44 E. G. WEST ON LISSAJOUS' CURVES. 



study to the problem of their illumination, has found nothing so 

 good as a brilliant dark-ground illumination by a large spot-lens. 

 The difficulty in this case is to get a sufficiency of light with a really 

 black ground. For the exhibition of " water-markings," a uni- 

 lateral oblique light is advantageous, and is, perhaps, best obtained, 

 as suggested by Mr. I. C. Thompson, of Liverpool, by stopping out 

 •^ or |rds of the hollow cone of rays given by dark-ground illumi- 

 nators, so as to secure a crescent of rays. Complete rotation of the 

 object is necessary to obtain all the " water-markings " characteristic 

 of the more complicated curves, and of superposed spirals. 

 Good effects are sometimes to be obtained with reflected light, and 

 many of the figures have a singularly solid or scroll-like appear- 

 ance, which, though sufficiently striking under the monocular, is 

 enhanced by the binocular microscope. 



I have traced a few curves, at Mr. Wenham's suggestion, on 

 polished steel. These to the naked eye, or under a low power, have 

 a brilliant iridescent appearance, but are not remarkable when more 

 highly magnified, as the best steel surfaces which I have been able 

 to procure are far too rough for any effective work of this kind. 



There is some difficulty in effectively mounting the glass-tracings. 

 Dry-mounting is, of course, the only available method. Both dust 

 and wiping have to be avoided ; while it is necessary to defer the 

 actual covering till the cement-ring is so far hardened that no 

 " damping " whatever can take place. Any condensation of vapour 

 beads the cut lines, and, in the most searching way, brings into view 

 defects of surface-polish, otherwise quite invisible even under a good 

 dark-ground illumination. 



In conclusion, I think I may claim for these tracings some special 

 interest ; mechanically, as successful examples of minute diamond- 

 graving under somewhat new conditions ; microscopically, as test- 

 objects, and as affording studies in illumination and in certain para- 

 doxical and deceptive appearances ; and aesthetically, as even surpas- 

 sing in beauty and brilliancy, and especially in stereoscopic effect, 

 the larger curves which are so well-known and so much admired. 



