192 THE president's address. 



liad obtained his two divergent beams by a lens of a short focal 

 length. But being guided by the lattei-'s misconception as to 

 the centrical course of the rays, even so far as to attempt the 

 impossible feat of illustrating it with a diagram, this distin- 

 guished oculist fell into inextricable entanglements in his 

 geometrical explanations of the j^henomena he thus observed. 



Yirtually, the idea of the usefu.lness of deeussant beams of 

 light in entoptical explorations lay fallow, until I turned my 

 attention to them, and proved that a single proposition and a 

 single diagram, would as easily suffice to embrace all the 

 elements of deeussant beams as those of divergent beams only, — 

 whether, it might be one in relative lateral motion with the eye, 

 or a pair of them relatively at rest with respect to it ; that it 

 would yield also, proportionally, the variations in size, and 

 inversions in movements, aspects and positions, which the 

 shadowy images of intraocular corpuscles evince in passing from 

 the convergent to the divergent portions of such beams. In 

 addition to which the contrasts impressed upon these images by 

 cliiiraction, refraction, and reflection at the corpuscles themselves 

 under such circumstances furnish criteria or experimenta crucis for 

 determining their nature. 



This joint or deeussant method is easier of application and 

 more efficacious than the partial or divergent one previously in 

 iise by myself and others. To expound it, therefore, and to 

 reinvestigate by its means the whole field of entoptical problems 

 which fall within the scope of these methods are, primarily, the 

 raison ^etre of my Entoptics. Secondly, outside of this field, 

 the singular movements of the shadows of the retinal blood 

 vessels, long since observed, but first explained by the late 

 H. MiiUer — and through measuring which he calculated, geo- 

 metrically, their distances from that layer of the retina that 

 constitutes its ''percipient" surface — to treat by a trigonometrical 

 proceeding of my own that entirely dispenses with an objection- 

 able assumption from averages involved in his plan. Finally, 

 both within and without these boundaries, as the preface affirms 

 " it ventures, too, upon untrodden ground in its investigations, 

 and to suggest explanations of phenomena that have reiiiained 

 unaccounted for. Many of its physiological conclusions are 

 peculiar. That is, in every sense, in the main, it is an original 

 essay." In a word it aimed at recasting the study of ento]Dtics 

 from root to branch. 



