[ 555 ] 
fleeting telefcope ; either of the Newtonian, Grego- 
rian, or Caflegrain condrudtion. And tho’ this laffc 
method is much the bed, and mod; convenient, of 
the three ; yet, as the fird is the mod: natural, as 
well as the ealieft to be underdood '• it will be proper 
to explain it fully, and to demondrate the principles, 
on which this micrometer is condrudted, by fuppofing 
it made ufe of in the fird way: Which being done, 
the application of it to other methods will be readily 
underdood. 
Having thus, by the foregoing obfervations, given 
a general idea of the nature and effedts of this di- 
vided objedt glafs, I fhall proceed to demondrate the 
principles, from whence the meafures of the angles 
are to be obtained by this indrument ; which will be 
done by the following proportions. 
Proposition T. 
Suppofe a divided, objecl-gla.fi fixed at the e?id of a 
tube , according to the firfi method , and the tube di- 
rected to the objeCt intended to be me a fur ed ; and 
f'nppofe , likewife , the figments removed from their 
original pofition , in the manner directed under Obf. 
8. till the oppofite edges of the two images are fieen in 
contaCi at the focus of the eye-gla/s : Tfhen, I J'ay\ 
the angle J\ ubtended , by the difiance between the cen- 
tres of the figments, from the focus of the eye-gla/s, 
where the edges are f 'een in contaCt , is equal to the 
angle fubtended by the diameter of the objeCi from 
that fame point. 
Demonflration. 
Let the line A B (fee the next page) reprefent 
the diameter of the objedt to be meafured ; and the 
4 A 2 points 
