SIR G. GREENHILL ON ELECTROMAGNETIC INTEGRALS. 65 



y' = cos APB, so that APB is the modular angle, 

 (2) L = TrPab + ^Mb, N = xPad^ + ^ + M (fa 2 -^), 



involving only the complete E.I. I. and II., given in LEGENDRE'S tables with extreme 

 accuracy, it would appear to be of practical advantage to make all the helical coils 

 of the same diameter. 



This would prevent one coil from going- inside another, and they would require to 

 be opposed in axial prolongation, as in the Lorenz apparatus at Teddington, described 

 in ' Phil. Trans.,' 1913, by F. E. SMITH. 



Here is a question to be decided by practical experience as to the advantage or 

 defects of this suggestion. 



The current weigher is designed for legal commercial use, in the definition of the 

 electrical units in an Act of Parliament, and these require to be measured to as many 

 significant figures as possible, warranted by the most careful measurement of skilled 

 observers. 



The legal definition must be specified with the same precision of language as we 

 find in the Act of Parliament on Weights and Measures, defining the standard 

 pound and yard, the length of the seconds pendulum with a view of checking and 

 preserving the standard, the volume of the gallon in cubic inches, and other standards 

 of measure in civilised life. 



LIST OF REFERENCES. 



VIRIAMU JONES, 'Phil. Mag.,' 1889 ; 'Phil. Trans.,' 1891 ; ' Roy. Soc. Proc.,' 1897. 



G. M. MINCHIN, 'Phil. Mag.,' 1893-4. 



W. BTJRNSIDE, 'Mess, of Math.,' 1891. 



COLERIDGE FARR, 'Roy. Soc. Proc.,' 1898. 



COFFIN, ROSA, COHEN, 'Bulletin of the Bureau of Standards,' 1906. 



NAGAOKA, 'Journal of the Tokyo College of Science,' 1903; ' Phil. Mag.,' 1918. 



A. RUSSELL, 'Phil. Mag.,' 1907. 



F. E. SMITH, 'Phil. Trans.,' A, vol. 214, 1914. 



S. BUTTERWORTH, 'Phil. Mag.,' 1915. 



