94 THE AMERICAN MONTHLY [April, 



ical ingenuity. The principle of the mechanism is as follows : 

 The objective to be tried is placed in a horizontal position, and 

 some poinL on it, either the front end or some point on the side, 

 is selected as a zero point for all measurements, a beam of paral- 

 lel rays is sent through the lens from the back and the distance 

 trom the zero point to the focus F^ of these rays measured. The 

 lens is reversed, and the focus F- of the rays issuing at the back is 

 measured from the zero point. Tlien two small glass micrometers 

 with coarsely ruled lines are placed one in front of the other be- 

 hind the lens, and moved by a screw until the image of one mi- 

 crometer is seen in focuson the other, and the lines superimposed. 

 The distances of these micrometers from the zero point is meas- 

 ured. We have now all the data for calculating the principal 

 planes. It is a well-known optical principle that when an image 

 of an object as shown on the screen is found to be the same size 

 as the object, the distance between the two will be four times the 

 focal length of the lens. In the present instance let F represent 

 the anterior principal focus. F^ the posterior principal focus, ob- 

 tained as above, S^ the anterior conjugate focus where one mi- 

 crometer was placed, and S- the posterior conjugate focus where 

 the second micrometer was placed. Then the distance S' S- is 

 equal to four times the focal length, plus the distance between the 

 two principal planes, because an objective is not equivalent 

 to a bi-convex lens. To get the distance between the prin- 

 cipal planes it is only necessary to subtract the distance 

 S' S' from twice the distance between the anterior and 

 posterior principal foci. Now, to find when these planes 

 are take the distance from the front focus or anterior prin- 

 cipal focus to the micrometer, this is the true focus, and meas- 

 ure it backward toward or along the objective, it will fall in the 

 tube, perhaps, a quarter of an inch from the front end ; this is the 

 first principal plane. Then measure from the back focus or pos- 

 terior principal focus to the other micrometer, and that will be 

 the distance to lay oft' on the tube from the back focus toward the 

 front end of the objective ; mark it on the tube, as it is the much 

 desired posterior principal plane from which the ten inches is to 

 be measured. To ascertain all this practically, perhaps, seems 

 hard, but it is not very difficult to get very close measurements. 

 A lower-power objective should be chosen and laid on a piece of 

 cork along the edge of a board or the table. For micrometers 

 take a stiff' piece of writing paper and rule a series of lines a fif- 

 tieth of an inch apart, using a Brown & Sharp's steel rule as a 

 guide ; cut this paper across the lines so as to make two micro- 

 meters, thus securing uniformity in the lines, as if each micro- 

 meter was ruled separately the lines might not agree. Dip these 

 papers in oil or hot paraffine to make them transparent, and mount 

 in a slit in a piece of cork at such a height as to be able to see 

 them through the objective. Take all measurements with a pair 

 of callipers and lay them otVon a rule. One ought to be able to 

 get the principal planes within a fiftieth of an inch, and iive times 

 this would only make an error of one percent, in the tube length. 



