THE OBJECTIVE. 31 



The negative sign indicates the inverted position of the image. 

 The total magnifying power of the Microscope depends, of course, 

 upon the action of the eye-piece, which will be more fully 

 discussed subsequently. 



If, in order to complete the objective, we now add the first 

 and strongest double-lens, and here, also, assume the distance 

 such that the posterior principal plane coincides with the anterior 

 surface of the second lens, then, for this combination, 



* = - (7) - - -mst = - - 1466137 ' 



and 



t' = 1-905158; 



and the result of the calculation gives us the abscissae-values of 

 the principal and focal points, which we will denote by E and E* y 



E = E? + -609039 = JV + 1-6907697 



E* = (E*) - 1-80008 = N Q + 3-175196 



F = E - 2-18042 = ^Y - -48965 



F* = E* + 2-18042 - N* - -69656. 



Consequently, the focal length amounts to only 2- 18, and the 

 distance of the focal point from the anterior surface '49 unit 

 of length. The distance of the object diminishes to '5 with a 

 tube-length of about 200 mm. 



To make these numerical relations clearly apparent, the objective- 

 system, which we have supposed with its principal and focal 

 planes, is represented in Fig. 7, enlarged five times (the millimetre 

 taken as unity). The cardinal planes (F) (E) (E*) (F*) of the 

 two posterior lenses are indicated by dotted lines, and the prin- 

 cipal planes of each double-lens by shorter lines. 



The distance of the object is, obviously, a quantity dependent 

 upon the focal distance ; it increases and decreases, ccetcris paribus, 

 with the latter, and is nearly equal to it in the strongest objectives. 

 It does not, however, stand in direct connection with the focal 

 length of the objective ; it is well known that objectives of different 

 makers often vary considerably in respect to object-distance, though 



