The Presidenfs Address. By Prof. P. Martin Duncan. 1 59 



These lines were most sharply seen though less than so^ot inch 

 thick." After noting the disappearance of distinctive shadows and 

 consequent obliteration of structural molecules with excessive 

 angular aperture, illustrating his meaning by the structure of 

 Podura scales, with different stops and under very varying condi- 

 tions, Dr. Pigott states that he has come to the conclusion that 

 residuary aberration was not the only cause of the obstinate 

 obscuration of minute crowded molecules in translucent organic 

 forms, but that 



" Excessive angular aperture, he found, attenuated mar- 

 gin. . . . There is, it may be said, something unnatural 

 in the mode of vision intrinsic to very high angled glasses. It 

 is undoubtedly true that such a glass presents an all-round 

 vision. It really conveys visual rays from a given brilliant 

 particle, at every inclination in azimuth and altitude, and 

 this too at one and the same instant. To illustrate this 

 position a minute die may be imagined the k^^qq q " inch 

 broad. The highest angled objective really enables the 

 observer to collect rays emanating from four sides and the 

 top at the same instant. The human eye could at most 

 view three sides at once. Doubtless the efiect of this 

 angular vision all round the corners, causes particles to look 

 spherical, when sufficiently minute, even if cubical." 

 Now it is necessary to say plainly that this view is founded 

 upon a fundamental error, " belonging," to use Professor Abbe's 

 words, " to the venerable relics of the past naive period of micro- 

 scopical science, which was characterized by an unshaken conviction 

 in the validity of the hypothesis that microscopical vision is in all 

 essential respects the same thing as ordinary vision." The " all- 

 round vision," by virtue of which we are supposed, when looking at 

 a minute cube, to see at the same time the top and all the sides 

 (with the result of rounding off the corners and angles !), does 

 not really exist, as can be shown by the application of the simplest 

 laws of geometrical image formation. The different obliquities of 

 the rays in an objective of wide aperture cannot give rise to any 

 all-round vision, for in the Microscope there is no difference of 

 jperspective attendant upon oblique vision as with the naked eye. 

 The difference of ^projection of successive layers which exists is 

 ineffective, except in the case of binocular vision. This absence 

 of perspective may be readily established by examining an object 

 alternately by an axial and an oblique ray ; it will be found that there 

 is no shortening of the lines in the latter case, and no capacity 

 in the Microscope, therefore, for "all-round vision." Indeed if 

 this theory were correct, microscopical vision, even oi plane objects 

 and with very moderate apertures, would be entirely destroyed. 



Equally mistaken is the second branch of the view which I 

 am considering, viz. that a wide aperture must, in the nature of 



