268 On a Method of ascertaining Magnifying Power, dec. 
If the lens be nearly 2 inches focus, and magnifies 9 times at 
20 inches, this method will not be sufficiently correct for so large a 
lens. In order to find its focal length, the distance of the “ centre ” 
of the lens from object and image is generally required ; but my 
formula obviates this difficulty. 
Ex. (3). To find the magnifying power at 36 inches of a 
supposed 2 -inch lens, which magnifies 9 times at 20 inches distance 
between object and image : 
First approximation, ( £ Phil. Tr.’ loc. cit.) 
cl 
m = distance -f- focal length less 2 = - — 2. 
/ 
But focal length (/), since m + 2 + ^ - j 
= distance divided by {^ni + 2 + 
= 20 - (9 + 2 + = 20 - 5 - —±1 
180 
= ioo = 1 ' 8=/ - 
Then 
m = new distance -i- focal length less 2 (approximately) 
qp 
= 36 ^ 1 • 8 less 2 = — - 2 = 20-2 
1 * O 
= 18 nearly. 
This is slightly too much. The square root of 1 less than the 
square of ~ or 's / 1 (d _ 2 J- 1 
therefore 
= a/ 81 — 1 = a/ 80 = 8-944; 
m = - 18 + V80 = 17-944, formula (II.) note. 
The magnifying power at 36 inches, when it magnifies 9 times 
at 20 inches, is 17-914 = 18 times nearly. 
On estimating Minute Magnitudes. 
When very great magnifying power is employed, as 4000 or 
8000, two thousandths upon the stage micrometer cannot be seen 
as the field of view in general cannot embrace two consecutive fines 
of the micrometer. In order to overcome this difficulty I devised 
the following method. A very coarse scale is drawn on glass with 
diamond lines, or photographic lines, and is mounted in a cap or 
tube that fits upon the under part of the sub-stage in a fixed 
distance ; into the upper part a good half-inch objective is inserted, 
