24 Transactions of the Societij. 



With regard to the manner in which apertures are indicated by 

 the apertometer — what Dr. Woodward calls the " arbitrary scale of 

 my own invention " — and the objections made against it by difierent 

 writers, the following explanations may be useful : — • 



The application of such a scale, instead of a simple angular 

 division of the glass disk, would be unwise if this scale were 

 intended as a device for making out the angle of an objective in 

 crown glass, or even balsam angles or air angles. But the idea 

 from which this part of the arrangement has arisen has no such 

 aim, as Mr. J. W. Stephenson * and Mr. K. Hitchcock f have clearly 

 explained. My intention has been to introduce practically as a 

 matter of simple and direct observation a new expression of aperture, 

 quite apart from the angles, which may be conveniently applied by 

 microscopists in all scientific discussions pertaining to apertures. 



In my opinion, apertures, until recently, have not been measured 

 in any strict sense of the word. Aioertures cannot he measured hy 

 degrees. Angles being measured by degrees, the angular aperture 

 i. e. the angle of aperture can be likewise, of course. But the 

 angle by itself is no measure of aperture — at least, nobody has 

 attempted to prove such an hypothesis. An angle is a mere indi- 

 cation or statement of an aperture, just as a number of degrees on 

 the thermometer may exactly indicate a quantity of heat, under 

 given circumstances, but does not measure it. Just so the angle 

 of divergence of the gold-leaves in an electroscope indicates or 

 determines an electric charge, but does not measure it. There is 

 not one point of view from which apertures can be compared 

 quantitatively by means of the angles, because there is not one 

 function in the performance of the Microscope in respect to which 

 twice the angle represents the double effect, and three times the 

 angle the triple effect, except when the angles do not exceed a few 

 degrees. Neither the quantity of light, nor the resolving power, 

 nor any other performance connected with the aperture, is increased 

 in the ratio of 1 : 2 if the angle (air or balsam or interior angle) 

 is increased, say, from 60° to 120^. Moreover, apertures cannot be 

 directly compared as to greater or less, by the angles, as long as 

 they do not relate to exactly the same medium. For example, no 

 comj)arison by means of degrees can be made between a dry lens 

 and an immersion lens, except by reducing the angles to an entirely 

 arbitrary common medium which has no actual existence either for 

 both objectives or, at least, for one of them. 



None of these defects of the angular expression of aperture can 

 be overcome by introducing, as Dr. Woodward suggests, the " first 

 interior angle " of the objective. The adoption of this plan, on the 

 contrary, would appear to me to be a serious change for the worse. 



* This Journal, i. (1878) p. 51. 



t 'Am. Quart. Journ.,' i. (1879) p. 286. 



