Bnnsen and Roscoe's Pendulum Actinometer. 459 

 0, e, 1] wj + [>, e, 2> a + . . . [>, <?, 21] u 2l = (a?, e), 



[*,/. i>i + [*,/, 2> 2 + . . . [*,/, 2i]t*i= (*,/), 



[>,y, 1]«! + [>,^,2> 2 + ... 0,#,21]r 21 = O,y), 

 [>, a, 1] i\ + [>, a, 2] v 2 + ... [a-, a, 21] w 8l = (#, a ), 

 [*, b, 1] Wl + [>, 6. 2] r 2 + . . . [>, 6, 21] t> 81 = (*, 6), 

 [x, c, 1] i?! + l>, c, 2] r 2 + . . . [>, c, 2 1] v 21 = (a, c) , 

 [*, t, l]r x + [*, *, 2> 3 + . . . [*, t, 21]r 2l =0», *)i 

 etc., &c, &c, with ?/ and 2 instead of x. 



In these equations v l5 v 9 , . . . t? gl denote the volta-electric 

 differences from copper which must he given to part 1, 

 part 2, . . . part 21 of the surface of the molecule in order that 

 the 21 piezo-electric and pyro-electric coefficients may have 

 their given values (#, e), (««,/) . . .(z,i) ; the meaning of 

 these coefficients being explained by the following three 

 equations :— 



X = (x,e)e + (*,/) /+ (x,g)g + (x, a)a+ (x, b)b + (x, c)c+ {x, t)t, 



Y={y,e)e+ +(y,t)U 



Z = {z,e)e + +{z,t)t, 



where X, Y, Z denote the components of the electric moment 

 per unit of volume, produced in the crystal by geometrical 

 change, and change of temperature (e,f,g,a,b,c,t). Thus, 

 the volta-electric difference of zinc from copper being taken 

 as unity, the 21 volta-differences from copper, of parts 1 to 

 21 of the surface of each molecule, are determined by 21 

 linear equations. 



§ 15. Thus we have, in idea, constructed a model for the 

 piezo-electric and pyro-electric quality of a crystal in which 

 each one of the 21 piezo-electric and pyro-electric coefficients 

 has an arbitrarily given value. 



XL VII. A Modified Form of Bunsen and Roscoe's Pendulum 

 Actinometer. By Dr. A. Richardson and Mr. J. Quick *. 



IN Bunsen and Roscoe's pendulum actinometer (Proc. 

 Royal Soc. 1862, p. 139), the time is measured in which 

 a given intensity of light will produce a degree of darken- 

 ing on sensitized paper equal in shade to a standard tint. 



Without going into details, the apparatus may be briefly 



described as follows : — The oscillations of a pendulum cause 



an attached sliding shutter to pass backwards and forwards 



over a slit, in the direction of its longer axis, beneath which 



* Communicated by the Authors. 



