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XI. Spontaneous Generation of Electrons in an Elastic Solid 

 JEtker. By Prof. Alexander M c Aulay, University of 

 Tasmania*. 



I. Notation and Terminology. 

 II. Enunciation of Mathematical Theorems. 



III. Description of first ^Ether Hypothesis. 



IV. Mathematical Development, initiated. 

 V. Second yEther Hypothesis. 



I. Notation and Terminology. 



THIS elaborate setting forth of the notation and assumed 

 theorems is chiefly necessitated by the prevalent 

 voluntary want of familiarity with quaternion methods on 

 the part of physicists. 



If in an arbitrary deformation, small or large, of an elastic 

 body, solid or fluid, an original infinitesimal length I is 



changed to hi, k — 1 will be called the elongation and k the 



i . . . 



total elongation. The three principal elongations required 



to pass from a standard state to the actual state at an instant 



will be denoted by e, /, y, and the three principal total 



elongations by E, F, G, so that 



E = l + <>, F = l+f, G = l+y. . . . (1) 



The position vector of a point in the standard state will 

 be denoted by p, and in the strained state by 



p'=p + v (2) 



The Unity %, given by 



% ft)=-Sa>y.?7, (3) 



where w is an arbitrary vector, will be called the strain 

 Unity or the strain. Two allied Unities T and u, each 

 obtained from % by the addition of a self-conjugate linity 

 are required. T the total strain Unity, or the total strain, is 

 given by 



Ta> = (l + x)et>= — SwV .p' = (o — So>V- V- - • (4) 



v is given by 



vcd = (1 + %x!) X <o = - So>V. V + i ViSa>V 2 Srh77 2 . ■ (5) 



v stands for the self-conjugate part i(y + v f ) of v ; similarly 

 for X, &c. v is called the pure strain linity or the pure 

 strain, v is the same as X only when the products of rj are 



* Communicated bv the Author. 

 Phil. Mag. Ser. 6. Vol. 19. No. i()9. Jan. 1910. K 



