280 CAUCHY ON THE THEORY OF LIGHT. 
which the celestial bodies move to the single hypothesis of uni- 
versal gravitation. 
In the second place, I shall remark, that, in order to establish 
the propositions put forth in this Memoir, we have had recourse 
to the formula (68.), of page 208 of the “ Hxercices de Mathéma- 
tiques,” and that, in order to reduce the differential equations 
of the motion of a system of molecules acted upon by the forces 
of mutual attraction or repulsion to the formule in question, we 
are compelled to neglect several terms; for example, those which 
include the superior powers of the displacements &, , &, and of 
their derivatives taken in relation to the independent variables 
x,y,z. When we do not neglect these same terms, we obtain, 
as I shall show in a new Memoir, already presented to the Aca- 
demy, formulz, by help of which we are able not only to assign 
the cause of the dispersion of colours by the prism, but also to 
discover the laws of this phenomenon, which, notwithstanding 
the numerous and important labours of natural philosophers 
on this subject, had remained unknown until the present day. 
Note. 
[The investigations here promised, as well as those before referred to, as to 
be published, seem to be furnished in the author’s subsequent papers, in his 
Exercices de Mathématiques, in his Mémoire sur la Dispersion (Paris, 1830), 
and his Nouveaux Exercices, &c. (Prague, 1855). But the more full deve- 
lopment of his views is to be found in a lithographed Memoir, published in 
Aug. 1836, sur la théorie de la lumiere, &e.—Eb. ] 
