TRANSACTIONS OF THE SECTIONS. 
547 
these problems of mathematical optics, it is not here intended 
to include investigations respecting the phenomena of inter - 
ference, yet it is easy to perceive, from the nature of the quan¬ 
tity which I have called the characteristic function, and which 
in the hypothesis of undulations is the time of propagation of 
light from one variable point to another , that the study of this 
function must be useful in such investigations also. My own 
researches, however, have been hitherto chiefly directed to the 
consequences of the law of least action, and to the properties of 
optical systems, and systems of rays in general. And having 
stated, in the foregoing remarks, the view that has guided these 
researches, I must refer, for the results, to the volumes already 
mentioned, of the Royal Irish Academy, and to the XVIIth 
volume, not yet published, in which a third supplement to my 
Essay on the Theory of Systems of Rays has been ordered by 
the Academy to be printed.” 
An Abstract of the Solution of the principal Questions which 
are treated in Fourier's “ Theorie de la Chaleur,” by an 
analysis different from that which that author employs, and 
founded on the Theory of Equations ,—was communicated by 
Robert Murphy, of Caius College, Cambridge. 
The principal object of Mr. Murphy was to point out the 
source of the want of generality in Fourier’s two methods of 
solution. 
2. OPTICS. 
On the Colours of Natural Bodies. By Sir David Brewster, 
K.H. LL.D. F.R.S. V.P.R.S.E. 
The object of this paper was to submit to a rigorous examina¬ 
tion Sir Isaac Newton’s theory of the colours of natural bodies. 
This theory is contained in the two following propositions. 
1. “ Every body reflects the rays of its own colour more co¬ 
piously than the rest, and from their excess or predominance 
in the reflected light has its colour. 
2. “ The transparent parts of bodies, according to their se¬ 
veral sizes, reflect rays of one colour and transmit those of an¬ 
other, on the same ground that their plates or bubbles do 
reflect or transmit those rays.” 
In estimating the truth of this theory, the author does not 
enter into any examination of the postulates, facts, and reason* 
2 m2 
