286 Mr. T. S. Davies on Geometry and Geometers. 



white image, the grooves or stri?e will give rise to the beautiful 

 prismatic images produced by interference*. 



Another analogous fact presented itself to me many years ago 

 in examining calcareous spar. Having had occasion to form an 

 artificial face upon one of the edges of the rhomb containing the 

 obtuse angle, I used a coarse file without water, and found that 

 it exposed faces of cleavage which had never been previously seen, 

 andwhichwere inclined to thegeneral surface produced bythefilef. 



In examining the optical figures produced by the disintegra- 

 tion of crystallized surfaces, I have found that by coarse sand- 

 stone, or the action of a rasp, or large-toothed file, we can expose 

 surfaces of crystallization with their natural polish differently 

 inclined to the general surface J. 



In all these cases the faces, exposed by the mechanical action 

 of grinding or filing, preserve their natural surfaces and polish, 

 and will preserve them more perfectly and readily if they are 

 faces of easy cleavage. The facility of exposing such faces by 

 the action of grinding must increase as the veins or strata be- 

 come thinner, and it is probable that their exceeding minuteness 

 in the diamond may have aided in the production of the struc- 

 ture which has been described. 



I have found it quite impossible to measure the inclination of 

 any of the faces by the goniometer ; but I have succeeded, 

 though with some difficulty, in taking an impression of the 

 grooved surface upon wax. 



This structure sufficiently explains the existence of three 

 images when the lens was used as a microscope, without sup- 

 posing that the veins had different refractive powers. Faces of 

 different inclinations would, of course, converge the rays to dif- 

 ferent foci on the retina, as effectually as if there had been only 

 a variation in their refractive indices. 



St. Leonard's College, St. Andrews, 

 February 11, 1841. 



XLI. Geometry and Geometers. Collected by the late Thomas 

 Stephens Davies, F.R.S.L. fy E. tyc.§ 



No. IX. 



[Continued from vol. ii. p. 446.] 

 "T^HIS appears to be an appropriate occasion for offering a few 

 -* suggestions for the consideration of geometers respecting 

 the ancient geometry and its modern cultivators. 



* See Pbilosopbical Transactions, 1814. 

 t Edinburgh Journal of Science, Oct. 1828, vol. ix. p. 312. 

 X Trans. Royal Soc. Edinb. vol. xiv. 



§ Communicated by James Cockle, Esq., M.A., Barrister-at-Law, who 

 adds the following note : — 



[" Unlike the two papers of this series, which I have already forwarded 



