nv 2 = J8v*- 



24 Mr. G. F. Fitzgerald on the Mechanical 



or, turning it into the form of a series of spherical harmonics, 



+ l(c-b)(l-{J)cos2<j> 



+ 2/V 1 —fju 2 . sin <£ cos $ + 2#/a n/ 1 — y? . cos (j> 



+ 2//*\/i-//.sin<£ 



_ +«yL6 + /3\/l— ^ 2 . SHI (£ + 7 VI— /Jb 2 ' cos <p, 



from which we see that 



6 3 =2/ ; h=2g, b 5 =U. 



We may evidently include the ~ (a + b + c) in the mean value 



of NvJ, and take B =l ; so that, calling MN=p the density 

 of the gas, our pressures become 



P*»= 3 K L 1 + 15 ( a ~ 2 ^ + C v] ? 



P ^= 3P v o[!+ X5 (&- 2 ( c + a ))]> 



P« = g K L 1 + J5 ( c ~ 2 ( a + 6 ))]> 



p ^= J5K-/= P 



p =1 



Z?/) 



15 



xw; 



= P 



XZ) 



Similarly, from ?zv 3 = !Nv . -y 2 we can get 



c = 2«, c 2 =2/3, c 3 = 2y, 

 and hence 



2 2 2 



Q*=3Vo- a ; Qy=g.fy>wS-& Qr=3^K-r 



