a new prifmatic Micrometer. - 807 
by the prifm pr to w, undergoes the refraction oroty 
Now Neat’, part of the angle meafured, is to nr2<?, the 
refradtion of the prifm Rs, as R w to cot; and oc w, the 
other part of the angle meafured, is to or ot, the refrac- 
tion of the prifm PB,in the fame ratio of rot to cot : there- 
fore ocn, the whole angle meafured, is to orn, the fum 
of the refradtions of the two prifm s, as rot to cot; 
that is, as the diftance of the prifm s from the focus 
of the objedt-glafs to the focal diftance of the objedt- 
glafs. 
When the prifms are placed in the manner repre- 
fented in fig. 3. the point e of the image we is illumi- 
nated only by the rays which fall on the objedt-glafs be- 
tween a and f, and the point zw only by the- rays which 
fall on the objedt-glafs between b and g. Now the an* 
gles crf, crg, equal to the refradtions of the prifms, 
being conftant, the fpaces fc, cg, will increafe in propor- 
tion as the diftances rf, rg, increafe, and the fpaces af, 
gb, diminifh as much; and therefore, the images at the 
point of mutual contadt ezw will be each illuminated by- 
half the rays which fall on the objedt-glafs when the 
prifms are placed clofe to the objedt-glafs; but will be 
enlightened lefs and lefs the nearer the prifms are 
brought to the focus of the objedt-glafs. 
But. 
