101 
the particles of magnetic bodies, &c. 
least sum in the other case. It is manifest then, that the 
introduction of the quantity e into the expression for the value 
of a, renders it essentially more accurate ; and the result of 
these different comparisons is, I think, quite decisive of the 
correctness of the formula, 
M ) 
(P + e ) 3 + £ 1 f 
a 
I have stated in my letter to Mr. Herschel,* that when a 
thick copper plate revolved under a needle, the force by 
which the plate urged the needle appeared to vary nearly as 
the inverse 4 th power of the distance, but that when magnets 
revolved horizontally under a copper disc, the force with 
which they urged it appeared to vary according to a law 
approximating rather towards that of the inverse square of 
the distance. The difference of the law in the two cases 
arose no doubt from a light copper disc having been sus- 
pended over strong bar magnets, in the second experiment, 
instead of suspending the heavy copper plate over the needle 
used in the first experiment, which could not have been con- 
veniently done, as its weight is about 16 lbs. but which would 
have reversed the experiment. To remove any doubt that 
might arise from this apparent incongruity, I determined 
now precisely to reverse the experiment in the two cases, 
making the copper ring revolve under the same magnets, over 
which it had been before suspended. As however I could 
not suspend the magnets vertically over the ring, without 
increasing so considerably the weight to be suspended, by 
the apparatus to fix them in, that the wire by which the ring 
had been suspended would no longer sustain them, and 
* Phil. Trans. 1825. 
