8 _ Transactions of the Society. 



one or the other it would undoubtedly be wise to choose fig. 2 in 

 preference to fig. 1. But since we can have both, both are Avorth 

 having. For, to instance one point only, in discussing the form of 

 the dot it is important to know whether the light which it trans- 

 mits is all refracted towards the margin of the aperture or evenly 

 distributed over its area. Fig. 2 taken alone cannot answer this 

 question. It tells you that a large proportion of the transmitted 

 light is deflected to the outer annulus, but it cannot tell you 

 whether any considerable proportion is left to follow a path closer 

 to the optical axis. In a word, it cannot tell you whether the 

 refraction is regular like that of a lens or irregular like that of a 

 surface of ground glass. Still less can it afford you any informa- 

 tion — even on the assumption that the refraction is regular — as to 

 what the rule is to which it is subject. On these points fig. 1 

 affords decisive evidence. It tells you at once that no substantial 

 quantity of light comes along the optic axis : therefore, the refrac- 

 tion is regular and the dot must have some simple geometrical form ; 

 and if you choose to vary the dimensions of the stop and of the 

 aperture you may determine by the comparison of a number of 

 pictures such as figs. 1 and 2, through what zones precisely the 

 refracted light comes, and thus obtain what I may perhaps call a 

 stop analysis of the transmitted light from which inferences may 

 be drawn both as to the form and as to the refractive index of the 

 structure in which the refracted rays originate. I must not, how- 

 ever, pursue this suggestion further, for I have other photographs to 

 bring under your notice. 



In plate II. fig. 4 you have a bright dot photograph of the 

 familiar Plenrosigma angulatum taken with a small aperture, and 

 exhibiting certain dark contours. The meaning of this appearance 

 would be inscrutable if we were only able to vary the illumina- 

 tion by substituting a beam of wider angle for the naiTow-angled 

 beam, for although the wide-angled beam lights up these darkened 

 areas, it causes them to present an appearance wholly indistinguish- 

 able from that of the other areas by which they are surrounded, so 

 that in this instance the beam of wide angle is actually less dis- 

 criminating than the narrow-angled beam. 



The significance of this appearance is however made quite 

 clear by altering the position of the small aperture in relation 

 to the large beam. We thus find a region through which, if we 

 examine the specimen, these particular areas appear bright while 

 the others, bright in fig. 4, appear dark. This contrasted image is 

 shown in fig. 5, which, however, is photographed from a direction 

 less tavourable to the resolution of the image than that from 

 which it was viewed in fig. 4. It is manifest that the light 

 transmitted by these parts of the specimen has been refracted 

 along an inclined axis, which we have now identified, and we 

 can at once conclude that the small surfaces which have pro- 



