132 



Mr. E. W. Smith on 



in the minds of those students who know very little about 

 mathematics, viz., almost all students of chemistry and mine- 

 ralogy, and a still larger number of geological students, the 

 apparatus will prove useful to mathematical students inas- 

 much as the arithmetical processes are tedious and complex 

 for even those forms in which the mathematical relations are 

 comparatively simple. For the forms with oblique axes the 

 advantages of a simple method of noting the weights neces- 

 sary to maintain equilibrium far outweigh the disadvantages. 



JNote. — Professor Wiltshire informs me that many years 

 ago, Mr. Mitchell, at the Royal Institution, showed a model 

 by which the derivation of the crystalline systems from the 

 octahedron was explained. 



Explanation of Plate IL 



Fig. 1. — u' t j8', y, 8', «', t)', octahedron. 

 p,p', weights. 

 ct, j9, y, 8, e, £, y, 0, double hexagonal pyramid. 

 Fig. 2. — a, b, c, d, e, /, octahedron. 



a' , b', c' f d' , e', f,g', h', cube. 

 A, B, C, D, E; F, weights. 

 Fig. 3. — The upper figure shows the hexagonal prism surmounted by- 

 hexagonal pyramids. The lower shows the rings with the rhombo- 

 ♦ hedron formed. 



XIX. A Shunt- Transformer. By Mr. E. W. Smith*. 



ALTHOUGH this experiment has already been described 

 by Professors Ayrton and Perry in a paper at the Insti- 

 tution of Electrical Engineers, it was thought to be worth 

 while occupying this Society's time in showing it here, as it 

 forms a good lecture-experiment, if nothing more, to illustrate 

 acceleration and lag of alternating currents. 



The experiment consists as follows : — Between two leads a 

 Fig. I. 



certain alternating potential difference, V, is maintained. We 

 have two resistances, A and B (fig. 1), in series, through 



* Communicated by the Physical Society : read June 8, 1889. 



