372 Prof. Lewis, On the [May 14, 



The images from k and t are multiple, and the faces are also 

 less bright than the others, so that the angles involving these faces 

 would be little suited for testing the accuracy of the several instru- 

 ments. The comparison of these angles, and of a large number of 

 angles, measured with both the large horizontal goniometer and the 

 Cary's goniometer, has given me confidence in employing several 

 of the angles obtained with the latter iustrument only, when the 

 images were definite enough to give good observations with the 

 small Galilean telescope, but were too faint to allow the higher 

 magnifying telescope to be used. In the accompanying tables of 

 angles those measured by the horizontal goniometer, with telescope 

 and collimator, are distinguished from the others by being printed 

 in thicker and larger type. Two angles given together are those 

 obtained from the corresponding pairs of faces ; but if the second 

 angle is enclosed in brackets one of the faces at least gave two 

 images and the angles are alternative, the enclosed one being the 

 least trustworthy. The planes observed on the various crystals 

 and the zones connecting them are shown in Fig. 1. A few of the 

 letters and of the corresponding zone-circles have been omitted to 

 diminish the complication of the diagram. 



The planes observed on the crystals examined by me are 

 a 100, m 101, L 703, A, (102) ? (105)? (104)? c 001, M 103, o 101, 

 R 201, N 301, (711), v 611, /*_922, <£ 411, d 311, e 522, s 211, 

 till, X 122, to 011, x 122, '<7_211, i311, 6 010, r 121, h 113, 

 /3 013, f 213, g 313, ^ 413, q 12 1 3, z 137, k 124^ x 212^ 7 414, 

 7T 515, p 616, w 12 1 15, £ 215, A 210, (1 6 16) ? (119)? (1 2 10) ? 

 (139)? 



Besides these n 301, fi 702, u_203, £_15 11, ©_811, F 511, 

 $13 44, A 111, ?181, E212(?), 1676, e 12 5 20, 7 36 13 39(?) <rf 

 233 (?), have been recorded by other observers. 



The angles I have adopted for the purposes of calculation are 

 co 48° 2T-17, a,o 50° 16'*25 and dd,96°2T'2. From these the 



* This plane / (922) was observed and so lettered by Nanmann. 

 t a is in all probability identical with x. It is largely developed in Weisbach's 

 Fig. 9. His measurements are only approximate and do not accord well either with 

 a or x. He gives 



W. calcd. calcd. for x. 



aa ; = 40°§ 42° 8' 39° 48'67, 



aa =98°i 99° 20' 96° 18'. 



set 42° 47' 



It has been also observed by vom Rath, who gives no measurements but calls 

 attention to the remarkable divergence he finds in the measurements of it, and also 

 to its great development on several crystals. The plane x was well developed on 

 nine of my crystals. It lies in the zones [mft], [£,«], [cfcj, [As,], [<7<r,] and [E/J. 

 These zones give a ready means of testing the true indices to be assigned to the 

 plane, when the angles in the zone [dt.r] are too little reliable to distinguish 

 between the two sets of indices. 



