16 The Rey. H. Lioyp on the Determination of the Earth’s magnetic Force. 
We are justified in concluding therefore, that, in the case of small magnets, 
the ratio of the two coefficients may be inferred d@ priori, by the formula 
hA=3(2P—3l”); 
and, consequently, that the coefficient @, or 2 -, may be obtained, from the 
result of observation at a single distance, by the formula 
__ D’tan u 
2 Eee 
It follows from this, as we have seen, that when / = 1-224/', h =O, and the 
value of Q is reduced to 
Q = pD* tan wu. 
Postscript.— While the preceding pages were passing through the press, I 
received a memoir from Professor Lamont, on the determination of the earth’s 
magnetic force in absolute measure, in which the author has proposed various 
modifications in the existing method, and has considered, with great minute- 
ness of detail, the many corrections which are required in the immediate results 
of observation. Some of the conclusions of the present paper are, I find, 
thus anticipated; in particular, the form of the equation of equilibrium of the 
suspended magnet, for the case in which the axes of the two magnets are at right 
angles. Professor Lamont seems to have considered, however, that no approxi- 
mation to the law of magnetic distribution was possible ; and he has accordingly 
not thought of deducing @ priori the ratio of the coefficients of the terms in the 
above-mentioned equation (except in the imaginary case in which the whole force 
is supposed to emanate from the two ends of the bars), or, therefore, of employing 
that ratio, as is proposed in the present paper, to supersede experiment, and thus 
evade the errors resulting from the process of elimination. 
I take this opportunity of stating, that the present paper was, in substance, 
written during the last summer; and that several instruments have been con- 
structed on the principle suggested in it. The delay in laying it before the 
Academy has arisen from the desire of obtaining, previously, an experimental 
confirmation of the accuracy of the results. 
H. LL. 
