306 Mr. L. "Wright on Optical Combinations 



symmetry there also. It is not necessary to add details of 

 explanation which will be familiar to all. 



Allow me next to illustrate the beautiful phenomena of 

 crossed films of mica in highly convergent light, such as will 

 take in biaxial angles of, say, 50°. Our starting-point will be 

 Norremberg's beautiful discovery, worked out entirely from 

 theory, that by crossing films of biaxial mica of gradually 

 increasing number and proportionately diminished thickness, 

 there was a gradual approach to the rings and cross of a uni- 

 axial crystal. He found three wave-lengths of retardation 

 the best approximate unit. Here is a single plate of mica — 

 the ordinary biaxial lemniscates; and here are two such plates 

 crossed at right angles — the ordinary figure of a " crossed " 

 crystal, in which we get the black cross. With four plates 

 crossed we get the first approach towards rings, each of the 

 "eyes " being now T bisected by a straight fringe placed as a tan- 

 gent to the figure. Norremberg's next preparation was eight 

 films crossed ; but I add one of six, which gives a single per- 

 fect though nearly square ring, wdiile eight films give two 

 rings. Twelve give three rings and signs of a fourth ; while 

 twenty-four, as you see, are absolutely undistinguishable from 

 a calcite. The whole series will be thus : — 



J^ _2_ _4_ _6_ _8_ 12 24 

 3\' 3A,' }\' ±\' §*.' £k' %\ 



Now there is no necessity for an exact total thickness of three 

 wave-lengths in constructing this series ; but an approxima- 

 tion to it is necessary, to preserve the gradation of the pheno- 

 mena and the gradual passage to the uniaxial figure. So far 

 Norremberg ascertained; but he does not seem to bave carried 

 his experiments with mica any further. Let us now do so. 

 The eight films gave us two rings, the outer one squarish in 

 figure. But if we combine eight very thin films (say J-\ 

 thick, as in this preparation), you observe that we get perfectly 

 circular rings at once ; and in fact even four very thin films 

 will give them ; and twelve thin films give us quite fine circles. 

 Now, on the other hand, let us employ four and eight thick 

 films — in this case over 1 X thick (we thus more than double 

 Norremberg's thicknesses); and observe that the rings now 

 have altogether disappeared, and the curved fringes are all 

 turned the reverse way, their convex sides to the centre. The 

 same thing is still more evident in this splendid figure, pro- 

 duced by twelve crossed films f X in thickness. We see easily 

 enough that it must be so, if we follow in our minds the de- 

 compositions and recompositions of the vibrations in traversing 

 the successive films ; but it is very interesting to notice how, 



