THE INTERNAL CONSTITUTION OF BODIES. 459 



•" / S — \ P„ sin r d 9' ./ -v. 



%J r Q r J 



+ r 



The functions 7"', F'^- of this ei nressiou remain arbitrary ; and, as 

 the sum oi'" an infinite number of these fund ions may be en ployed to 

 represent any lu'icf.'on v.'hai.soever, they w-'l serve as two arbitrary 

 functions which are 'o comnleLe the iotegral of the equation (I). 



When in some particu'ar cases the integrations of the preceding for- 

 mula shall have been pe<-roi'med by substiuuting its expression in the 

 equation ('-I'), the functions 1\ and V^ will be determined by com- 

 paring them with those of the same order introduced by means of the 

 different e::pressIons for G ; so that this etjuation may become identi- 

 cal. All being thus determined, the densi> q given by the formula (2) 

 will be known. 



We have hitherto left our formula in all their generality, so that one 

 may be ihe better alile to judge of the restrictions to which we shall 

 subject them while making the fii'st amplications of them. In the pre- 

 sent state of our physical knowledge, the figure of the material mole- 

 cules is totally unknown. We will therefore begin by coiisideiing the 

 most simple case, — that in wliich their form is spherical, and their den- 

 sity uniform. We will, besides, assign to these molecules a very small 

 volume, and suppose them in their state of equilibrium at a mutual di- 

 stance, which is very considerable as compared with their dimensions. 

 This manner of considering the constitution of bodies has been adopted 

 by several philosopliers as that which is most conformable to truvii, and 

 presents at the same time a considerable advantage in an analytical 

 point of view. In adopting it we shall be able, by aijprorciniation, to 

 consider the sether as if it were contiiiuonsly d-iTused in all diroetions; 

 and to disregard, in the integration of the ibrmiila (,5), the small spaces 

 occupied by the material molecules. But as, by proceeding in this man- 

 ner, we should include in the repulsion of the aether a surplus which is 

 due to the actions answering to the points of space which are really 

 occupied by the molecules, we shall compensate for this surplus b\ add- 

 ing to the action of eacli molecu'e an action equal and contrary to that 

 of a quantity of aether of the same volume as the molecule, and of the 

 same density as that which answers to the point of space which the 

 molecule occupies. This is done by substituting g m +fq for g C7 in 

 the expression for G (q representing the density which the a^her would 

 have at tlie point occupied by the molecule, and within so small a space 

 we will suppose that density constant), and l)y extending the intt grals 



Vol. I.— Part III. '2 i 



