88 
IMA TORE 
[May 27, 1886 
flexure ; of course if the disks are polished while in a state of 
flexure, the resulting surface will not be true when the cause of 
flexure is removed. 
For small-sized lenses no very special precautions are neces- 
sary, but for all sizes over 4 inches in diameter I use the equili- 
brated levers devised by my father, and utilised for the first time 
on a large scale in supporting the 6-foot mirror of Lord Rosse’s 
telescope. These have been elsewhere frequently described, but 
I have a small set here as an example. 
I have also sometimes polished lenses while floating on 
mercury. This gives a very beautiful support, but it is not so 
convenient, as it is difficult to keep the disk sufficiently steady 
while the polishing operation is in progress without introducing 
other chances of strain. 
So far I have spoken of strain or flexure during the process of 
working the surface ; but even if the surface be finished abso- 
lutely perfectly, it is evident from the experiment I showed you 
that very large lenses when placed in their cells must suffer con- 
siderable flexure from their own weight alone, as they cannot 
then be supported anywhere except round the edge. 
To meet this I proposed many years ago to have the means 
of hermetically sealing the tube, and introducing air at slight 
pressure to form an elastic support for the objective, the pressure 
to be regulated by an automatic arrangement according to the 
altitude. My attention was directed to this matter very pointedly 
a few years ago from being obliged to use for the Vienna 27-inch 
objective a crown lens which was, according to ordinary rules, 
much too thin. 
I had waited some years for this disk, and none thicker could 
be obtained at the time. ‘This disk was very pure and homo- 
geneous, but so thin that, if offered to me in the first instance, 
I would certainly have rejected it. Great care was taken to 
avoid flexure in the working, but, to my great surprise, I found 
no difficulty whatever with it in this respect. This led me to 
investigate the matter, with the following curious results. 
If we call / the flexure for any given thickness 7, and /’ the 
2 
flexure for any other thickness 2’, then 3, ~ ym for any given 
load or weight approximately. But as the weight increases 
directly as the thickness, the flexure of the disks due to their 
own weight, which is what we want to know, may be expressed as 
Ft. 
ft 
Let us now consider the effect of this flexure on the image. 
In any lens bent by its own weight, whatever part of its surface 
is made more or less convex or concave by the bending has a 
corresponding part bent in the opposite direction on the other 
surface, which tends to correct the error produced by the first 
surface. This is one reason why reflectors which have not this 
second correcting surface are so much more liable to show 
strain than refractors. If the lens were infinitely thin, moderate 
flexure would have no effect on the image. The effect increases 
directly as the thickness. If then the flexure, as I have shown, 
decreases directly as the thickness, and the effect of that 
flexure increases directly as the thickness, it is clear that the 
effect of flexure of any lens due to its own weight will be the 
same for all thicknesses ; in other words no advantage is gained 
by additional thickness. 
This has reference, of course, only to flexure of the lens in its 
cell after it has been duly perfected, and has nothing to do with 
the extra difficulty of supporting a thin lens during the grinding 
and polishing processes. 
Polishing.—The polishing process can be, and is often, con- 
ducted precisely in the same manner as the grinding, except that 
the abrading powders used (oxide of iron, rouge, an oxide of tin, 
putty-powder) is of a finer and softer description, and the surface 
of the polishing tool is made of a softer material than the metallic 
grinder. 
Very nearly all my polishing is done on the machine I shall 
presently describe ; but before doing so, I will, with your per- 
mission, say a few words on the general principles of the polish- 
ing process. Various substances are used for the face of the 
polisher—fine cloth, satin or paper, and pitch. Pitch possesses 
two important qualities which render it peculiarly suitable for 
this work, and it is a curious fact that we owe its application for 
this purpose to the extraordinary perspicuity of Sir Isaac Newton, 
who we may fairly say was the first to produce an optically 
perfect surface, and that that material is not only still used for 
the purpose, but is, as far as I know, the only substance which 
possesses the peculiar qualifications necessary to fulfil the required 
conditions. With skill and care, moderately good surfaces can 
be obtained from cloth polishers ; but it is easy to see why they 
can never be perfect. There is a certain amount of elasticity in 
cloth and in its ‘‘nap,” and there is consequently a tendency to 
round off the surfaces of the pits left by the grinding powder, 
and to polish the bottom or floor of these pits at the same time 
as the upper surface. It is easy to show mathematically that 
any process which abrades the floors of the pits at the same time 
as general surfaces even in a very much less degree, can never 
produce more than an approximation to a perfect surface, and 
practice agrees with the theory. Paper is said to be much used 
by the French opticians. I can say nothing about it. I have 
tried it and failed to produce a perfect surface with it, nor indeed 
should I expect it. It is of course open to the same objection as 
cloth. Pitch possesses, as I said, two most important qualities 
which render it suitable for the work ; the first, in its almost 
perfect inelasticity ; the second, a curious quality of subsidence, 
which we utilise in the process. 
If we watch with a microscope, or even a magnifier, the cha- 
racter ofgtwo surfaces during the process of polishing, the one 
with cloth, and the other with pitch, the difference is very 
striking. With the cloth polisher, the polish appears much 
quicker, and it would at first sight appear as if the same polish- 
ing powder abraded more quickly on the cloth than on the pitch 
polisher, but I do not believe that such is the case, for if we look 
at the surface with a magnifier we shall find that, while all the sur- 
face has assumed a polished appearance, the surface itself has 
retained some of the form of the original pitted character with 
the edges rounded off; while in the pitch half-polished surfaces 
the floors of the pits are as gray as ever, and the edges are 
sharp and decisive. In pitch polishing, too, a decided amount 
of polish appears very quickly, and then for many hours there 
appears to be little or no further effect. Suddenly, however, 
the remaining grayness disappears, and the surface is polished. 
The reason of this is very obvious. The polisher being very 
inelastic, polishes first only the tops of the hills, and has to 
abrade away all the material of which these hills are composed 
before it reaches the valleys or floors of the pits. When it does 
reach them, the proper polish quickly appears. The second 
quality of pitch, that of subsidence, is also most valuable. 
Pitch can be rendered very hard by continued boiling. By pitch 
I mean the natural bituminous deposit which comes to us from 
Archangel, not gas-tar pitch. It can be made so hard that it is im- 
possible to make any impression on it with the finger-nail without 
splitting it into pieces ; and yet even in this hard condition, if 
laid on an uneven surface it willin a few days, weeks, or months 
subside and take the form of whatever it is resting upon. The 
cohesion of its particles is not sufficient to enable it to retain its 
form under the action of gravity; and as this condition is that 
which science tells us marks the difference between solids and 
liquids, we must, paradoxical though it may appear, class even 
the hardest pitch among liquid instead of solid substances. 
Now how do we utilise this peculiar quality ? 
The polishing tool is made by overlaying a metal or wooden 
disk formed to nearly the required curves by a set of squares 
of pitch, and while these are still warm pressing them against 
the glass, the form of which they immediately take. 
In the grinding process I showed you that the regulation of 
the abrasion was managed partly by the character of the stroke 
given, and partly by the local touches given to the tool by the 
stoning process. 
In polishing we still retain the same facilities for modifying 
the stroke, and the same rules I gave apply generally to the 
polishing process as well as the grinding ; but we have not got 
any process equivalent to that of the local stoning, and even if 
we had it would be useless, for this very quality of subsidence 
of the pitch would in a few minutes cause any part of its 
surface which had been reduced to come into good contact 
again; we must therefore look for some other means for pro- 
ducing more or less abrasion whenever we require it. This we 
effect by modifying the size of the squares of pitch in the various 
zones. Practically it is done in this way by a knife and mallet. 
Whenever the squares are reduced, the abrasion will be less. 
This is a well-known method of regulation; but the rationale 
is, I think, not generally understood. It is generally explained 
that there is less abrasion because there is less abrading surface. 
I do not think this is the true, or at least the entire, explanation. 
In order to understand the action, you must conceive the pitch 
to be constantly in a state of subsidence, the amount of that 
a 
