AS EXPLAINED BY THE HYPOTHESIS OF FINITE INTERVALS. 181 



to recur in a separate Memoir, and for that reason shall defer any fur- 

 ther consideration of the subject until then. 



Another observation that suggests itself is, that since p is a factor 

 of -, and <7 of ., the product /y is independent of e, and consequently 

 would, were the action of the particles of aether alone influential, be 

 the same for aU substances. By a reference to the numerical values 

 above given, it will appear that this only holds as a very rude approxi- 

 mation for the glasses, and altogether fails for the fluids. Thus much 

 however may be gathered from an inspection of the tables, tliat there 

 IS a tendency to verify the result, and that we should not be induced 

 to regard the effects of the material particles of such considerable mag- 

 nitude, as to vitiate the general conclusions. When, however our re 

 suits are pursued into details, the action of the material parJicles (or 

 whatever other actions we choose to consider, if these be rejected) pro 

 duces a sensible effect. For it will be observed, that all the solids 

 have / negative; whilst, on the contrary, water and solution of potash 

 make it positive. Now the distances between the particles cannot affect 

 these signs, nor can the absolute forces, as long as these forces are sup 

 posed all of the same nature. This, then, is a difficulty in our way 

 which it would be weU to remove. I cannot, however, enter into this 

 subject further than to observe, that if there were no extraneous forces 

 the quantity I would undoubtedly be positive; and that, as the action 

 of the particles on each other is attractive, an alteration in sio-n must 

 ansa from an addition of repulsive eff-ects; and that since these effects 

 are not particularly great in aff-ecting ;, and q, the function to which 

 they will give rise wiU be a series not so rapidly converging as that 

 which expresses the velocity due to the actions of the particles of aether 

 on each other. 



I ought, however, to state that it is not impossible that this effect 

 would have been explained, had we taken into account the terms in 

 the expansion of {r + p).(p{r + p), &c. to the third order. This expla- 

 nation I have not been able to succeed in deducing, as the equation of 

 motion then assumes the following form: 



