114 Dr. C. Chree on the Law 
temperature coefficients, r the true distance between the 
centres of the two magnets, H the horizontal component of 
the earth’s magnetic force, u the deflexion-angle, and P, Q, 
R... constants depending on the dimensions of the two 
magnets and their distribution of magnetism. 
In 1899* I pointed out that the assumption usually made 
that all the higher constants Q, R.. are negligible did not 
seem fully justified for the ordinary Kew pattern magneto- 
meter. Before investigating this point further, I shall explain 
how Horizontal Force observations may be carried out when 
Q is not negligible. 
§ 2. Let us for shortness put 
: = 
47° sin u(1— = —qt-y'e) =W, . ee 
and employ suffixes 1, 2,3 to refer to deflexions at three 
distances 71, 72, 73; then from observations at these distances 
we have 
(m/H) (1 + Pr,-? + Qr,-*) = Wj, 
(m/H)(1+ P23? + Qr.-*) = Wa, 
(m/H)(1+ Pr;-? + Qr3~ 4) = W3. 
Vv 
(3) 
The induction and temperature coefficients are supposed 
known, the angle u and the distances 7 are observed, thus the 
only unknowns in the above relations are m/H, P,and Q. Our 
primary object is to determine m/H. T'o do so, we eliminate 
P and Q in the usual way, and find 
Wr. noc 
| i Cyr Ti, 
7A GA i 9 ae) i a 
or 
m/H. = A, W, ce 5 A.W, + A;W;, . . . es (4) 
where Ay=17'(13?— 19”) 
+ { (01 —12)(%a— 13) (13— 11) (71 + 72) (72 +73) (1°3 + 7) }, (5) 
and A,, A; may be written down from symmetry. 
In reality, the distances 7,, 7, 73 vary slightly with the 
temperature; but assuming the deflexion-bar uniform, the 
distances all alter in the same proportion. Thus the co- 
efficients A, being of dimensions 0 in length, are absolutely 
independent of temperature, and once calculated cause no 
further trouble. 
* Roy. Soc. Proc. vol. Ixv. p. 411. 
ail Oe 
