196 



Prof. H. Lamb. 



[Mar. 24, 



77. We may regard an aspect A, B, 0, .... in the aggregate as 

 a single unit V, which may be termed a unified aspect of a, b, c, ... . 

 Section 167 is erroneous, and should be omitted. 

 I may add the following errata : — 



In Sec. 69, line 3, for " undistinguished " read " distinguished." 

 „ „ 122, „ 1, „ " aspects " „ " collections." 



„ page 43, footnote, „ " G-rassman " „ " Grrassmann." 



„ „ 56 „ „ "Pierce" „ " Peirce." 



„ Sec. 385, line 8, „ " m units " „ " r units." 



III. " On Ellipsoidal Current Sheets." By Horace Lamb, M.A., 

 F.R.S., Professor of Pure Mathematics in the Owens 

 College, Victoria University, Manchester. Received March 2, 

 1887. 



(Abstract.) 



This paper treats of the induction of electric currents in an 

 ellipsoidal sheet of conducting matter whose conductivity per unit 

 area varies as the perpendicular from the centre on the tangent 

 plane, or (say) in a thin shell of uniform material bounded by similar 

 and coaxial ellipsoids. The method followed is to determine in the first 

 instance the normal types of free currents. In any normal type the 

 currents decay according to the law e~ tlr ; the time-constant t may be 

 conveniently called the " modulus of decay," or the " persistency " of 

 the type. 



When the normal types and their persistencies have been fonnd, it 

 is an easy matter to find the currents induced by given varying 

 electromotive forces, assuming these to be resolved by Fourier's 

 theorem, as regards the time, into a series of simple harmonic terms. 

 Supposing then that we have an external magnetic system whose 

 potential varies as we can determine a fictitious distribution of 

 current over the shell, which shall produce the same field in the 

 interior. If denote the current-function for that part of this 

 distribution which is of any specified normal type, that of the 

 induced currents of this type, it is shown that 



where t is the corresponding persistency of free currents. When 

 is very great this becomes 



0= -0, 



in accordance with a well-known principle. 



This method can be applied to find the currents induced by rota-- 



