Jddit tonal Notes. 411 



the index cuts degrees, if the variation be noted, this constantly 

 added or subti-acted, according as it tails, will fully rectify all 

 other errours. So in fixing the speculum £F to another angle, at 

 has been proposed, tlie like method may or must be taken, viz, 

 to observe two stars at the distance of about 45 or 50 degrees, by 

 the speculum, in its first situation, and thon tlie same stars by it 

 again in its second, and the diflerence of the intervention of the 

 index on the Hmb being noted, and constantly added to the arches 

 tiiken in the second situation, will give the true distance. This 

 method of observing one and the same star, in the first manner, 

 or two stars in the second, as has been mentioned, will nljo rectify 

 jerrours even in the speculums : for the line of the ray KO is in all 

 cases constantly tlie same , and, upon the whole, I may safely 

 say the instrument will be found much more certain in practice 

 than at first it may appear in theory, even to some good judges. 

 But I am now sensible 1 have trespassed in being so particular 

 •U'hen writing to Dr. Halleyj for I well know, that to a gentle- 

 man noted for his excellent talent of reading, apprehending, and 

 greatly improvmg, less wotild have been sufficient ; but as this 

 possibly may* be communicated by thee, 1 shall crave leave further 

 to add, that the use of the instrument is very easy, for if the 

 index be set so near the distance of the moon and htars, and the 

 limb so held as to cut the body of the moon, upon directing the 

 telescope to the star her image will, of course, be reflected on some 

 part of the speculum GH. There is no absolute necessity tlie 

 etar and moon should coincide exactly at the line limiting tlie 

 silvered and unsilvered part of the latter speculum ; for the trans- 

 parent part of that glass will often reflect on the moon's image 

 sufliciently for the telescope to take it, and if her limb in that and 

 the star exactly coincide near it, it may be sufficient, though the 

 nearer to that line the better. Now tlieir distance being found, 

 the tables that give the moon's place may be depended on for 

 her diameter and her latitude 3 Mhich last being known, there are 

 three sides of a triangle given to find the angle at tlie pole of tJie 

 ecliptic, which, compared with the star's longitude, determines 

 her place for that instant : for, in respect to her latitude when she 

 is sv/iftest in motion, when nearest her nodes, and w hen the in- 

 clination of the orbs is greatest (if these eould all happen toge- 

 ther), yet the vai-iation of her latitude, in the space ot one hour, 

 equal to 15 degrees of longitude on tiie earth, if a star be Uiken 

 fe^)me\\hat near the ecliptic, and not very near tlie moon, will not 

 alter the angle at the pole but a very few seconds. The neaniess 



