C 551 ] 
LXXIV. An Explanation of an Inflrument 
for meafuring fmall Angles , the firfl Ac- 
count of which was read before the Royal 
Society May io, S753. By Mr . John 
Dollond. In a Letter to James Short, 
M. A . and F. R. S, 
Read Apr. 25, 
, 7 S 4 - 
T 
S I R, 
H E account which I gave you, fomc 
time ago, of a new micrometer, 
was contained in as few words as poffible ; being ra- 
ther defirous, that experiments might be made, before 
I faid much concerning it : But fince your many 
repeated experiments have confirmed what was ex- 
pected from it, I have endeavoured to draw up a 
more full account of this inflrument, with demon- 
ftrations of the principles which it is founded upon, 
which I here fend you inclos’d, and which you may 
lay before the Royal Society, if you think proper. 
I am, Sir, 
Your moft obedient humble fervant, 
Denmark-Court, T 1 11 j 
April 4. 17 54. J°i ln Doliond. 
B Efore I enter upon particulars relating to this mi- 
crometer, it will be proper to make a few pre- 
paratory obfervations on the nature of fpherical glaffes, 
fo far as may be neceffary to render the following ex- 
planation more eafily underflood, 
Obfervation 1. It is a property of all convex fphe- 
rical glaffes to refraCt the rays of light, which are 
tranfmitted through them, in fuch a manner, as to 
colled all thofe that proceed diverging from any one 
point 
