Monthl iT Y yi G C ° - 
Sa a, of Microscopie Objectives. 151 
obtained by direct experiment, and f is the principal focus sought. 
Even if the triple objective had an optical centre, this formula 
could not be applied directly, owing to the practical impossibility 
of finding this centre, which, moreover, would change with the 
relative change of position of the lenses composing it in varying 
the adjustment for different thicknesses of the glass covering the 
object. The direct use of the formula would require the distances 
~p and p' to be known. Some modification must, therefore, be 
adopted. 
The method ordinarily in use by the makers seems to be to 
erind the lenses with certain radii, which are assumed to give ap- 
proximately definite “focal lengths.” The glasses, if tested at all, 
are compared with some standard objective, by means of their 
magnifying powers with the same eye-piece, a method liable to con- 
siderable errors. 
The method which I use is based upon two equations, the one 
: 1g aes it p _ size of object : 
given above, ; Tag a. (1) and aig ep a nm (2), in 
which n is the ratio of the size of the object to the size of the 
image, the conjugate foci being p and p'. It is clear that though 
we cannot measure p and p' separately, we can measure their sum, 
that is the distance between the object and the image, which we 
eallZ; m can be found by measuring the size of the image of an 
object of known magnitude, a finely-divided scale throwing this 
image on a second divided scale. 
We have from (1) p\ f+pf=pp', or lf=pp'=(l—p’) p' (8), 
as p+p'=l. But p=np' from (2); therefore, p'+-n p'=/, and 
a ne peeact tire = 
1 aaa (4). Combining (8) and (4) fl= (ep? ang eae 
Ea, . If, therefore, we find » and 7, we can easily find f, the 
focal length of the equivalent lens. 
Two sets of experiments were made with a somewhat different 
arrangement of apparatus in each. In both the image of a glass 
scale divided to 74> millimetres (zzo9 inch) was thrown upon an 
engine-divided paper scale (;!5 or > inch), the image and the 
paper being the focus of a double-convex lens used as an eye- 
piece, so that the size of the magnified image was read directly 
on the paper scale, estimating by the eye to tenths of the divi- 
sions. The distance from the glass to the paper was measured 
with a steel rule graduated to millimetres. The magnitude of the 
image varies so slowly for any variation of 7 that this was taken 
only in whole millimetres. Any error in the measurement would 
be less perceptible in the results, the shorter the focus of the lens 
measured. 
VoL. IV. M 
