1894.] Measurement of the Magnetic Properties of Iron. 49 



an irregular system of moving molecules (or a "disturbed gas") is 

 unaltered in form by collisions between the molecules. In the second 

 application the functions are used to find the mutual potential energy of 

 two layers of gravitating matter on two spheres, the density at any 

 point on each sphere being expressed in terms of spherical harmonics 

 referred to fixed coordinates upon it, and the spheres having any 

 position with reference to the line joining their centres. The case of 

 two ellipsoids not differing much from spheres is also worked out 

 numerically, and the stable positions discussed. A stable orbit is 

 possible with the major axes of the ellipsoids constantly in a straight 

 line. If one ellipsoid is fixed and the other projected so as to de- 

 scribe a nearly circular orbit about it, with its major axis initially 

 pointing to the centre of the other, the orbit will be possible if in 

 a plane perpendicular to the least axis of the greater, but the devia- 

 tion of the major axis of the second from the line of centres will con- 

 tain a term which to the first approximation is secular, and may 

 ultimately cause this axis to deviate from its initial position. There 

 are three stable positions for the second ellipsoid if the first ellipsoid 

 is fixed and the centre of the other fixed. These positions will iii 

 general be with the major axis of the second pointing towards the 

 centre of the first, and in a line with the major, mean, and least 

 axes of the first, but if c, the distance between the centres, is so small 

 that 



/ 9 1 1\ /1 9 n ^ ^ / 1 9 *? ^' 



- / -5 -L J-\ / 1.6 t O \ o t ~t / 1.4 I O 



Pf jr, jj- ) c < I TT, o) a i> or than I r 



n\* a.] 3 di 2 / \ai 2 ai J 0,1 / \a\ ~ aj 2 i 



rhere a^a/a/' are the least, mean, and greatest axes of the first 

 sphere, the stable positions will be different. Thus the stable positions 

 fill always be with major axis of the second in the line of centres if 

 2 /ai 2 is greater than 7/5. 



The " functions of the second kind," which are the two remaining- 

 alutions of the differential equation of the fourth order satisfied by 

 v mr , are also briefly investigated. 



[V. "On the Measurement of the Magnetic Properties of Iron.'' 

 By THOMAS GRAY, B.Sc., F.R.S.E., Professor of Dynamic- 

 Engineering, The Rose Polytechnic Institute, Terre Haute. 

 Indiana. Communicated by Lord KELVIN, P.R.S. Received 

 April 6, 1894. 



(Abstract.) 



This paper gives the results of a continuation of the investigation 

 rhich formed the subject of a paper communicated to the Royal 

 Society in 1892, and published in the 'Philosophical Transactions,' 



VOL. LVI. E 



