966 Transactions of the Society. 



says that his expression is "the rational expression of the magnifi- 

 cation or ' power ' of an optical system, because every observer will 

 see eyery object enlarged through different systems in the exact 

 proportion of the value of that quotient," it must be remarked 

 that exactly the same service is done by the amplification numbers 

 determined by the old method. 



But I cannot see either that the form in which Prof Abbe 

 wishes to define the notion of "linear amplification" is dis- 

 tinguished advantageously from the commonly adopted way of 

 defining that notion. At first sight it might appear that Prof. 

 Abbe's definition is free from such an arbitrary factor as the value 

 chosen for the distance of distinct vision, for which the "linear 

 amplification " is determined ; in reality this is not the case. For 



the numerical value of the ratio — 7 — = -^ depends, of course, 



upon the value of the unit which is chosen. The value of - is 



different if / is expressed in millimetres, than if / is expressed in 

 centimetres, or in inches. In fact it is clear that the angle under 

 which the unit of length is seen depends upon the dimensions of 

 that unit. With any change in the choice of the unit, the numbers 

 which indicate the amplifying power will therefore vary. The 

 values, however, which are obtained for different systems, will always 

 be in the same relation, independent of the exact value of the unit. 



But does, in reality, such a difference exist between this and 

 the old mode of determining the amplification, in which the numbers 

 depend upon the value which is chosen for the " distance of distinct 

 vision," whilst the amplification numbers of different systems are 

 always in the same ratio, independent of the exact value of that 

 distance ? 



Both methods, I think, are in so far identical, as they give for 

 different systems numbers which represent the ratio of the dimen- 

 sions of images on the retina, which are obtained when one and the 

 same object is seen through these systems. 



Yet it appears to me there is a practical difference between 

 them. 



Prof Abbe himself has little hope that his expression for 

 amphfying power will be generally adopted, as it will seem " too 

 abstract." In fact I think it is too abstract. 



The old method suggests to the mind to a certain extent a 

 direct idea of the practical value of the lens-system. If I know, 

 for instance, that the linear amplification of a system is 600, I can 

 immediately recognize the efi'ect of the system, if I consider that an 

 object of 10^ will be seen at 25 cm. as of the length of 6 mm. 

 But I think the idea is at first sight less clear, if I only know that 



