52 American Quarterly Microscopical Journal. 



3. It must be applicable to all objectives, dry or immersion. 



4. It must be an angle measured under such conditions as the 

 objective will work in practice. That is to say, a dry objective 

 must be measured dry, an immersion must be measured in its 

 fluid. 



It is claimed upon the other side, that all apertures should 

 be given in air. That is, that in order to make the angular 

 apertures comparable with each other, the air angle should be 

 stated, whether the objective is dry or immersion. 



This, it seems to me, is merely an arbitrary demand made by 

 a few of the present day, but without the least pretense for a 

 scientific basis. What is the air angle of a glass that does 

 not work in air ? Is it not purely hypothetical ? What pos- 

 sible knowledge can it convey to us ? I will grant that when 

 the balsam angle, for example, is increased beyond a certain 

 point, the corresponding air angle, if it were possible to have 

 such, — which I emphatically deny, — would exceed 180°, or, in 

 fact, would not enter the lens at all. It must follow that the 

 expression 180° is a vagary, and we must discard it for scien- 

 tific discussion. I base my argument on the undeniable fact 

 that the aperture of an immersion objective is the angle which 

 the light actually forms within the medium of immersion ; 

 this cannot be fairly denied. I claim, too, that any hypo- 

 thetical angle, without the fluid intermedium, is one for which 

 the objective is not adapted, an angle which it cannot possibly 

 utilize, and that no angle can express anything as to the value 

 of an objective unless it is an angle which can be put into 

 actual use. 



As regards the method to be employed in measuring aper- 

 ture I do not hesitate to say, very frankly, that in my opinion 

 no method has yet been devised free from objections, which 

 attempts to measure the angle with a candle flame. 



There is, however, a method which is simple, easily under- 

 stood, and which can be practically carried out. It is the only 

 one by which results can be obtained in any wise comparable. 

 I propose to call it the "triangle method" to distinguish it in 

 speaking from the others. 



This method measures the angle formed by two lines drawn 

 from a point in the centre of the field of view, and in the plane 

 of the focus, to the extremeties of the available diameter of 

 the field lens. In order to get this angle, we simply measure 



