of Action between Magnets. 115 
If we were to work out a value for m/H from (4), em- 
ploying values actually found for W,, W., and Ws; on an 
individual occasion, slight errors in these values might pro- 
duce undesirably large errors in the result. The above 
method, in short, though theoretically perfect, cannot be re- 
commended for the separate treatment of individual day’s 
observations. Let us suppose, however, that a large number 
of observations have been made at one station, with an in- 
strument whose magnets may be regarded as of constant 
moment, and that the mean values of the W’s so observed 
are denoted by Wy, W2, and W;. Let us put 
A,W,+A,W,+A;W;=N, ; (6) 
Ad = N/3W,, Ao 7 N/3W2, A; ae N/3 Ws. 
If now W,, W., W; refer to any individual set of obser- 
vations, 
(m/H),= 3A,W), 
(m/H),=3A, Wo, 
(m/H.)3= 3A,W; 
are three values for m/H given by the deflexions at the three 
distances 7), 72, 73, after applying a correction for P and Q 
based on the whole series of observations, and 
m/H = A,W,+ A,W,+A,;W; ou. 5S. PRES. ue (7) 
the arithmetic mean of the three values may be accepted. 
If the coefficient R in (1) also required to be taken into 
account, a similar procedure would apply, observations being 
taken at four instead of three distances. 
§ 3. There is always a certain advantage in observing at 
two distances, as this leads to the detection of errors of 
setting and reading which otherwise might escape notice. 
But observations at a third distance, whilst adding materially 
to the labour, provide little additional security against obser- 
vational errors. It is thus desirable to consider whether it 
is really necessary always to observe at three distances when 
Q requires to be allowed for. Obviously this is not necessary 
if the magnets and the apparatus employed remain in an 
absolutely constant state, for then P and Q and Aj, A,, A; 
are absolute constants, and once determined remain available 
for all future use. It is also conceivable that whilst changes 
in P may be sufficiently large to be taken into account, there 
is no such necessity in the case of Q, in which event observa- 
tions at two distances might suffice. 
12 
