182 TESTING THE MICROSCOPE. 



measurement is sufficient. From these data, however, the focal 

 length may be very easily calculated. Let D and d, where D > d, 

 be the diameters of the image and the object, or conversely, and 

 p* the longer of the two foci ; then we obtain, from the proportion 



Did = p* : p, and from the above equation - H - = ~ , the 



P P* f 



, . 1 1 D + d , . .. . , , 

 relation - = . - , and hence the simple formula 



* d 

 ~ P 'lT+~d' 



or, if d is infinitely small as compared with D, 



* d - 



The determination of p* t d, and D can be accomplished as follows : 

 (1.) A suitable object of known size (for instance, a micrometer- 

 division, or an air-bubble, whose diameter can be accurately 

 measured) is adjusted in the middle of the field of view, and then 

 the objective-image is received on a screen of ground glass, which 

 is placed on the body-tube after the removal of the eye-piece. 

 If the correct adjustment is found at which the image appears 

 sharply defined, its magnitude can be measured with sufficient 

 accuracy with the compasses. The measurement is more accurate 

 if we observe the objective-image through an eye-piece micrometer 

 from which the field-lens is removed. 1 Since, however, the divi- 

 sions of the eye-piece micrometer are, as above mentioned, at 

 a known distance, generally of *1 mm., the diameter of the real 

 image can be determined within a small fraction of a millimetre. 

 Finally, we measure the distance p* of the plane of projection 

 from the objective (really from its second principal point) with 

 the compasses or scale, in which an error of 2 to 3 mm. is of no 

 importance. 



If, for instance, d 100 mic. = -1 mm., D = 7'8 mm., and 



p* = 210, then jj will equal T V ; consequently / = ^/- = 2'658. 



If p* is taken as 207, this value falls to 2-620, differing, therefore, 

 only by -038, or about ^ mm. 



(2). The objective is placed upon the stage with its plane 



1 We assume here also an ordinary Campani eye-piece. In a Ramsden eye- 

 piece it is not, of course, necessary to remove the field-lens. 



