1882.] 



MICKOSCOPICAL JOUENAL. 



65 



microscopic angles, in the example 

 given. 



First. — The telescopic angle at o is 

 less than the microscopic angle at o" . 

 This results from the primary laws of 

 refraction, but is also clear from in- 

 spection. The measure of the tele- 

 scopic angle is not, therefore, the 

 measure of the microscopic angle. 



Secojid. — The telescopic angle at o 

 diminishes with the shortening of the 

 tube; that is to say, by the approxi- 

 mation of the point o' to the lens and 

 the consequent increase of the dis- 

 tance between the lens and the con- 

 jugate point o. But by the shorten- 

 ing of the tube when using the instru- 

 ment as a microscope, the field in the 

 image a' b' remains of the same 

 size, being determined by the field- 

 glass of the ocular, and the rays 

 / b' and /' a' become more conver- 

 gent. They will, therefore, cut the 

 axis nearer the front of the lens, and 

 the angle at o" will grow wider as the 

 tube is shortened. Thus the effect 

 of shortening the tube is just the op- 

 posite in the telescope from what it 

 is in the microscope. 



There are reasons, growing out of 

 the construction of the instrument, 

 which prevent the angle at o" from 

 increasing sensibly when the tube of 

 the microscope is shortened. These 

 will be noticed hereafter, but in no 

 case can the angle at o" vary in the 

 same manner as that at o. The mea- 

 sure of the one, therefore, can never 

 be the true measure of the other. 



Some interesting facts observed in 

 the practical application of the fore- 

 going principles are worthy of notice. 

 The application was made to four 

 low-power lenses, viz.: a three-inch, 

 an inch-and-a half, and a three-quar- 

 ter-inch, all double system objectives, 

 and a one-inch of a " student " series 

 having only one achromatic lens. A 

 wooden slide with a large hole, had 

 the top covered with thin, black pa- 

 per, in which a pin-hole was made 

 .0125 (or a little more than a hundredth 

 of an inch) in diameter. To get rid 

 of the burr around the edge of the 



hole punched with a needle, a little 

 dark-colored wax was melted upon it, 

 rubbed down thin, and the hole was 

 then made smooth and neat with the 

 needle heated. This slide was placed 

 upon the stage in the usual way and 

 a micrometer-scale was fixed to the 

 substage to serve as an object. I soon 

 found, however, that there was no 

 need of the graduated scale upon the 

 substage, but a bit of white card- 

 board there gave the best light for the 

 examination of the field — much bet- 

 ter, and more free from glare, than 

 the illumination from the mirror. The 

 purpose in using the paper stop and 

 slide rather than a blackened glass 

 slide with a slit, was to avoid any re- 

 fraction in the glass and to make the 

 diaphragm opening circular. In the 

 manner stated, I interposed a dia- 

 phragm in mid-air between the object- 

 ive and the object, and the intent of 

 the experiment was to measure the 

 angle of aperture of the microscope 

 at the principal focus 0" . 



I first measured the actual field of 

 the objective with the stage-micro- 

 meter, using the ten-inch tube and 

 the y4-ocular, of which the field-glass 

 is slightly over i.i-inch in diameter. 

 The working-distance from the top 

 of the slide to the front of the object- 

 ive was also measured very carefully 

 with dividers. A vernier upon the 

 body of the instrument would have 

 been useful for this purpose. The 

 paper diaphragm was then placed 

 upon the stage instead of the micro- 

 meter, and the hole brought to the 

 centre of the field. The tube was 

 next racked down until the apparent 

 enlargement of the hole was equal to 

 the field, as was shown by the round 

 and well defined margin of the mount- 

 ing of the ocular. If a piece of dark 

 cloth was laid over the stage and tube, 

 as the photographer shields his ca- 

 mera, the growing size of the circle 

 of light was very easily observed. 

 Removing the diapraghm-slide, but 

 leaving the tube in position, the sub- 

 stage was then racked up till the di- 

 vided scale upon it was in focus. 



