ELECTRO-CHEMICAL EQUIVALENT OF SILVER, 
425 
We have now to deduce the ratio of mean radii. For the ebonite coil the correcting 
factor is 
h'~ k' 2 
1 +i—~ l —= 1 -f '000741 --002269. 
cr * a 2 
For the dynamometer coil 
+-000225--000457. 
Thus 
A 
= fff X 2-60070 X 1 -001296 = 2-42113 ; 
and from this when A is known the value of a can be deduced (§ 13). 
Calculation of attraction. 
§ 15. The attraction between two coaxal circular currents of strength unitv, of 
which the radii are A, a, and distance of planes is B, is (Maxwell, § 701) 
7tB sin 7, 
\/(A«) c 
2F y -(l + 
sec 3 y)E y } 
( 1 ). 
where F y and E y denote the complete elliptic integrals of the first and second kind 
whose modulus is sin y. The value of sin y itself is 
sin y— 
2 y/(A a) 
\/{(AT «) 2 + B 2 } 
( 2 ). 
The functions F y and E y were tabulated by Legendre. In an Appendix (p. 455) will 
be found a table of 
sin y {2F y —(1+sec 3 y)E y }.. (3), 
calculated with seven figure logarithms from those of Legendre for the purpose of the 
present and similar investigations. It has been carefully checked, and it is hoped is 
free from error, except of course in the last place. 
The value of (1), with omission of the factor 7 r, is denoted by f( A, a, B), and, as has 
already been explained, it is a function of no dimensions. To calculate it for the 
central windings of the fixed and suspended coils, we have first to find y from (2). 
With the data already given y=58° 57y-f§ whence with use of the table 
/(A, a, B) = l*044576. 
This multiplied by 77, by the product of the numbers of terms in the two coils, and by 
the square of the strength of the current, gives very nearly the force of attraction, but 
MDCCCLXXXIV. 2 1 
