307 
2. If lis small with regard to a (liquids and solid bodies), then 
12a, z-O may be put, and (4) holds therefore again, in which 
now, however, P,, P,, ete. approach according to (3) to the following 
values : *) 
1 1 1 0,1637 0,6548 
BS = — | eae fence 2 
a a 
Rowe ae 8 
Pp b/f Aa eg 1 0,1710 ge 1,3680 
=S toa” 5) hae. ba RESTS kad (° 
1/1103 1 0,1560 1,8718 
REDT fg Bates paws EP Th 19 p05 
a’ \ 11664 128 a’ a’ 
so that now F’: e? will approach 
F 0,655 at as 
ee eT LOS ed lee ld bate ay 
e? a’ a’ af 
It is self-evident that this expansion into series is now only valid 
for small values of « with respect to a. For x= +a of course #' 
becomes = + o. I will just point out here, that when in w=a sin p 
means are taken over all values of p between O and 2x, according 
to (2) and (4) the total force would become —= 0 only at z= 0. 
But when z is not =O, hence when JM is no longer halfway 
between P and Q, this is evidently no longer the case (even powers 
of x). And according to the above separate expressions of PF, and 
F, they do not become =O at z=O even when averaged. The 
separate forces “averaged” with respect to xz, and also the mean 
total force will always be repulsive (excepted at z = 0 in the last case), 
because the terms with even powers of z have all of them the — sign. *) 
And this refutes Drpir’s assertion (see § 8), that without special 
suppositions (polarisation of the molecules in each other’s electric 
field) the resulting action would always be =O according to a 
well-known electric theorem. It is possible to verify by calculation 
that this is also true for the problem in three-dimensional space. 
1) For the quantities cj, @3, etc. in (4a) the values 9, = Zen 0,6548 = 1,7459; 
12 
d= a X 1,3680 = 2,9184; 9, = = X 1,8718 = 5,7045; etc. are easily found. 
4) ie has of course vases to do with the question of the Vzrzal of 
attraction and repulsion, as in the calculation of gg the (a -average plays 
a part. Indeed, in the equation of state for cin ee aly also the 
aT Le RT 
Virial of repulsion b/v predominates at high temperatures. This question must 
afterwards be treated separately. 
