ifSSl.] Crystallized Bodies on Hoviogeneous Light, fST 



ihen a node, as 4 ; after which it separates into two conjugate 

 ovals, as 5 ; which ultimately contract themselves into the poles 

 P, P'' as conjugate points. The general idea bears a striking 

 resemblance to the variation in form of the curve of the fourth 

 prder, so well known to geometers under the name of the lem- 

 niscate, whose equation is 



when the parameter b gradually diminishes from infinity to zero^ 

 2 a being the constant distance between the poles. In order, 

 however, to put this to a satisfactory examination, accurate 

 measures must be taken, which, in the case of nitre, from the 

 minuteness of the system of rings, presented at first some diffi- 

 culties. These I obviated, after many fruitless trials, by a mode 

 of observation which I have found extremely convenient and 

 accurate, and which applies particularly well to the present pur- 

 pose. It consists in projecting the rings by solar light on a 

 screen in a darkened room, by which means they may be magni- 

 fied to any required extent, examined at perfect leisure, and la 

 all their phases, and measured or traced with a pencil with the 

 utmost exactness and facility. They may be thus exhibited too 

 to a number of spectators at once ; a thing which may prove 

 ^iserviceable to the lecturer, for which reason I have subjoined ta 

 this paper a brief description of the apparatus I employ. 



Having cut a very perfect crystal of nitre at right angles to its 

 axis of crystallization, and adjusted it properly on this apparatus, 

 the rings were projected on a large sheet of paper, stretched, 

 while moist, on a drawing board, by which means it assumes a 

 truly plane surface by the contraction it undergoes while drying. 

 The poles were then marked, and the loci of the successive 

 maxima for red rays carefully outlined. The screen being then 

 ^removed, a series of lemniscates were laid down by points, hav- 

 ing the same poles, and one common point in each , chosen 

 where the tint was most decided. It is unnecessary to give any 

 .comparative statement of measures in the observed and con- 

 structed curves, as the points, graphically laid down, uniformly 

 fell on the pencilled outlines, or, in the few instances to the con- 

 trary, within limits less than the very trifling irregularities of the 

 outlines themselves. 



The graphical construction of these curves is rendered 

 extremely easy by the elegant and well-known property of the 

 lemniscate, in which the rectangle under two lines drawn from 

 the foci (or poles) to any point in the periphery, is invariable 

 throughout the whole extent of the curve. This is easily shown 

 sfrom its equation, and the value of this constant rectangle in any- 

 one curve is expressed by a b. 



We must next enquire how the constant parameter b varies in 

 passing from ring to ring. To this end I projected the rings, 

 illuminated by red light only, on a screen as before, and having 



