ELECTRO-CHEMICAL EQUIVALENT OF SILVER, 
413 
wire stretches very appreciably under the tension necessary for winding a coil 
satisfactorily. It is possible that the difficulty might be satisfactorily met by an 
electrical determination of the area of the windings after the method given by 
Maxwell,* or that employed in the present investigation. 
§ 4. In the researches of Joule and Cazin the electromagnetic action is a simple 
attraction or repulsion, and can be evaluated directly by balancing it against known 
weights. This method has been followed by Mascart in his recent important work 
upon this subject.! A long solenoid is suspended vertically in the balance, and is 
acted upon by a flat coaxal coil of much larger radius, whose mean plane coincides 
with that of the lower extremity of the solenoid. If the solenoid is uniformly wound, 
it is equivalent to a simple magnet, whose poles are condensed at the terminal faces. 
The electromagnetic action then depends upon (M — M 0 ), where M is the coefficient 
of mutual induction between the fixed coil and the lowest winding of the solenoid, 
and M 0 the corresponding, much smaller, quantity for the uppermost winding. 
This arrangement, though simple in conception, does not appear to us to be the one 
best adapted to secure precise results. It is evident that a large part of the solenoid 
is really ineffective ; those turns which lie nearly in the plane of the flat coil being but 
little attracted, as well as those which lie towards the further extremity. The result 
calculated from the total length of wire (even if this could be trusted), the length of 
the solenoid, and the number of turns, has an appearance of accuracy which is illusory, 
unless it can be assumed that the distribution of the wire over the length is strictly 
uniform. In order to save weight, it would appear that all the turns of the suspended 
coil should operate as much as possible, that is, that the suspended coil should be 
compact and should be placed in the position of maximum effect.| 
§ 5 . Neglecting for the time the small corrections of the second order rendered 
necessary by the sensible dimensions of the sections, let us consider the attraction 
between two coaxal coils of mean radii A and a, situated at distance x. If M be the 
coefficient of mutual induction for the central turns, n, n, the number of windings in 
the two coils, i the current which passes through both, the attraction is 
. 0 dM 
nn i* — 
ax 
In this expression i 2 is already of the dimensions of a force, and M is linear. 
Accordingly clM/dx, though a function of A, a, and x, is itself a pure number, and 
independent of the absolute dimensions of the system. Its value is a question only of 
the ratios a/ A, x/A. If we write dM/dx=Trf(A, a, x), and consider the variation of/ as 
a function of the three linear quantities, the coefficients in the equation 
* ‘Electricity,’ § 754. McKichan, PliiL Trans., 1873, p. 425. See also Kohlkausch, Wied. Ann,, 
Bel. xviii., 1883. 
f ‘ Journal de Physique,’ March, 1882. 
+ BA Report, 1882, p. 445. 
