252 Prof. Young’s New Criteria for 
pass any photographic production I have yet seen, and which 
indeed it seems impossible to go beyond. Most unfortunately, 
they cannot be preserved. Every attempt to fix them has 
resulted in the destruction of their beauty and force; and even 
when kept from light, they fade with more or less rapidity, some 
disappearing almost entirely in three or four days, while others 
have resisted tolerably well for a fortnight, or even a month. 
It is to an over-dose of tartaric acid that their more rapid 
deterioration seems to be due, and of course it is important to 
keep down the proportion of this ingredient as low as possible. 
But without it I have never succeeded in producing that pe- 
culiar velvety aspect on which the charm of these pictures 
chiefly depends, nor anything like the same intensity of colour 
without over-sunning. 
230. I might here describe many other curious and inter- 
esting photographic results to which, under the genial in- 
fluence of such a summer as, possibly, has never before been 
witnessed in England, I have been conducted. But in so 
doing I should surpass the reasonable bounds of a Postscript 
illustrative of my text, and abuse the privilege accorded me. 
Yet I cannot forbear noticing one at least, in which a line or 
dot engraving of any degree of delicacy is imitated, line for 
line, and dot for dot, in a manner which might deceive any but 
a practised artist to the point of rendering him unable to de- 
clare that the photograph had not been struck off from the 
original plate with common printing ink, by the ordinary pro- 
cess of copper-plate printing. The details of this process, 
which are delicate and somewhat tedious, cannot properly be 
stated here; if for no other reason, because I have not yet 
obtained a complete command over the result: but a micro- 
scopic examination of the specimens placed in the hands of 
our worthy Secretary, though somewhat marred by the acci- 
dents of manipulation, will I think suffice to justify the terms 
employed above. 
XLII. New Criteria for the Imaginary Roots of Equations. 
By J. R. Youne, Esq., Professor of Mathematics in Belfast 
College. 
[Continued from p. 188 and concluded.) 
ite is easy to see that the foregoing criteria furnish the rules 
proposed by Newton, in the Universal Arithmetic, for 
detecting imaginary roots in an equation. These rules have 
not, I believe, as yet been demonstrated ; although, on account 
of their obvious utility and ready application, a rigorous proof 
of their truth has frequently been sought. The earliest dis- 
