A Suggested Theory of the Aluminium Anode. 301 



manner (22) must be incapable of stimulating a motion similar 

 io u = cosy. The necessary conditions are 



jj cos x { (a- — o-q) cos x + 2n cos y}dx dy — 0, 



ft* cos y {{or — o-q) cos y + "In cos x}dx dy = 0, 



the integration being taken over the whole area. On account 

 o£ the symmetry the two conditions coincide ; and it is 

 sufficient to integrate for x and y between the limits and \tt. 

 Thus 



(a- c- ).-i7r.i7r=+2»i.l.l, 

 so that 



«_,„= + J£. (23) 



Since ?z and <r are of the same dimensions, this result holds 

 good, whatever may be the side of the square. 

 ;^It may be of interest, and serve as a confirmation of the 

 above procedure, to mention that when applied to the principal 

 vibration in a rotating circular trough it gives 



<^-^=±-|^t, (24) 



where z 1 is the first root of J/ (z) = 0, equal to 1*841, so 

 that 



^-^= ± ik (25) 



An accordant result may be deduced from the analysis given 

 by Lamb, § 203, by putting 5 = 1, and taking account of the 

 properties of the function J : . The corresponding value of 

 f is given bv 



^^J^foOfcosfl + zsinfl}. ... .(26) 



XXIX. A Suggested Theory of the Aluminium Anode. B// 

 W. W. Taylor, M.A., D.Sc, and J. K. H. Inglis, 

 M.A., B.Sc* 



ALTHOUGH aluminium is one of the metals which de- 

 compose water, it is very slowly acted upon by dilute 

 sulphuric acid, even at moderately high temperatures. With 

 dilute hydrochloric acid the action is violent, and it is found 

 that, if a little hydrochloric acid or soluble chloride (c. g.. 

 potassium chloride) be added to dilute sulphuric acid, the action 

 is, to all appearance, as violent as with hydrochloric acid of 

 similar concentration. 



* Communicated by the Physical Society: read November 14th. 1902. 



