154 A. ASHE ON THK DRTEIIMTNATION OP OPTICAL TUBE LKNGTIT. 



As it is a rule in optics that the relative sizes of images 

 formed by a lens at different points in its axis are in strict 

 proportion to the distance of those points from the focus of the 

 lens, we may arrange the following formula : — 



^ - D 



"Where A = Amplification of the instrument with the tube closed, 

 ^j B = Distance the ocular has been withdrawn. 

 „ C = Increase in power produced by the effect of B. 



D is, therefore, the equivalent of the distance separating the 

 focus of the objective from the anterior focal plane of the ocular. 



To illustrate this simply, suppose an instrument magnifies 

 lOG times, and that on withdrawing the eye-piece three inches 

 the power is found to be increased to 130 times, the equivalent 

 of the tube length will be by the above rule, 10 inches. 



That it can be nothing else can be shown by the old Euclidean 

 process of assuming it to be something else and ascertaining 

 how far this hypothesis agrees with observation, which, of 

 course, will end in a reductio ad absurdmn. 



The chief drawback of this proposed method is that it does 

 not enable the worker to place his finger on any point on the 

 tube and say with certainty, " Here lies the posterior focus of 

 the objective and there the anterior focus of the ocular," but 

 it faithfully gives us a figure which is the equivalent of 

 the distance separating these two points, and this, after all, 

 is the only concern of practical import. 



In conclusion, I may point out that there is frequently an 

 extraordinary discrepancy between the true optical and the 

 actual mechanical tube lengths ; thus in the case of an instru- 

 ment in my possession a certain combination of lenses gave an 

 optical tube length of 4J inches, whilst the substitution of 

 another objective in a much shorter mount increased the tube 

 length from 4J to 1\ inches, which, if not allowed for, would 

 introduce errors amounting to 60 per cent, in the calculated 

 powers. 



Perhaps this may be considered an extreme case, but it 

 serves to emphasize the importance to the microscopist of 

 knowing something more about the optical length of his instru- 

 ment tube than can be ascertained by comparing its outside 

 dimensions with a foot-rule. 



