126' Transactions of the Society. 



Place the Microscope in a horizontal position, and by means of the 

 objective to be measured, but without any eye-piece, project the image 

 of a stage micrometer on to a ground-glass screen,* making the distance 

 of the screen from the micrometer exactly 100 in. Divide the size 

 of the image on the screen by the size of the ruling on the micro- 

 meter, the quotient giving of course m, the magnifying power. Add 

 2 to m and move the decimal point one place towards the left hand, 

 and the result will be the initial magnifying power of the objective. 



Look out this initial power in a table of reciprocals, and move 

 the decimal point one place to the right, the result will be the precise 

 local length of the objective. We see, therefore, that when once the 

 magnifying power for a projection distance of 100 in., measured 

 from the object to its image, is known, the focal length of the objec- 

 tive may be accurately determined, and that practically without calcu- 

 lation. 



The next step is to select an eye-piece, of about 1-in. focus, or 

 10 power, and treat it exactly as if it were an objective, project the 

 image of the stage micrometer upon the screen at the distance of 

 100 in. (the eye-lens being used as the front lens of an objective), 

 and determine its precise focal length as above. One more measure- 

 ment is required, viz. the magnifying power of the objective when 

 combined with the eye-piece upon a fixed mechanical tube length ; 

 this also is better measured by projection than in any other manner. 

 The distance from the screen to the point beyond the eye-lens, where 

 the window bars would be brought to a focus, if the field-lens of the 

 eye-piece were pointed to them, should be exactly 10 in.| ; this com- 

 bined power we will call p. Returning now to the formulae, viz. 



ff 10 



F= , JJ ., = and F = — , previously mentioned, if these two are 



f+f'-d .-.!>. 



combined and simplified (p being negative changes the sign in 



front of the fraction in which it occurs) ; the equation becomes 



V ff 

 d = 2 J - +/ + /'• Now, as p the combined magnifying power, 



f the equivalent focus of the objective, and / ' that of the eye-piece, 

 have all been determined, d the natural optical tube length is found. 

 By omitting to add the two last terms of the expression, the value of 

 A is obtained. 



The following Table, which comprises a heterogeneous selection of 

 objectives, illustrates not only the variations in the lengths of the two 

 different optical tubes d and A, but also the effect these variations 

 have upon the power. 



* It is convenient for this kind of work to have a scale engraved upon a glass 

 slip ; this, when held in the hand in contact with the ground-glass, may be moved 

 about until the lines of the projected image cut those upon the ruled scale. 



t The precise spot from which the measurement shoul i be made is the posterior 

 focal point of the entire Microscope, but this is very close to the posterior focal point 

 of the eye-piece. 



