ON ‘OPTICAL TUBE-LENGTH.” 17 
But the posterior focal planes of the two objectives, instead of coin- 
ciding, may have different positions, every variation producing of 
course a change in the value of A. With the 1-8th in. objective the 
posterior focal plane may be very near the back lens, and we have 
along A; with a 1 in. objective its posterior focal plane may be 
further from the back lens (higher up the tube), and we have 
a diminished A. We might have with the 1-8th in. objective 
A=1Io in., and a power of (80x 1o=) 800, but with the 1 in. 
objective we should not have (10 x 10=) 100, or a total power in 
proportion to the powers of the objectives. A might be 8 in. only 
instead of ro in., and the total power would be only 8o. 
The converse case of different eye-pieces with the same ob- 
jective is similarly explicable. The anterior focal planes of the 
eye-pieces may be at different points of the tube, and we shall have 
a varying A. 
As to the general character of the variations in A, it may be 
noted that the position of the anterior focal plane of the eye- 
plece does not vary much in the Huyghenian form ; a substantial 
difference is, however, found in this respect between the Ramsden 
and Huyghenian, the former having its anterior focal plane at 
some distance below the field lens, and the latter above it. With 
the objective, however, a very wide range is possible. Its posterior 
focal plane may be (1) some distance above the last surface of the 
objective; (2) close to this surface outside or within the objective ; 
or (3)—though a more exceptional case—as a virtual focus below the 
stage or even below the table. Practically, however, with objectives 
of ordinary construction, the difference in position of the posterior 
focal plane is not great with powers higher than 1-2 in., and it is 
only when we come to the lower powers that the difference is a 
substantial one. 
Greater differences in the power will also be found with short 
tubes than with long ones. With a ro in. tube a difference of 2 in. 
reduces the ro to 8, but with a 6 in. tube from 6 to 4, quite diffe- 
rent percentages of variation. 
The process, therefore, of multiplying together the powers of 
the eye-piece and the objective to obtain the focal power of the 
Microscope is a fallacious one, as it supposes a constant tube- 
length ; whilst, as we have seen, the true tube-length varies with 
the different, objectives and eye-pieces used. 
To determine the power of the Microscope from the powers of 
the eye-piece and objective, it is necessary, in addition, to know 
the position of the focal planes of each of the latter. How these 
may be readily determined must be deferred for a subsequent 
occasion.—/ournal Royal Microscopical Society. 
