ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
121 
and dividing by / and collecting, we get 
A / 00 f+hiP + l)- 
This is still a minimum (for positive values of p and q ) when p = q, or 
when the conjugate foci are taken at the symmetric points. 
Principle of Focometer for determining ilie Focal Planes and Principal 
Planes of any given ( Positive j Optical Combination, such as a Microscope 
Objective, or other Lens . — The abstract principle of this focometer was 
described as follows by the author two years ago, in a memorandum 
accompanying an application made to the Royal Society for a grant in 
aid of the construction of the apparatus : — 
“Let A B (fig. 14) be the objective (or lens); IT X II 2 its principal 
points ; F x F 2 its principal foci ; and S x S 2 the two symmetric points 
Fig 14. 
situated each at double the focal distance from the respective principal 
points, S x S 2 are conjugate points, and the planes through them are 
planes of unit magnification. 
“ Suppose a parallel beam to be sent (from a lamp provided with a 
reticle in front of it and a collimating lens, all placed in air at some 
convenient distance away) through A B from left to right. An image 
will be formed at Fj, thus determining that point. Then, with the same 
source removed to a distant point on the right, send a parallel beam from 
right to left, thus determining F 2 . Small glass plates, having micro- 
meters cut on surfaces (respectively) nearest to Hj H 2 , and each provided 
with a reading lens behind, should be used to receive these images, and 
to ascertain their precise position in space. The said micrometers 
should be mounted on supports sliding along a suitable bench, over the 
middle of which the objective has been clamped in a special support. 
The micrometers, or, at least, one of them, should be so arranged that 
they can be thrown out of the axis laterally when not wanted. They 
should be provided with verniers to read off their positions on the bench. 
They should also be furnished with clamps, which, after each has been 
once set at its principal focus, will permit it to be clamped to a screw 
below on the bench. The distance from F, to F 2 is equal to 2/ -f as 
(where / is the true focal length and x the unknown distance between 
the two principal planes). 
“ Now, let there be a gearing, such as a right and left-handed screw, 
which will enable the observer to move the two micrometers from F, 
and F 2 at exactly equal rates outwards. Whon one of them arrives at 
S! the other will at the same moment arrive at S 2 , and this will bo 
