On the Principles of the Science of Motzon. 4] 
as a direct consequence of Lagrange’s theory, that he is permitted 
to express* 
Xn(@1s Lo; ++ Ws) 
as a rational function of 
PD, (21) Vay «+ Xs) 
Such an assumption is clearly inadmissible. It is not a little 
remarkable that a most striking confirmation of the validity of 
my method may be derived from that very theory +. 
8. Again, the objection which he urges against a statement of 
mine in reference to Taylor’s theorem, is founded on a misap- 
prehension of my meaning. The statement relates to equations 
of conditiont. But Mr. Cockle, ignoring their existence, speaks 
of a remainder. It would be easy, from what has been said in 
art. 7, to show the irrelevancy of the rest of his objections. It 
seems needless, however, to proceed further. 
December 1860. 
VY. On the Principles of the Science of Motion (Mechanics, 
Physics, Chemics)§. By J. 8. Stuart Guenniz, M.A. 
1. ii is proposed in the following paper to give a brief intro- 
ductory exposition of the conceptions by the analytical 
application of which it has been found that the laws and methods 
of mechanics can be more fully applied to the phenomena of 
physics and chemics. 
2. In order that mechanical principles may be rigorously ap- 
plied to physical and chemical phenomena, it seems clear that 
physical and chemical forces must be conceived in the same way 
as mechanical forces. Now a mechanical force, or the cause of 
a mechanical motion, we know to be, in general, the condition of 
a difference of pressure. Whether the motion is uniform, or 
accelerated, depends on whether the force, or difference, is in- 
stantaneous, or continuous. And whether that difference is 
between polar or extreme pressures, depends on whether the 
moved body transinits pressure with, or without, a tangential 
resistance. Hence the condition of the translation of a solid is 
* See his paper in the Philosophical Magazine for March 1860. The same 
error runs through all his subsequent papers on the subject of equations, 
and thus renders nugatory every objection based on Mr. Harley’s paper. 
+ Compare arts. 107; 112 of my ‘ Essay.’ 
~ See note on art. 44 of my paper for June 1845. 
§ Communicated by the Author, being a restatement of principles 
enounced in papers read at the two last Meetings of the British Associa- 
tion, and of which abstracts have been published in the ‘ Reports’ for 
1859 and 1860 (Trans, of the Math. and Phys. Section). 
