and Pyroelectric Properties of Matter. 13 



(x , y > z o> ? o? ^oj So) ^y *he e( iges of the cube being elongated by 

 x— x , y—y , z—z , and the angles meeting in three contermi- 

 nous edges receiving augmentations of f— f , v~Vqi ?~~ So* 

 It is clear, since the altered angles differ each infinitely little 

 from a right angle, that the strains represented by £— £ , 

 V—Vo? f~ "£o mv °lve no change of volume, and are simple de- 

 formations, each of a perfectly definite kind, in the planes 

 YOZ, ZOX, XOY respectively, and that the change of vo- 

 lume due to the six coexistent strains is actually an infinitely 

 small augmentation amounting to 



x— x +y — y + z— z . 



13. Considering still x— x &c. as each very small, we have 



the following development by Maclaurin's theorem, the zero 



suffixes to the differential coefficients being used for brevity to 



denote the values of the different coefficients at (x , y Q , z , 



So? ^0? 'O )' 



+* {(£).<-- °> 2+ (S^«> 2 + (S)/-») 2 



+ <|l) <"X*-*o) + i££)(- z - z ^-° •> 



+2 (S>-*»x«> 

 + <£&<'-*o<f-» + <li) ^- »»-« 



+2 (S) (— »xr-r») 



2 (S,)/—»)^-"») +2 (li) (— .)«-« 

 2 (|i)^-^(f-« +2 (li)^-^(f-f") 



+- * 



