THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



JULY 1874. 



I. On different Forms of the Virial. By R. Clausius*. 



MY theorem of the virial has already given rise to some 

 discussions on the forms which the virial can assume. 

 I myself, in my first memoir relative to itf, indicated that when 

 the movable points partly exert forces upon one another, and 

 partly are acted on by forces from without, the virial can be 

 analyzed into an internal and an external, and gave their forms 

 for certain frequently occurring cases. Yvon Villareeau subse- 

 quently {Comptes RenduSj vol. Ixxv.) effected other transforma- 

 tions of the equation relating to it, especially by resolving the 

 total motion of the system of material points into the motion of 

 the centre of gravity and the relative motions of the individual 

 points about the centre of gravity, and referring the equation to 

 each of these two constituents singly. Prompted by this, in a 

 note published in the same volume of the Comptes Rendiis I 

 added a series of further transformations. As, however, in that 

 brief note results only, without demonstrations, could be com- 

 municated, and those but imperfectly, a more connected treat- 

 ment of a subject so important in itself will not be void of 

 interest. 



1. The simplest form of the equation in question is the fol- 

 lowing. If m denotes the mass of a material point which is hi 

 stationary motion together with other material points, x, y, s 

 its rectangular coordinates at the time t, and X, Y, Z the com- 



* Translated from a separate impression, communicated by the Author, 

 from Pbggendorff's Annalen, Jubelband, p. 411. 



t Berichte der Niederrhein. Gesellsch. filr Natur- u. Heilkunde, June 

 18/0; Phil. Mag. S. 4. vol. xl. p. 122 ; Pog<?. Ann. vol. cxli. p. 124. 



Phil. May. S. 4. Vol. 48. No. 315. July 187 1. 1 



