Law of Molecular Force-, 115 



terms sensible and insensible, the only method of removing 

 which is to stipulate that the law of force is to be such that if 

 the actions between molecules in an experimental body farther 

 apart than a certain distance L are taken account of, they 

 will contribute to the quantity whose amount is to be investi- 

 gated a portion negligible in comparison with the portion 

 contributed by the actions between molecules at a distance 

 apart less than L. 



But although this is the only stipulation to begin with, the 

 above triple integral involves important tacit assumptions. 

 The use of infinite upper limits in an expression to be applied 

 to finite bodies involves nothing really objectionable ; they 

 merely express loosely in a symbolical form the above con- 

 dition, that actions at sensible distances are insensible ; but 

 when we come to examine the meaning of the lower limit 

 in the last integration, it is quite otherwise; two fundamentally 

 important assumptions are involved. It must be remem- 

 bered that the triple integral is intended to replace a double 

 sum 2j* 2 X mM/(r) cos 0, w 7 hichis the true expression for the 

 resultant attraction of the liquid mass on the column, m being 

 the mass of any molecule of the column, M of any molecule of 

 the liquid mass, r the distance betw r een m and M, and 6 the 

 angle which r makes with the axis of the column, n the num- 

 ber of molecules in the column, and N the number in the 

 liquid mass. Comparing the sum with the integral, we see 

 that the assumption is made that the discontinuous molecules 

 may be imagined to be spread out into continuous matter, and 

 that the base of the continuous column may be considered to 

 be in actual contact with the continuous liquid mass, no 

 matter what w 7 as the original distance of the bottom layer of 

 molecules of the column from the top layer of the liquid mass. 

 We might allow 7 the same latitude to the meaning of as we 

 have to go and take it as meaning some small limit ; but we 

 are not entitled to assume that this small limit is fixed and 

 independent of the original distance that separates a molecule 

 and its neighbours before the imaginary continuous distribu- 

 tion was made. Thus, while the adoption of a fixed upper 

 limit in the integrations, independent of the distance between 

 a molecule and its neighbours, is only in strict accordance 

 with the first express stipulation, the fixing of the lower limit 

 of the last integration as independent of that distance is an 

 additional condition of the first importance. Of course, within 

 such range of values as experiments permit, the integral may 

 be independent of variations in the true small lower limit; but 

 the fact must not be lost sight of that, when we assume this to 

 be the case, we are tacitly stipulating for another special 

 property for the unknown function/. 



12 



