r 558 ] 
From this proportion it appears, that the angle 
Subtended by the diameter of the object from the 
glafs, is found without any regard to the diftance of 
the object, or to the diftance of the refpedtive focus, 
where the image is feen ; as the meafure depends en- 
tirely upon the focus of parallel rays and the opening 
of the fegments. We may likewife, from hence, de- 
rive a rule for the quantity of the angle, without con- 
fidering the length of the glafs. Let an objedt, whofe 
diameter is known, be fet up at fome known diftance; 
the angle it will fubtend from the glafs may then be 
found by trigonometry : Then let it be meafured by 
this micrometer, and the diftance, between the cen- 
tres of the fegments, found on the fcale already men- 
tioned, will be the conftant meafure of the fame 
angle, in all other cafes : Becaufe the diftance of the 
objedt makes no alteration in the meafure of the 
angle, as has been demonftrated : And thus having 
obtain’d the diftance between the centres of the feg- 
ments, which anfwers to any one angle, all other di- 
stances may be computed by the rule of three. 
All that has been hitherto laid relates to the firft 
method of ufing this micrometer; that is, by fitting 
it to the end of a tube fuited to its focal length, and 
by viewing the images with a proper eye- glafs, in the 
manner of an aftronomical telefcope. But the length 
of the tube, in this way, would be very troublefome ; 
and therefore it will be proper to conlider other me- 
thods, for an eafier management. I Shall, therefore, 
proceed to the Second method, mention’d in Obf 10. 
which is, by ufing another objedt- glafs to Shorten the 
focus of that which Serves for the micrometer. To 
faci- 
