On Tube Length. By Edivard M. Nelson. 



125 



Some of you will perhaps be wondering why the subject should 

 he complicated by the introduction of a new optical tube length. 

 The reason for it is that p, the magnifying power, is directly propor- 

 tional to the optical tube length A, but it is not proportional to that 

 of d. Thus, with the same objective and eye-piece, if we double A 



Fig. id. 



/ 



we double the magnifying power ; but this obviously will not be true 

 with regard to d. 



Now, in order to ascertain practically the optical tube length 

 called d, we must find the position of the last surface of the lens 

 which is equivalent to the objective, and the first surface of that 

 equivalent to the eye-piece. (The terms first and last being referred 

 to a movement from the object towards the eye.) 



Very often in Microscope lenses, both in objectives and eye- 

 pieces, we find the surfaces of the equivalent lenses crossed over, 

 i.e. the front surface lying behind the posterior surface ; and for this 

 reason it was previously stated that the equivalent lenses could be 

 neither made nor drawn. In the Huyghenian eye-piece, for example, 

 this inversion of the surfaces takes place, and the front surface E of the 

 equivalent lens of this eye-piece lies as far beyond the eye-lens as 

 the diaphragm is in front of the eye-lens ; and this is the point from 

 which the tube length d should be measured. 



As to the objective, the position of the back surface of its equivalent 

 lens varies, so that it cannot be assigned once for all to any definite 

 place with regard to objectives generally ; sometimes it will be found 

 in front of the front lens, and sometimes behind it. So too in the case 

 of tube length A, the position of the back focus of the equivalent 

 lens of the objective cannot be defined generally ; but in the Huy- 

 ghenian eye-piece the front focus is situated half-way between the 

 diaphragm and the eye-lens. With Kamsden and positive eye-pieces, 

 the position of the front focus is at the diaphragm, or if there should 

 be no diaphragm, it can be easily found by turning the eye-lens 

 towards a window and by focussing the image of the window bars 

 upon a piece of paper. 



We have now found a point in the eye-piece from which the 

 optical tube may be laid off, when its length is known ; and the 

 length of the optical tube may be determined in the following manner. 



