80 Dr. W. F. G. Swann on 



of cylinders under internal pressure point out what the 

 genera] nature of the conditions musi be. Anv entirely 

 general criterion of rapture must demand, among other 

 things, that there be a free space to contain the fragments 



when rupture occurs, and must also demand that the nature 

 of the rupture be such as to relieve tli" applied stresses. 



The Jefferson Physical Laboratory, 



Harvard University, 



Cambridge, Mass., U.S.A. 



VI. The Earth's Magnetic Field 1 ". B>, W. F. Gh Swans. 

 J).Sc, A.R.C.S., Assistant Lecturer in Physics at the 



University of Sheffield^. 



A 



LARGE amount of work relating to the earth's mas- 

 netic field has been done by Prof. Schuster, who by a 

 critical analysis of its form has deduced several important facts 

 with regard to its cause and variations. The present paper, 

 while not definitely formulating- a theory to account for the 

 field, comprises a discussion as to the possibility of its expla- 

 nation, as a phenomenon arising out of the rotation of the 

 earth. Tn order not to encumber the paper with mathe- 

 matical analysis, such work whenever possible has been 

 relegated to an appendix, the results of the analysis only 

 being quoted in the paper. 



The first idea that suggests itself is that of the rotation of 

 a surface charge, but the horizontal magnetic field at the 

 equator of a sphere of radius a, rotating with angular velocity 

 o>, and charged to a potential V is (see appendix. Problem 1 ) 



Vco 



-7?-, a result depending only on the angular velocity, and 



independent of the size of the sphere, for a given potential. 



A more hopeful l>a>is is to be found in the view, that each 

 volume (dement of the earth contributes a portion to the 

 field, as a result of its rotation. In this case, the fact that 

 the volume of the earth depends on the cube of it- linear 

 dimensions insures that a very small contribution by each 

 cubic centimetre of matter shall give rise to an appreciable 



effect »>n the earth's surface, in spite o\' a possible variation 



* While tin' present paper was being written a note came into my 

 hands of ;> presidential address recently given by Professor Sehuster 



before tin' Physical Society oJ London, ami judging from that note, it is 



ile that, the grounds covered in the address and in the present 

 paper maj to some extenl overlap. 

 t Communicated by the Author. 



