512 Prof. Miller's Crystallographic Notices. 



But on the assumption that a gas expands in an envelope 

 impervious to heat, we have, if p^ denotes the pressure corre- 

 sponding to ?\,*, 



■-odf. 



in which K denotes the relation of the specific heat of the gas 

 for a constant pressure and constant volume. It follows from 

 the integral, 



Work = p-\ . 

 Jv— 1 



C C 

 A gramme of the powder used by us gives for ro= ^ — w^, 



Op Or 



5836 cubic centims. ; and for p^, 1029-8 x 4373-6 grms. K is 

 found from the composition of the gases to be 1-39. A kilo- 

 gramme of the powder, in undergoing the above decomposition, 

 effects therefore a theoretical work of 67410 metre kilogrammes. 



LXIII. Crystallographic Notices. By W. H. Miller, M.A., 

 F.R.S., Professor of Mineralogy in the University of Cambridge f. 



An Improved Method offin,ding the position of any Face in 

 Crystals belonging to the Anorthic System. 



IN the Numbers of the Philosophical Magazine for February 

 and May 1857, it is proved that the anharmonic ratio of 

 the axes of four zones having a face in common, is a simple and 

 symmetric function of the indices of two of the zones, and of two 

 faces one in each of the other two zones, of the same form as the 

 expression for the anharmonic ratio of four faces in one zone. 

 This expression enables us to find the position of any face of a 

 crystal of the anorthic system much more directly than by the 

 methods given in my ' Crystallography,' Chap. VII., and in the 

 new edition of Phillips's 'Mineralogy,' arts. 217, 218. The 

 expressions referred to above, beginning with the latter, may be 

 enunciated as follows. 



Let P, Q, R, S be the poles of any four faces, no two of which 

 are parallel, in one zone ; hkl, uvw the symbols of Q, S ; efg, 

 pqr the symbols of any two zones containing the faces P, R 

 respectively, neither of which is the zone PR. Then 



eh + fk + gZ pw -f qr + rw _ pA + qA' + rl eu + h + gw , , 



smPQ sin RS ~ sin RQ sin PS " ' " ^*^ 



This expression may be easily remembered, if we observe that 



* Poisson, Mech. ii. p. ()47. Claiisius, I'ogg. Annalen, vol. Ixxix. p. 3y6. 

 t Commuuicated by the Author. 



