212 
CORRESPONDENCE. 
after the manner of watcb. faces, thougli I am doubtful how far such 
a material would be susceptible of polish : but upon this point I would 
fain have the opinion of others. The amount of polish required and 
the difficulties in the way may be inferred from the following extract 
from Dr. Miller's 'Chemical Physics' (5th ed., p. 161): "Bodies 
in general do not possess surfaces actually flat. To common observa- 
tion they may be flat ; but, when optically examined, their surface is 
found to consist of an indefinite number of minute planes inclined to 
each other at all possible angles, and therefore receiving and reflecting 
light in all possible directions. When by the operation of polishing 
they are so much reduced as not to be elevated or depressed more 
than about the millionth of an inch, they appear to become incapable 
of acting separately, and produce the effect of a uniform surface." 
Compare also ' Nageli u. Schwendener,' p. 86. 
It will be seen from this that the degree of smoothness required to 
convert the surface I have spoken of into an efficient reflector is to 
the millionth of an inch. I have seen it stated that, if put under the 
microscope, the surface of few microscope lenses would fail to show 
lines and scratches left by the polishing material. Perhaps some 
may be tempted to submit their objectives to this ordeal, and then to 
calculate how far the marks so found exceed the millionth of an inch, 
that is, how far the polishing of their glasses comes short of perfection. 
The difficulties, then, are considerable. On the other hand, 
popular report credits Mr. Whitworth with having constructed a 
machine to measure to the millionth of an inch ! If this be anything 
better than a stupid canard, and if to measure to the millionth of an 
inch be really within the ability of our ordinary mechanics, surely to 
polish to that degree of exactness cannot be an insuperable difficulty 
to our London opticians, who are confessedly the very flower of 
artistic skill. At any rate, I think the attempt ought to be made ; 
and what has been done in the way of reflecting telescopes may serve 
as a guide. It is just possible that such reflecting surfaces might 
fail to furnish sufficient light for very high powers; but they certainly 
would be a comfortable and trustworthy aid to all powers under a 
^inch. 
Speaking of opticians reminds me that, though I found most of 
the German opticians knew little more of Schacht, Harting, Frey, 
and Dippel than their bare names, yet I always found them furnished 
with a well-thumbed copy of ' Nageli u. Schwendener,' and some of 
them were especially emphatic in their opinion of its merits, giving me 
to understand that, in their estimation, it was the book par excellence.* 
I set it down at the time for just an ordinary German book on optics, 
copiously dotted with trigonometry and optical diagrams, exhibiting 
a fair quantum of good sense, — and certainly of botany, — by two 
editors at once, one of them apparently supplying the good sense, and 
the other the botany. Perhaps there is a trifle too much of botany 
and crystallography, and what the editors call " Mikrochemie " ; but 
* 'Das Mikroskop, Theorie und Anwendung desselben, von ^Karl Nageli, 
Prof, ill Miinchen und S. Schwendener, Docenten der Botanik in Miinchen. 
Mit 276 Holzschnitten. Leipzig, 1867.' 
