406 Professors Perry and Ayrton on a new 



and 



dV 



Tri is the force directed towards the north, 



du 



dV . 

 — -J- is the force directed downwards towards the earth's 



dr centre ; 



therefore, if I be the magnetic intensity, 



*-o*m 



M 2 sin 2 fl , 4M 2 cos 2 fl 



4. "T ft < 



or, putting r equal to unity (that is, for a point on the earth's 

 surface), 



I=M v / l + 3cos 2 ^ 



= 1*1^1 + 3 sin 2 X, 



which is Biot's expression. 



ISTow this is a result which could not have been anticipated, 

 and speaks well for our new theory of terrestrial magnetism. 



It is well known that many forms of distribution of iron 

 inside the earth may be found which, with the existing poten- 

 tial given above, will produce Gauss's distribution of potential 

 over the surface of the earth ; and it would be very interesting 

 to try how close an approximation to the real potential would 

 be obtained by considering the iron of the earth to form a 

 hollow ellipsoid, one of its principal axes coinciding nearly, 

 but not quite, with the earth's axis. This calculation would 

 be comparatively easy ; but we prefer at present merely con- 

 fining ourselves to simple illustrations of our theory. 



Thus, let us, for simplicity, assume that the magnetic matter 

 of the earth is iron, with everywhere a coefficient of magneti- 

 zation 



*=30*; 



then the terms involving « 2 will be large compared with the 

 others ; so that if, for a very rough approximation, we assume 

 aj to be nought, and a 2 equal to unity, or the whole earth to 

 consist of iron, we find 



Tr 16tt cos 



* k for ordinary iron is probably between 20 and 30 ; and in our igno- 

 rance of the internal state of the earth, or what effect the great heat or 

 pressure may have on the coefficient of magnetization, we are compelled 

 to use this value ; but it is possible, of course, that the real value of k 

 may be very different. 



