426 Transactions of the Society. 



called a proposal. Helmholtz appears to have been himself dis- 

 satisfied with the constants of his own standard eye, and probably 

 wonld have recommended revision if the standard were to be adopted 

 for general use. But the scheme is there, and it has already appeared 

 by comparison how entirely unscientific is the method of apertometer 

 measurement. We do not want to know what is the extreme 

 angle of incident wave-front that we can squeeze into our objective 

 if we release it from duty and flood it with light. We want, on 

 the contrary, to know what is the widest angle that can be dealt 

 with under the conditions of actual use, that is to say, with a 

 certain breadth of field under full illumination, and the instrument 

 yielding its best performance — or to adopt Mr. Nelson's nomen- 

 clature — we want to know its working aperture. This can be 

 ascertained by measuring its normal magnifying power under 

 properly determined conditions of use, but it cannot be ascertained, 

 even approximately, by mounting an apertometer upon the stage 

 and reading off the angle at which an ill-defined image of a flame 

 is extinguished by the limit of aperture. It may be that the time 

 has not yet come for elaborating Helmholtz' suggestion into a 

 definite scheme, and no doubt it would be premature to ask at the 

 present time for any authoritative adoption of even the best scheme 

 that could be elaborated. But it is surely time to bring this long 

 neglected proposal under consideration, and to endeavour by 

 experiment and discussion to form the views, at present embryonic, 

 of the world of microscopists concerning the theory and practice of 

 objective rating. 



APPENDIX. 



Note I. — The Sixe Law axd Sixe-taxgext Relatiox. 



The sine law and what I may perhaps be allowed to call the sine 

 tangent law are of so great importance in the theory of optical instru- 

 ments, that I will take the liberty of adding in this place a few observa- 

 tions which could not be introduced without too great a digression in 

 what purported to be a resume of Helmholtz' paper. 



The proof of the sine law which is commonly put forward and known 

 as Hockin's proof is faulty, for the reason that it applies only to an 

 imaginary image of infinitesimal dimensions situated on the axis of the 

 system. 



Helmholtz' proof is much more adequate. It applies equally to all 

 parts of the field of the instrument — not simply on the axis — and it shows 



