On " Optical Tuhe-length." By Frank Crisp. 819 



diminished, and the focal length of the whole Microscope increased. 

 The magnifying power will therefore be diminished. 



Again, take the case of two objectives of say l-8th in. and 1 in. 

 focal length used with the same eye-piece (2 in.) and tube. If the 

 distance A remained constant, say 10 in., the total focal length 

 would vary with that of the objectives, 



i X 2 _ 1 1x2 ^1 



•^ ~ 10 ~ 40 ' °^ -^ 10 5 ■ 



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 l-8th in. objective the 

 posterior focal plane may be very near the back lens, and we have 

 a long 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 l-8th in. objective 

 A = 10 in., and a power of (80 x 10 = ) 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 10 in., and the "total power would be only 80. 



The converse case of different eye-pieces with the same 

 objective 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- 

 piece does not vary much in the Huyghenian form ; a substantial 

 difference is, however, found in this respect between the Kamsden 

 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. 



Grreater differences in the power will also be found with 

 short tubes than with long ones. With a 10 in. tube a difference 

 of 2 in. reduces the 10 to 8, but with a 6 in. tube from 6 to 4, quite 

 different percentages of variation. 



The process, therefore, of multiplying together the powers of 

 the eye-piece and the objective to obtain the total power of the 



