170 
The constant p=1; for if m be made equal 160, the conven- 
tional focus F=-};, when d=10, and hence (d being large 
and F small) approximately, 
d 
If (f) be the focal length of a small lens whose thickness 
is neglected, a very similar approximate result can readily be 
obtained from the optical formula 
Je esd ghee 
uo ff 
For by construction 
utv=d, 
and by similar triangles 
mv=u. 
Eliminating the unmeasured distances u and v of the object 
and image from the “ centre’ of the lens, it will be found 
that 
ibe 
m-+-2-+-— 
m 
and m being very large in these experiments, 
eR 
f = gy nearly’, oe 
or 
d 
n= a-— oe . . . ° ° . 5 
e iE e . ‘ ) 
But in the case of the miniature images employed, m is so 
d 
near for their measurement. ‘ 
The thermometer was now placed 100 inches’ distance from 
the microscopical focus; the one sixteenth being employed 
to form the image, f=-+!;, d=100; hence 
large that (— 2) may be neglected, so that m = = is sufficiently 
m= 100+-~!;=1600 very nearly. 
The divisions on the thermometer would be therefore reduced 
in the image to a miniature 1600 times less than the original, 
or about 40,000 to the inch, whilst the breadth of a single 
line would be only the 400,000th. 
The means being thus obtained of readily estimating the 
1 This method also gives the focal length of a minute lens, to determine 
which accurately is attended with no little difficulty. 
