveable lucid point to the same distance 

 of the 2 stars, so that the 2 lucid points may be exactly covered by, or coincide 

 with the stars. A little practice in this business soon makes it easy, especially to 

 one who has already been used to look with both eyes open. 



What remains to be done is very simple. With a proper rule, divided into 

 inches and 40th parts, I take the distance of the lucid points, which may 

 be done to the greatest nicety, because, as observed before, the little holes are 

 made with the point of a very fine needle. The measure thus obtained is the 

 tangent of the magnified angle under which the stars are seen, to a radius of 

 10 feet ; therefore, the angle being found, and divided by the power of the 

 telescope, gives the real angular distance of the centres of a double star. For 

 instance, Sept. 25, 1781, I measured aHerculis with this instrument. Having 

 caused the 2 lucid points to coincide exactly with the stars centre on centre, I 

 found the radius, or distance of the central lamp from the eye, 10 feet 4.15 

 inches ; the tangent or distance of the 2 lucid points 50.6 fortieth parts of an 

 inch ; this gives the magnified angle 35', and dividing by the power 4<5o, which 

 I used we obtain 4" 34'" for the distance of the centres of the 2 stars. The 

 scale of the micrometer at this very convenient distance, with the power of 46o 

 (which my telescope bears so well on the fixed stars that for near a twelvemonth 

 past I have hardly used any other) is above a quarter of an inch to a second ; and 

 by putting on my power of 932, which in very fine evenings is extremely distinct, 

 I obtain a scale of more than half an inch to a second, without increasing the 

 distance of the micrometer ; whereas the most perfect of my former micrometers, 

 with the same instrument, had a scale of less than the 2000th part of an inch 

 to a second. 



The measures of this micrometer are not confined to double stars only, but 

 may be applied to any other objects that require the utmost accuracy, such as 

 the diameters of the planets or their satellites, the mountains of the moon, the 

 diameters of the fixed stars, &c. For instance, Oct. 22, 1781, I measured the 

 apparent diameter of aLyrae ; and judging it of the greatest importance to in- 

 crease my scale as much as convenient, I placed the micrometer at the greatest 

 convenient distance, and (with some trouble, for want of longer handles, which 

 might easily be added) took the diameter of this star by removing the 2 lucid 

 points to such a distance as just to inclose the apparent diameter. When I mea- 

 sured my radius, it was found to be 22 feet 6 inches. The distance of the 2 

 lucid points was about 3 inches ; for I will not pretend to extreme nicety in this 

 observation, on account of the very great power I used, which was 6450. 

 From these measures we have the magnified angle 38' 10": this divided by the 



vol. xv. H H 



