390 



OBJECTIVES, EYE-PIECES, THE APEKTOMETEK 



very severe test, as it is of the nature of a full cone, so to speak, and 

 only the lower powers will stand it. If a dark ground is required 

 with the higher objectives it can be obtained by using an oil-immer- 

 sion condenser, but the aperture of the objective will have to be 

 reduced by a stop. 



The apertometer, as its name implies, is an instrument for mea- 

 suring the aperture of a microscopic objective. As correct ideas of 



aperture have only obtained dur- 

 ing the past few years, it may be 

 inferred that apertometers con- 

 structed before the definition of 

 aperture was given and accepted 

 were crude and practically use- 

 less. 



The controversy on the ' aper- 

 ture question,' which was in full 

 operation some eighteen years 

 since, is not an altogether satis- 

 factory page in the history of 

 the modern microscope, and for 

 many reasons it is well to JKISS 

 it unobservantly by. It will 

 suffice to state that during its 

 progress an apertometer was de- 

 vised by R. B. Tolles, of America, 

 which accurately measured the 

 true aperture of an objective. 

 About the same time Professor 

 Abbe gave his attention to the 

 subject, and with the result, as 

 we have seen, that he has given 

 a definite and permanent meaning 

 to numerical aperture, making 

 it, as we have seen, the equiva- 

 lent of the mathematical expres- 

 sion n sine u, n being the refrac- 

 tive index of the medium, and u 

 half the angle of aperture. 1 



The application of this for- 

 mula to, and its general bearing 

 upon, the diffraction theory of 

 microscopic vision has been given 

 in its proper place ; but as the 

 aim of this manual is thoroughly 



practical, we shall be pardoned for even a small measure of repeti- 

 tion in endeavouring to explain the use of this formula in such a 

 manner that only a knowledge of simple arithmetic will be required 



1 A knowledge of the meaning of the trigonometrical expression ' sine ' is not 

 necessary in solving any of the following questions. As the values are all found in 

 tables, it is only necessary to caution those who are unacquainted with the use of 

 mathematical tables to see that they have the ' natural sine ' and not the ' log sine.' 



FIG. 333. 



