266 On the Advaneing Aplanatie Power  [Moivnd,'Now i hna 
then the space separating the image flames is almost exactly one 
hundred thousandth of an inch. 
If a number of globules be selected of various diameters from 
the +4,th to sj/soth of an inch in diameter, the miniature intervals 
of the same flames undisturbed in position may thus be tabulated :— 
DIAMETER OF MINIATURE TEST 
GLOBULE. INTERVAL. 
1000 ZO00T 
500 T0000 
Too z000 
These results are obtained in the following manner; the flames, 
3 inches apart, being 15 inches from the globule, 
Let a be the distance between the minute images, 
A the diameter of the globule (7 its radius). 
= q the distance of the images from its centre. 
” 
: 1 4 1 , 4-4. 2 
Then optically Spa + 55 (1) Since A = 2r and A ae 
Also by similar triangles a : g 3: 3: 15, or 
a= 4 (2) 
To find g, A being known by equation (1). 
dy bil Abie ihe 1 
Vir ae hae te ee 
ray 3 A ( 60 ) 
A A A \2 A \3 
= 96 Ut - (a5) + (ao) — (ao) #28} 
LA = < as the other terms are so exceedingly small as to be neglected. 
The interval between the images is =;th of the diameter of the 
globule,* within the three thousand millionth of an inch when 
the diameter is sy'o0- 
If therefore microscopists will take the trouble to measure the 
diameter of the smallest globule which just divides or fairly divorces 
1 
5000 
A iv 1 1 1 1 
A 
20 * Go ~ 120 * 500 * 500~ 120 *~ 25000000 
* The 2nd term of the series when A = 
is 
1 
= 3000000000 © 
the three thousand millionth of an inch. The other terms are smaller still. 
