524 Mr. 0. J. Lodge on a Mechanical Illustration 



This at once suggests the proper mode of enunciating (1) so 

 as to include this case ; viz. the theorem is: — 

 If 



_ cf){.v + n^/(a 1 a 2 ...a n )} ■ 



c/Ovs-or 1 ) ' 



then 



oV l v _ d n v 



dx n da 1 da 2 . . . da n 



which is evidently true, and gives (1) if the arbitrary sign <f> 

 be replaced by exp ; (2) is of course a very special case. 



If the theorem in the September Number be similarly ex- 

 tended, it takes the form : — 



If 



v= </){^ + 2 2 ( 1 -2^ v / an , i/a n _ 1 .ya n _ 2 ...ya 1 .^a } 



then 



V(a 1 a 2 a 3 ... a n ) 



cf 

 do* 



v --(A\(A\(iy(±\ (A.Y' 1 



2 " " \daj \claj \da 2 ) \daj '" \da»J V ' 



I may here mention two errata in my previous note ; viz. in 

 p. 208, equation (3), and p. 209, line 2, the exponents of -= — 



should be 2 n_1 i and T~ l respectively instead of 2 n i and 2 n . 

 Cambridge, October 25, 1876. 



LXIY. On a Mechanical Illustration of Thermo-electric Phe- 

 nomena. By Oliver J. Lodge, B.Sc* 



THE publication of the following speculation requires an 

 apology. It is in continuation of a paper on a Mechanical 

 Illustration of Electric Induction and Conduction, published in 

 the November Number of the ' Philosophical Magazine ;' and the 

 sections are numbered on continuously with those in that paper ; 

 but whereas the mechanical analogies suggested in the former 

 part of the paper are useful as mere analogies even if they do not 

 (as I believe they do) throw some light on the actual molecular 

 processes, the present portion contains nothing of sufficient 

 mechanical simplicity to be of much sendee as mere illustra- 

 tion, and it therefore has little value unless the imaginary me- 

 chanical actions are really analogous to those which actually 

 do produce thermo-electric currents. I have accordingly laid 



* Communicated by the Physical Society. 



