118 
M?'. Christie 07i the mutual action of 
M Y 
*+ ’ 
obtained from the experiments. 
It appears from the experiments (Tables II. and III.) that 
is very nearly -15, and r is nearly 5-5, or r® nearly 50: so 
that putting 2 r" (1 — cos. ^) = e^, we have cos. = *9975, 
and 4^ 1= 4° 3'. In the extreme case, in the experiments in 
Table I. the distance from the upper surface of the magnets 
to the middle horizontal section of the ring is 2*5 inches, and 
therefore, from the value afterwards deduced for p, d = 6 
nearly, which is less than i r; but supposing c' = ^r, and 
taking only the first two terms, the expression for the force 
will be 
16 M = 
f-i- 
^ I'040^ 
-^1 
Here, without even taking into consideration the diminution 
of the second term by those multiplied by the error 
arising from the omission of this term in the expression for 
the force, will not in this, an extreme case, amount to ~ of 
the whole. 
We have obtained the expression for the force with which 
the magnets urge the ring, on the supposition that the mag¬ 
nets revolve with the same uniform velocity in all cases, 
considering that velocity as the unit of velocity ; but it is 
evident that for any other velocity, this expression must be 
multiplied by the velocity. As the value of 4 / will also de¬ 
pend upon the velocity, this value may be so considerably 
increased, that the first term will no longer give an approxi¬ 
mate value of the force. Beyond a certain velocity, the value 
of 4/ may increase with the velocity, and we may even con¬ 
ceive the velocity to be so far increased, that 4^ becoming ^ tt. 
