INTENSITY OF THE EARTH'S MAGNETIC FORCE. 259 



We are therefore justified in concluding that, in the case of 

 small magnets, the ratio of the two coefficients may be inferred 

 <l priori, by the formula 



and, consequently, that the coefficient Q, or 2^-. may be obtained, 

 from the result of observation at a single distance, by the formula 

 Q m P'tanu^ 



It follows from this, as we have seen, that when t = 1-224 /, // = 0, 

 iiud the value of Q is reduced to 



Q = JD 3 tan u. 



POSTSCRIPT. While the preceding pages were passing through 

 the press, I received a memoir from Professor Lament, 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 minuteness of 

 -detail, the many corrections which are required in the immediate 

 results of observation. Some of the conclusions cf 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; and 

 the ratio of the coefficients of the terms in that formula, which 

 Professor Lamont has deduced in the case of what he calls a 

 ximple magnet, that is, the imaginary magnet in which the 

 attractive and repulsive forces are supposed to emanate solely 

 from two points or poles. The value, so inferred, he naturally 

 regarded as a mere approximation.; and he has accordingly not 

 thought of employing it, as is proposed in the present Paper, to 

 supersede experiment, and thus evade the errors resulting from 

 the process of elimination. 



