32 



THEORY OF THE MICROSCOPE. 



the powers are equal. The question, as to what circumstances 

 influence this quantity, is, therefore, not without practical interest, 

 and it may be easily answered from the preceding consideration, 

 if the focal distance (N F) is determined from the formula* 



FIG. 7. 



for the cardinal points of the system, and the values of the 

 quantities I and k are substituted. If /, as before, is the focal 

 length of the whole objective, </> that of the first double-leas, 

 and (/) that of the two other lenses of the system, we get 



, i = L. 



k u^t f + u + u' ' + (/) - *" 



and, similarly, we get, for the first principal point, 

 I - 1 u't 



E = 





The subtraction of this latter value from the focal length gives as 

 focal distance 



(/)- f 



If the lenses and their principal points and focal lengths are 

 given, then N F evidently attains a value which is the larger 



ji 



the smaller t' is, since the denominator 1 + 777- ,, increases and 



(J) ~ * 



decreases with f. The focal distance is, therefore, greatest when t f 

 is as small as possible, i.e., when the first lens is brought as near as 



