VOL. LXII.] PHILOSOPHICAL TRANSACTIONS. 281 



in or out till you make the object appear most distinct, or till it has the least 

 motion on the threads when the eye is moved to and fro ; for then the threads 

 of the micrometer will be in the common focus of both glasses, and that will be 

 the proper distance that the object-glass ought always to be at from the threads ; 

 and there should be made some mark or ketch in the wooden tube, in order to 

 set it always at the same distance. 



The proper distance of the threads from the object-glass being thus settled, 

 the table for turning the revolutions, &c. of the screw into angles, or minutes 

 and seconds of a degree, may be made several ways; but as good and easy a me- 

 thod as any is, carefully to measure how many inches and parts of an inch the 

 object glass is distant from the threads, and with the same scale to find also how 

 many inches and parts of an inch 100, &c. revolutions or threads of the screw of 

 the micrometer are equal to: then, making the first distance radius, the last 

 will be the sine or tangent of an angle answering to 100 revolutions. And hav- 

 ing the angle answering to 100 revolutions, the angle for any other number will 

 be easily known and set down in the table, as also the parts of a revolution : for 

 in small angles, such as can be observed with the micrometer, their sines, tan- 

 gents, or chords, are nearly in the same proportion with the angles themselves. 

 The distance before mentioned, to be used as radius, ought strictly to be taken 

 from the threads, to a point within the object-glass, about one third of its thick- 

 ness, from that surface which is towards the wires, if the glass be, as usual, 

 equally convex on both sides; but if the focus of the object glass is pretty long, 

 and its thickness not great, the error that can arise by measuring from any part 

 of the object-glass will become insensible as to the alteration in the angle. 



The table for the micrometer may also be made by setting up two marks at a 

 distance on the ground, and observing with the micrometer the revolutions, 

 &c. which they subtend when seen through the telescope, and then computing 

 the angles those objects subtend at the object-glass, by measuring their distance 

 from each other and from the object-glass. The like may also be done by open- 

 ing the threads to any number of revolutions, and then making a star move 

 exactly on the perpendicular thread, and noting the time it is passing from one 

 parallel thread to the other; for that time turned into minutes and seconds of a 

 degree, by allowing for the star's declination and going of the clock, &c. will be 

 the angle answering to the number of revolutions ; from which the whole table 

 may be made. This method perhaps might be most advantageously practised in 

 stars near the pole, where the apparent motion being slow, a second in time will 

 answer to a much smaller angle than towards the equator. But he believes, on 

 trial, the first method will be found most easy and practicable, especially if the 

 scale made use of be well divided. ' 



VOL. XIII. O o 



