of Action between Magnets. 139 
coefficient of —3<*/r? from unity is quite negligible. The 
subsidiary terms in the coefficients of 2A?/7? and 3X”/r? are 
also very small, but might come in. At all events they 
cannot safely be assumed negligible. The terms depending 
on the angles and on z inside the bracket in the last line are 
wholly negligible, but ciearly the last line is not safely 
negligible as a whole, unless somewhat greater care is taken 
about the level of the suspended magnet than is suppesed in 
the concrete case. It is, however, mainly the fault of the 
observer if the last line is not negligible. 
Experiments on Pole-Distance. 
§ 26. Let us suppose that two magnets 1, 2, closely iden- 
tical in size and pattern, can deflect each the other in the 
same magnetometer. Let the suffix 1 distinguish the pro- 
perties of the first magnet, and let P,, Q, &c. answer to the 
case when it is the deflector ; similarly, let the suffix 2 relate 
to the second magnet. Then we have 
2r,” = one = Pi (Ay, A2) = late —f(m, dy) —AQ, = BR, 
2A" —3rAP~= P, (Ao, Ay} = Pf (de, a) —AQ,— BR, 
where f(a@,, dz) = (3/4){3(ae? + bg”) —2(a;? + b,’)}, 
1 0) 
r, and 7, being the two deflexion-distances. 
_ Differences between the values of p for the pole-distances 
of the two magnets are, as we have seen, generally much 
less effective in altering Q and R. than in altering P, and the 
contributions from @ and R in the above equations are re- 
latively small. Thus a close approximation may be expected 
from the formula 
(A? Aq”) =P,’ — f(a, Gy) — 4 Ey 7 (ayy 2) 5, « (A1) 
which neglects the difference between Q, and Q, and between 
R, and Ry». 
I have found in this way approximations to the differences 
between pole-distances in two sets of mirror magnets. The 
first set consisted of three very old magnets AN, Na, and Ne 
by Jones, practically identical in length, and differing only 
slightly in diameter. Their great similarity led one to anti- 
cipate:a very close approach to equality in their pole-dis- 
tances. This expectation was fulfilled for two of the magnets, 
but not for the third, Ne. At first I was disposed to look for 
an explanation in a difference between the directions of the 
