1883.] Prof. Lewis, On the Crystallography of Miargyrite^ 365 



The results in the two cases are as follows: — 



1 . Case of oscillatory waves in a fluid of infinite depth 



2. Case of a solitary wave 



*(»)- JE J t .1/(0 + ») -/(0 - «)I ^ !%/» ■ 



In the former case, partly as a severe test of the method, and 

 partly for other reasons, I took as the trial outline a serrated line 

 composed of straight lines inclined at angles 1 of ± 30° to the 

 horizon, giving ridges formed of wedges of 120°, and troughs formed 

 of similar wedges inverted. Even in this case, where the assumed 

 form is so egregiously wrong as regards the troughs, the first 

 approximation led to a form presenting ridges of 120°, which for a 

 considerable way down hardly differed from the original, while 

 in lieu of the angular troughs I got a curved outline, with a depth 

 from crest to trough of about 0*22 of the wave length, instead 

 of 1/2*J3 or 0'309 as in the serrated outline assumed for trial. The 

 results of some other trials are encouraging as to the success of the 

 method, but as I mentioned already the numerical calculations are 

 not finished. 



(2) On the Crystallography of Miargyrite. By Professor 

 W. J. Lewis. With Plate X. 



[Revised and enlarged. July 19, 1883.] 



In the description of this mineral given by Naumann, in Pogg. 

 Ann. XVII., 1826, the planes fall into three prominent zones, those 

 denoted by him [abo] (the zone of symmetry), [bfdst] = [100, 111], 

 and [opg] — [101, 313] ; and the cleavages are stated to be parallel 

 to b and m. In Miller's Mineralogy (1852) two new zones 

 [^hrMxy], [vzkty t g] are added to those already given by Naumann. 

 Owing to the relation between the angular elements, the angles in 

 the zone [^hrMxy] approximate closely to those in the zone [bfdst]. 

 Miller retains the orientation and axial system adopted by 

 Naumann, but he has misplaced the angles ao and bo, possibly 

 owing to a confusion in changing the letters used to denote the 

 faces. For Miller always uses a, b and c in the oblique system to 

 denote the poles (100), (010), (001). Hence Naumann's b becomes 



1 In the case of a simple serrated outline, / (<£), and therefore F (<£), is 

 independent of the assumed inclination. 



20— 2 



