282 American Quarterly Microscopical Journal. 



nicely by the object glass of which the angle was to be measured, 

 and the substage, fitting in the tail-piece, held the examining mi- 

 croscope. In arrangement and use this instrument is the same as 

 Professor Smith's. I will, however, call his attention to the following 

 experiments, not as indicating any defect in the principle, which I 

 consider to be quite correct, but in the mode of use, which I sub- 

 mit may be the cause of error in the measurement. 



In order to well define the transmitting diameter, or boundary 

 of the light spot, on the front of the glass. Professor Smith applies 

 a piece of tissue paper or ground glass to the open end of the ob- 

 ject glass tube. This gives results in excess of truth, which may 

 be attributed to the diameter of the screen. Instead of following 

 this course, set a lamp a few feet away, exactly in the axis of the 

 object glass, and focus the microscope on the index line ; the 

 flame of the lamp will be beautifully in focus at the same time, 

 showing that the examining microscope does not in the least alter 

 the focal distance of the object glass under test. On traversing 

 the lower microscope sideways, the flame appears curiously pro- 

 jected, as if it were actually strung on to the lines ruled on the 

 glass. At an obliquity greater or less, according to the aperture 

 of the objective, the flame shows a tendency to leave the line be- 

 fore it vanishes. Now, with the flame this limit gives a result 

 less than when the ground glass is used. The former, I opine, is 

 therefore the limit of aperture. The ground glass does not in- 

 crease the transmitting diameter of the front, which remains the 

 same under all circumstances ; but it allows oblique rays from 

 a screen or field of view to pass through. The lamp flame is dis- 

 tant and in one fixed, axial, focal point. As the image of the flame 

 and the ruled line are kept in the direction of the axis of the ex- 

 amining microscope, the angular traverse of the line of this axis 

 must indicate the true aperture. Perhaps Professor Smith will 

 kindly investigate this question. 



The old sector is now considered almost obsolete for the meas- 

 urement of large apertures, for when we come to near 180° its 

 utility ceases. Immersion angles, either in water or glass, must 

 then be resorted to, as 180° is thus refracted to within a sector of 

 82°, for, though 180° may not yet havie been reached for any cen- 

 tral angle, it is desirable to bring these exterior angles into view, in 

 order that we may distinguish and separate them from the true one. 



For the correct measurement of the angle of an object glass it is 

 advisable to effect this without the addition of any eye-piece or 



