156 Mr KELLAND, ON THE DISPERSION OF LIGHT, 



It appeared to me at the time doubtful whether this series might not 

 be a diverging one, and thence it became extremely probable that the 

 existence of the function in form above, was owing to the absence of 

 terms omitted in this expansion. Lately M. Cauchy's Memoir on the 

 same subject has fallen into my hands, and an opportunity has been 

 afforded me of comparing his results with my own. The comparison 

 has shewn me that although in some points we differ, in the essentials 

 of principle, at least, we coincide. 



Whatever difficulty may attach itself to my hypothesis as to the 

 sphere of action of the particles, will attach itself equally to his, as they 

 are identical : at least I have reduced mine to the same state as his. 



Although there were many points of coincidence in our processes, 

 there were not a few of difference, to many of which the present 

 Memoir is indebted ; as I have not scrupled to adopt anything which 

 would tend either to simplify or generalize the results ; my object being 

 by no means to regard my formula as a re-discovery of what M. Cauchy 

 had published in 1830, but rather to attempt an improvement on 

 what is already known. I may be allowed to add, that M. Cauchy's 

 equations, owing to his proceeding with great generality at first, and 

 only adding new hypotheses to simplify them when they became per- 

 fectly unwieldy, are so buried in symbols, that a person must possess 

 no ordinary sagacity to give to them any interpretation. And further, 

 there are some points in which the result is more general than the 

 hypothesis would render necessary. 



The plan which I have pursued is to simplify the equations as 

 I proceed, and not to i-etain any result which admits of reduction. 



SECTION I. 



Analytical Investigation. 



The problem about which we are to occupy ourselves, is the mo- 

 tion of any system of material particles, exerting on each other forces 



