Hill G. GREP]NHILL ON ELECTiiOMAGNETIC INTEGRALS. 
65 
y' = COS APB, so that APB is the modular angle, 
(2) L = 7rPa6 + |-M7>, N = 7rPa{|a^ + 6-) + M (fcP— 
involving only the complete E.I. 1. 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 Avould I’equire 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 Beferences. 
ViRiAMU Jones, ‘Phil. Mag.,’ 1889 ; ‘Phil. Trans.,’ 1891 ; ‘ Boy. Soc. Proc.,’ 1897. 
G. M. Minchin, ‘Phil. Mag.,’ 1893-4. 
W. Burnside, ‘Mess, of Math.,’ 1891. 
Coleridge Farr, ‘ Boy. Soc. Proc.,’ 1898. 
Coffin, Bosa, Cohen, ‘ Bulletin of the Bureau of Standards,’ 1 906. 
Nagaoka, ‘Journal of the Tokyo College of Science,’ 1903; ‘Phil. Mag.,’ 1918. 
A. Bussell, ‘Phil. Mag.,’ 1907. 
F. E. Smith, ‘Phil. Trans.,’ A, vol. 214, 1914. 
S. Butterworth, ‘Phil. Mag.,’ 1915. 
lEB 
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