INVERTEBRATA, CRYPTOGAMIA, MICROSCOPY, ETC. 783 



the Microscope as a telescope, some distant object is viewed so small 

 that it only occiij)ies an extremely minute portion of tlie field, and so 

 bright that it can easily be discerned as the slit of a spectroscope 

 placed at about 10 feet and illuminated by monochromatic (blue) sun- 

 light. This appears when the adjustments are rightly made as an 

 extremely minute blue star in the centre of the field. The radial arm 

 is then swung until the star comes to the extreme margin of the field, 

 the adjustment is made as exact as possible with the tangent screw, 

 and the vernier read. The radial arm is then swung till the star 

 comes to the opposite margin of the field where the same process is 

 repeated. The difference between the two readings is the aperture of 

 the objective for any medium of the same index of refraction as the 

 crown glass semicircle. The apparatus reads to half minutes, which 

 is closer than the observations can be accurately made. In fact, 

 after the star comes to the edge of the field, it usually begins to fade 

 just before it entirely disappears, and a motion of several minutes is 

 necessary to effect the change. The best plan is to adjust the instru- 

 ment as exactly as possible at the point at which the star begins to 

 fade and then read to the next lowest sixth of a degree, neglecting the 

 small fractional remainder. The same instrument answers very well 

 to measure the glass angle corresponding to the actual air angle of 

 dry objectives of any power, or the semicircle of glass being removed 

 and the Microscope still used as a telescope to view the blue illu- 

 minated slit as before, air angles may be directly read with a degree 

 of precision not attainable when the sector is used in the ordinary 

 way. 



From the angles of aperture measured in the semicircle of crown 

 glass, it is quite as easy to compute air angles, water angles, glycerine 

 angles, balsam angles, &c., as from the numerical scale of Abbe. It 

 is only necessary to subtract the logarithm of the index of refraction 

 of the rarer medium in which the aperture is to be expressed from 

 that of the index of the glass semicircle, and to preserve the difference 

 as a constant for use whenever the aperture in the selected medium is 

 to be computed from the angle observed with the semicircle. Then 

 to perform the computation, it will only be necessary to add this 

 constant to the logarithmic sine of half the observed angle, and take 

 from the table of logarithmic sines the angle corresponding to the 

 sum, which will be half the angle required. 



It will readily be understood that if the crown glass semicircle of 

 the apparatus is of precisely the same index of refraction as the crown 

 glass front of the objective, the rays of light passing into the objective 

 from the semicircle will, after more or less refraction as they enter 

 and leave the immersion fluid, resume in the crown glass front, pre- 

 cisely the same course they had in the semicircle. In this case the 

 angle measured in the semicircle would be precisely equal to the 

 aperture of the pencil passing through the crown glass front, and might 

 be called the first interior angle of aperture, or briefly, the inferior 

 aperture of the objective. As this is the angle which after all deter- 

 mines the resolving power of the objective (provided its aberrations 

 are properly corrected), Colonel Woodward thinks it would be better 



3 F 2 



