12 
ME. J. E. H. GrOEDON ON THE DETEEMINATION OE 
dco' 
A =irc 2 . 
The force exercised when the strength of the current is C is of course C 
we may write 
-p ^ W /, , 9_£ 2 _j_75 P-4- ^ 
^o— *7“ ? ,2 + r 28 - J.4T---J) • * • 
Then 
(14) 
where F 0 is the force on a unit pole due to a unit current. 
But the small dynamometer consists of windings all of the same diameter, and 
approximately all in one plane, and therefore this expression is so nearly true that it 
may he used for it. When thus used it will be distinguished by dashes on the letters. 
The second and third terms are required because in the experiments the small dyna- 
mometer is placed very close to the suspended magnet. 
The effect of the helix may be got by a much simpler method (see Maxwell, Art. 676). 
Let 2 1 be the length of the helix, c its mean radius, then the outside effect at the 
distance of (say) a metre or more is that of a disc of (-j-) magnetism at one end and of 
( — ) magnetism at the other. 
For unit current the moment of the magnet is 5(A) ; hence its strength is which 
is the quantity of magnetism at each end. 
Then the value of the potential will be ( — — - ) , and the value of the force at 
2^ vi r J 
» „ 2(A) 2 l 2A 
O will be ± 0 =-gj-.^.-=-^3- per unit current. 
Thus the force — F' exerted by the dynamometer is 
— F= 
C'mXjAy 
while F, that exerted by the helix, is 
„ CS(A)m 
F=— 
(15) 
(16) 
But in my experiments C= — C'; and when we have no action on the magnet at O, 
we have 
F=— F. 
Adding the two expressions we have 
( 17 ) 
Now let r, i* be the values of r for the helix and small dynamometer respectively, we 
have, when the force on the suspended magnet is zero, 
F=(82 - 8”+ & 2 )£, where 2^=26-34 centims., 
and 
r 3 =log _1 5-7703411. 
