26 Prof. R. Clausius on the Theorem of the Mean Ergal, 



changed when heated in a bath of melted silver. These limits, 

 although considerably wide apart, are interesting as giving a 

 possible clue to the temperature at which anthracitic metamor- 

 phism of coals has been effected in different districts. Mr. W. C. 

 Roberts has recently shown that the alloys of silver and copper 

 have very definite melting-points ; it will be possible therefore 

 to determine more nearly the lowest temperature necessary to 

 produce the change. 



In the South Wales anthracite district it is well known that 

 no great amount of disturbance has taken place in the position 

 of the coal-seams, while in North America and Peru the change 

 has been accompanied with much more violent action, as evi- 

 denced by the greater disturbance of the rocks ; and probably a 

 correspondingly higher degree of heat was developed in the mass. 

 The evidence afforded by the coals that have been actually altered 

 by intruded rocks, and must have been highly heated, appears to 

 bear out this view. On the other hand, long-continued exposure 

 to a lower temperature might possibly produce the same effect, 

 and further experiments upon this point would be desirable. 



VI. On the Theorem of the Mean Ergal, and its Application to 

 the Molecular Motions of Gases. By R. Clausius*. 



§ 1. IN a memoir published in 1870f, for the elucidation of 

 JL the second proposition of the mechanical theory of 

 heat, I employed an equation which referred to a motion of a 

 material point in a closed path ; and in one which appeared in 

 1873 J, I advanced an equation of greater generality, expressing 

 a new and, as I believe, more fruitful proposition in relation to 

 stationary motions. 



Given any system whatever of material points which, under 

 the influence of forces that possess a force-function or ergal, 

 move in a stationary manner. In order to determine the posi- 

 tion taken by the points at the time t, rectangular coordinates, 

 or polar coordinates, or other suitable quantities can be employed. 

 We will admit universally for this purpose the introduction of 

 arbitrary variables, which may be denoted by q v q 2 , . . . q n . Then 

 the ergal U is also to be considered as a function of these vari- 

 ables. Further, according to Lagrange, the vis viva T of the 



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

 having been read at the Meeting of the Niederrheinische Gesellschaft fur 

 Natur- uiid Heilkunde on November 9, 1874. 



t Sitzungsber. der Niederrhein. GeseMsch. fur Nat. und Heilk. 18/0, 

 p. 167; Pogg. Ann. vol. cxlii. p. 433; Phil. Mag. S. 4. vol. xlii. p. 161. 



% Sitzungsber. fyc. 1873, p. 137; Pogg. Ami. yol cl. p. 106; Phil. Mag. 

 S. 4. vol. xlvi. pp. 236, 266. 



