Elasticity of a Crystal according to Boscovich. 415 



original description of his discovery of the magnetic polariza- 

 tion contains ample warning. 



§ 3. These questions, however, of chirality and magnetic 

 rotation do not belong to my present subject, which is merely 

 the forcive * required to keep a crystal homogeneously strained 

 to any infinitesimal extent from the condition in which it rests 

 when no force acts upon it from without. In the elements of 

 the mathematical theory of elasticity f we find that this 

 forcive constitutes what is called a homogeneous stress, and 

 is specified completely by six generalized force-components, 

 Pi, P2, i? 3 , . . . , Pei which are related to six corresponding 

 generalized components of strain, s 1? s 2 , s 3 , . . . , s 6 , by the 

 following formulas : — 



to = i(p l s 1 -\-p 2 s 2 + ...+p 6 s 6 ) .... (1), 

 where w denotes the work required per unit volume to alter 

 any portion of the crystal from its natural unstressed and 

 unstrained condition to any condition of infinitesimal homo- 

 geneous stress or strain : 



dw dw 



where — , . . . , -7- denote differential coefficients on the 



d_ d_ 



dsi '"' ds e 



supposition that w is expressed as a homogeneous quadratic 

 function of s l9 . . . , s 6 : 



s ^r P r-" H = w, (3) - 



where -7- , . . . , -j— denote differential coefficients on the 

 dpi dpe 



supposition that w is expressed as a homogeneous quadratic 

 function of p ly . . . , p$. 



§ 4. Each crystalline molecule in reality certainly expe- 

 riences forcive from some of its nearest neighbours on two 

 sides, and probably also from next nearest neighbours and 

 others. Whatever the mutual forcive between two mutually 

 acting crystalline molecules is in reality, and however it is 

 produced, whether by continuous pressure in some medium 

 or by action at a distance, we may ideally reduce it, according 

 to elementary statical principles, to two forces, or to one single 

 force and a couple in a plane perpendicular to that force. 

 Boscovich's theory, a purely mathematical idealism, makes each 

 crystalline molecule a single point, or a group of points, and 

 assumes that there is a mutual force between each point of 

 one crystalline molecule and each point of neighbouring 



* This is a word introduced by my brother, the late Professor James 

 Thomson, to designate any system of forces. 



t Phil. Trans. April 24, 1856 ; reprinted in vol. iii. < Math, and Phys. 

 Papers, Sir W. Thomson/ pp. 84-112. 



