784 RECORD OF CURRENT RESEARCHES RELATING TO 



hereafter to express the angle of objectives in degrees of interior 

 aperture instead of speaking of air, water, or balsam angles, or using 

 the numerical scale of Abbe. This end will be obtained with sufficient 

 exactness if the crown glass semicircle has an index of refraction of 

 1 • 525. In this case the angles read by the apparatus with each ob- 

 jective will be its interior aperture, and no computation will be neces- 

 sary. But equally exact results can be obtained from a glass semi- 

 circle of hijiher or lower index, provided only its index of refraction 

 is known. In this case it is simply necessary to compute the corre- 

 sponding angle in a medium of 1 • 525 from the observed angle by the 

 method already explained. 



The index of refraction of the glass semicircle may be exactly 

 determined in the ordinary way by measuring the angular deviation 

 produced by a prism cut from the same piece of glass. But in the 

 absence of conveniences for this determination it is one of the advan- 

 tages of this apertometer that it affords the means of measuring the 

 index of the glass semicircle with sufficient accuracy, for if the angle 

 of any immersion objective that exceeds 90^ of interior aperture be 

 measured by it, and then the immersion fluid wiped away, and the 

 angle measured with a very thin film of air between the front of the 

 objective and the semicircle, the observed angle will be reduced to a 

 figure which is constant for all objectives of the same or greater 

 aj^erture, and which is independent of variations in the angles of 

 such objectives, representing in fact doiible the angle of total reflection 

 from the glass of the semicircle to air. If the sine of half this con- 

 stant angle be divided into unity the quotient will be of course the 

 index of refraction of the glass semicircle. 



Provided the glass semicircle is nicely centred, the silvering of 

 the glass cover which prevents vision from taking place except through 

 the small hole or slit directly over the centre of the semicircle, would 

 be unnecessary with the highest powers ; for the diameter of the cir- 

 cular spot through which rays can pass into the objective is so small, 

 as compared with the diameter of the semicircle, that the gi-eatest 

 l^ossible chance of error from this source will be very small indeed. 

 Biit with dry lenses of low power this is not the case ; the greater the 

 transverse diameter of the objective, the more readily would those 

 rays enter it, which having passed through the semicircle but not 

 through its centre, would indicate a greater aperture than the objective 

 actually possessed. This is. Colonel Woodward supposes, the source 

 of the erroneous readings which Professor Smith obtained* when he 

 attempted to use his apparatus after the method of Abbe with low- 

 power objectives. He did not use the opaque cover with a small 

 central hole which is indispensable in this case. 



Microscopical Researches in High-power Definition.f — Dr. 

 G. W. Royston-Pigott presented a paper on this subject to the Royal 

 Society in their last session (not yet printed in extenso), but of which 

 the following is an abstract by the author. 



* 'Am. Quart. Micr. Journ.,' i. (1879) p. 203. 

 t ' Proc. Koy. Soc.,' xxix. (1879) p. 164. 



