120 Sir J. F. W. Herschel on the Action of the Rays 
argument on it against the Newtonian Law (Hwercices d’ Ana- 
lyse, p. 304). But that the second solution is the true one, 
will appear from considering that it only changes a circular 
function into an exponential one, which will, in general, not 
appear in the operations from its coefficient being zero. 
2. But we have an argument against the solution, or rather 
an assertion, that the appearance of an exponential in place of 
a circular function ‘violates the hypotheses on which the re- 
ductions and transformations in the former part” (I should 
like to know what part) “‘ of my paper are effected.” If they 
mean those in p. 158, and which they refer to, I reply, so does 
Newton’s problem of central forces violate his hypothesis of 
motion in an ellipse about the centre. But if these gentlemen 
assert that exponentials cannot be used for circular functions, 
and vice versd, I refer them to the memoir of Cauchy just 
quoted, where nothing but exponentials are used, and to my 
‘ Theory of Heat,’ p. 156. I may add that this objection is so 
vaguely and cautiously stated, that I do not imagine the wri- 
ters seriously entertain any belief in its force, but rather throw 
it out as a probable difficulty. 
XIX. On the Action of the Rays of the Solar Spectrum on the 
Daguerrcotype Plate. By SirJ. ¥. W. HErscue., Bart., 
K.H,, F.RS., §c. 
To the Editor of the Philosophical Magazine and Journal. 
Sir, 
ts PROFESSOR Draper of New York having, in his 
communication to the Philosophical Magazine for 
November last (Art. LXII.), referred to a specimen of a Da- 
guerreotyped impression of the solar spectrum obtained by 
him in the south of Virginia as having been forwarded by 
him to me through your obliging intervention, I should 
hardly be doing justice, either to his urbanity or to the beauty 
of the specimen itself as a joint work of nature and art, were 
I to forbear acknowledging its arrival and offering a few re- 
marks onit. And I do so the more readily, because, though 
forced to differ with him in some of the conclusions he has 
drawn from it, I recognize in him a zealous and effective con- 
tributor to this most interesting branch of scientific inquiry, 
and the only one, so far as I am aware, besides myself who 
has attacked it in the only mode in which it can lead to di- 
stinct and definite results, that of prismatic analysis.* It can 
never be too often repeated, that the use of coloured glasses 
* Since this was written, M. Becquerel’s interesting paper on the Spec- 
trum, read to the French Academy, June 13, 1842, has come into my 
hands. M. Becquerel has also used the prism, and with excellent effect, 
