1899] MICROSCOPICAL JOURNAL. Ill) 



rays ; p the distance of the lens from the object, p' its 

 distance from the image, and m the true magnifying 

 power, that is, the size of the image divided by the size 

 of the object : p and p' are termed the conjugate foci, 

 and are variable quantities ; / is termed the principal 

 focus, and has an unchangeable value for each single lens. 



"If now we combine the above equations, represent- 

 ing p-\- p or the sum of the conjugate foci by I, we may 



m I 



deduce the formula/ = ,which represents in the 



{m -+- 1) 2 

 case of any single convex lens the relationship existing 

 between the length of the principal focus, the magnify- 

 ing power, and the distance from the object to the screen. 

 This formula, which I think rather more convenient than 

 that of Mr. Cross, differs from it only in using m = the 

 magnifying power, instead of n = the reciprocal of the 

 magnifying power. It may be deduced from his by sub- 



1 

 stituting for n its value — , and reducing ; or it may be 



m 

 derived directly from the primitive equations. In either 

 shape the formula yields the same numerical results, and 

 if for any single convex lens m and I are given, the accu- 

 racy of the value of / resulting will be the degree of pre- 

 cision with which m and I have been measured. 



"If, now, there were any such actual equivalence be- 

 tween achromatic objectives and single lenses as the 

 nomenclature assumes, it would only be necessary to set 

 up the objective to be rated in such a manner that the 

 image of a micrometer should be focussed upon a white 

 screen, using, of course, no eyepiece, to measure the dis- 

 tance from the micrometer to the screen, to determine the 

 magnifying power by measuring the image of the mi- 

 crometer, and substituting these values of I and m in the 

 working formula to calculate the value of /. Unfortu- 



