TRANSACTIONS OF SECTION A. 473 



For copper r — 1640, so that 



L a' 

 r = — - = -r— r— ■ on the C. G. S. system. 

 E 1810 ■' 



In the case of a shilling the time-constant can scarcely be so high as a ten- 

 thousandth of a second, but periods smaller than this may be concerned when a 

 microphone clock is employed. 



For similar discs or coins the time-constant varies as a^ r~ *, a being the linear 



dimension and /• the specific resistance. Equal coins cannot in general be balanced 



if the specific resistances are difierent. To obtain a balance, a~ should vary as r. 



In this case 



M,. M„„ . a^ . a» . 



■ • \, -^ - varies as , vanes as — varies as a, 



m M^^ +Ii r a- r 



on the supposition that the positions of the coins relatively to the primary and 

 secondary coils are the same. 



A perfect balance is not to be expected in general without two adjustments, 

 though in some cases a fair approximation may be obtained with the sliding 

 wedge employed by Hughes. 



If the condition of equality of time-constants be satisfied, the remaining condition 

 is independent of the value of n, so that a perfect balance for one pitch secures a 

 perfect balance for all pitches. From this it follows that the results are not 

 limited to simple tones, and that the two conditions are sufficient to secure a 

 balance in all cases. It should be remembered, however, that this indifference to 

 pitch does not apply to approximate balances, which may be satisfactory with one 

 sound, but quite inadequate when another is substituted. 



SATURDAY, AUGUST 28. 



The following Reports and Papers were read : — 



1. Beport of the Committee on Mathematical Tables. 

 See Reports, p. 30. 



2. Report of the Committee appointed to calculate Tables of the Funda- 

 mental Invariants of Algebraic Forms. — See Reports, p. 38. 



Report on the present state of hnoxvledge of the application of Quadratures 

 and Interpolations to Actual Data. By C. W. Merrifield, F.B.8. 

 See Reports, p. 321. 



4. On Maximum and Mhiimum Energy in Vortex Motion. 

 By Professor Sir Willum Thomson, M.A., F.B.8. 



I. A finite volume of incompressible inviscid fluid being given, in motion, filling 

 a fixed, simply continuous, rigid boundary, the fact of its being in motion implies 

 molecular rotation, or (as it may be called for brevity) vorticity. Helmholtz's 

 law of conservation of vorticity shows that, whether the boundary be kept fixed as 

 given, or be moved or deformed in any way, and brought back to its given shape 

 and position, there remains in every portion of the fluid which had molecular 

 lotation a definite constant of vorticity ; and his formula for calculating energy for 

 any given distribution of vorticity allows us to see that the energy may be varied 

 ■fcy the supposed operation on the boundary. 



