23* MAXWELL'S LAW 401 



suspicion, as in the deduction of the formulas for composite mole- 

 cules the theorem of the conservation of areas, which was applied 

 to the case of simple molecules in 17*, was not regarded. I will 

 therefore take this theorem into account by way of supplement. 



According to this theorem the following equations hold for 

 molecules whose mass m is made up of atoms of mass m, viz. 



d = SS.m \(y + \))(w + ) (z + j)(v + t>)} 

 c 2 = 2S.m {(z + &)( + u) (x + y)(w + )} 

 c 3 = Z8.m{(aj + jr)(t> + a) - (y + \))(u + u)}, 



where c 1} c 2 , C 3 are constants, and the summation S is extended 

 over all the atoms of a molecule, while the summation 2 embraces 

 all the molecules of the whole gas ; further, by x, y, z the coordinates 

 of the centroid of a molecule are denoted, and r, p, j are the co- 

 ordinates of an atom referred to this centroid as origin. Hence we 

 have the equations 



S.m = 0, S.mp = 0, S.mj = 0, 

 and, since we have also 



S.mu = 0, S.nn> = 0, S.mw = 0, 

 S.m = m, 



the equations first given reduce to 



zv) + 2S.m(wtt> $t>) 



xw) + SS.m($u rn>) 



yu) + SS.m(xt) pu). 



The two parts into which each sum in this way breaks up are 

 independent of each other. For the second parts, which have 

 still remained double summations, depend only on the position 

 and motion of the atoms inside the molecule, and cannot alter 

 with the velocity and position of the centroid of the molecule, 

 that is, with u, v, w or x, y, z. If, for instance, to the gas as a 

 whole a constant velocity u were given in the direction of the 

 #-axis, or if it were displaced in this direction by a constant 

 amount x, such an alteration would be without effect on the pro- 

 cesses occurring inside the molecules. Hence it follows that the 

 three equations can only be satisfied if each of the six magnitudes 



zv) 2 S. 



D D 



2.m(xv yu) SS.m() 



possesses a value that always remains constant. 



