238 Prof. Lewis, On the measurements of a bead [May i5, 



85, 44"(?), 39, 59(f)]. The angles (30, 42) = 27° . 44' 1 ; (30, 

 33) = 20° . 51' ; (33, 54) = 28" . 4'i have been calculated. Assuming 

 them to be in a zone, the anharmonic ratio was found to =1. 

 Other angles were determined approximately from the stereo- 

 graphic projection, but none of those found seemed to be near 

 those between the common planes of cubic ciystals : (71) and (69) 

 are nearly at 90° to (30), as also the planes (119) and (136) below 

 the paper. 



The following are Professor Miller's notes which I have done 

 no more than edit. 



W. J. LEWIS.] 



In 1874, I received from Major [now Colonel] Ross what 

 appeared to be a bead of platinum, of approximate diameter 

 0"73 mm., which he had fused with the aid of a blowpipe, and 

 which on cooling exhibited a large number of crystal-faces. The 

 measurement of the crystal was undertaken under the impression 

 that it would be comparatively easy, but the small size of the 

 faces, which are not arranged in zones, rendered their identification 

 all but impossible. The following method of determining their 

 position was therefore adopted. The bead was attached to the 

 axis of a small Wollaston's goniometer in a convenient position 

 but without any special orientation. The small goniometer was 

 then secured in an upright position on the graduated horizontal 

 plate of the large goniometer so that the crystal lay in the inter- 

 section of their axes. The position of all the faces, which were 

 not obscured by the vertical circle, could now be determined, 

 by reference to the circles of the two goniometers, in the same 

 way that the positions of stars can be referred to two planes 

 by means of an altazimuth. In this way 147 faces, occupying 

 somewhat more than a hemisphere were determined, and a stereo- 

 graphic projection of their poles made, in which the centre 

 represents the zero of the horizontal circle, whilst the zero of 

 the vertical circle is placed at the top of the projection and the 

 angles read towards the left. As far as examined, the bead seems to 

 differ from a crystal, (1) in that the planes do not seem to occur in 

 pairs of parallel ones, (2) in that they are not arranged in zones. 

 The relations of the planes to one another cannot therefore be very 

 simple. 



