TRANSACTIONS OF SECTION A. 495 



■which meet in AQ. The equations to these traces, combined with the equations 

 of the former traces on ABC, completely determine the lines. 



10. The theorem of § 3 may he thus proved. 



Let ( f,g,h,k) denote P in the preceding tetrahedral system ; then A',B',C',D',E' 

 have for their co-ordinates (F,g,h,k), (f,G,h,k,), (f,g,B.,k), (f,g,h,K) : where 



^ j- rL Ti j, v i W + 13/t 2 + 14/c 2 



F+f=G + g = K + h = K + k=^-f ^ ttt~= = 



J " \2g + 13A + 14A 



Then the coordinates of Q,R,S,T have this type : 



(/,G,H,K), (F,g,H,K), (F,G,^,K), (F,G,H,A) ; 



and the points (a,b), (a,e) ... have the type (F,G,h,k), (F,</,H,&) 



With these data the theorem is as readily established, as its Plane analogue. 

 ' Quarterly Journal of Mathematics,' vol. xv. p. 203. 



8. A New Form of Trap-Door Electrometer. By Professor Barrett. 



9. On Unilateral Conductivity in Tourmaline Crystals. 

 By Professor Silvanus P. Thompson and Dr. Oliver J. Lodge. 



The authors regarded the phenomena of pyroelectricity as exhibited by the 

 tourmaline and other crystals as of the utmost significance in the theory of the 

 relation of electricity to the particles of matter. Dr. Lodge had read a paper at 

 the British Association Meeting at Glasgow on a mechanical model illustrating the 

 flow of an electric current through a circuit of molecules. (See Phil. Mag., Nov. 

 and Dec. supp. 1876.) 



The considerations therein advanced had led the authors independently to con- 

 clude that the phenomena of pyroelectricity could be explained if it could be shown 

 that such crystals as were pyroelectric possessed unilateral conductivity (§ 25 of 

 above paper). The term " unilateral conductivity " had been given by Dr. A. 

 Schuster to a phenomenon of some obscurity observed by him in certain cases, and 

 which formed the subject of a communication to a former meeting of the Asso- 

 ciation. The term " unilateral conductivity " was defined as follows : — If the con- 

 ductivity of a substance in a given direction between two points A and B was 

 greater when the flow was in the direction from A to B than when the flow was 

 in the direction from B to A, then such a substance was said to possess unilateral 

 conductivity. 



It had been argued by the first-named of the authors of the paper that if the 

 tourmaline possessed a unilateral conductivity for electricity, it would also be 

 found to possess unilateral conductivity for heat, since the researches of Tait and 

 Kohlrausch had shown that the two conductivities are comparable in almost all 

 points of analogy. The experimental research, therefore, had divided itself into 

 two branches — a thermal and an electrical. 



Owing to the difficulty of procuring suitable specimens of tourmaline crystal 

 a delay of some months occurred, but eventually this difficulty was overcome 

 through the kindness of Professor N. Story Maskelyne. Other crystals had also 

 been procured from France. 



The method first suggested for comparing the two heat-conductivities as 

 measured in opposite directions along the axis of the crystal was that of De 

 Senarmont. A slice of the crystal was cut with parallel faces containing the 

 crystallographic axis, and having been covered with a film of wax, or with Meusel's 

 double iodide of copper and mercury, was heated from a point by a hot wire. 

 When the experiment was rapidly made, the elliptical isothermal line marked 

 out by the melted wax or the blackened iodide, was found to be displaced from the 



* A Model was exhibited. 



