May 27, 1886] 
ed 
NALGORE 
87 
remark that it is sometimes possible to make a better objective 
by deviating from the curves which give a true correction for 
spherical aberration and correcting that aberration by figuring, 
rather than if the strictly theoretical curves were adhered to. So 
far, then; as any calculation is required, the ordinary formula 
given in the text-books may be considered amply sufficient. 
Having now determined on the curves, we have to consider 
the various processes which the glass has to undergo from the 
time it is received in this form from the glass manufacturer to 
the time when it is turned out a finished objective. 
The work divides itself into five distinct operations: (1) 
rough grinding ; (2) fine grinding ; (3) polishing ; (4) center- 
ing ; (5) figuring and testing. 
4 (1) The rough grinding or approximate shaping of the glass 
is a very simple process. The glass is cemented on a holder, 
and is held against a revolving tool supplied with sand and 
water, and of a shape which will tend to abrade whatever por- 
tions are necessary to be removed to produce the required 
curves. These diagrams will illustrate the various operations. 
(2) Fine grinding. The tools used for fine grinding are of 
this form, and are made of either brass or cast iron.» I prefer 
cast iron, except for very small sizes. They are grooved on the 
face, in the manner suggested by the late Mr. A. Ross, in order 
to allow the grinding material to properly distribute itself. 
If two spherical surfaces be rubbed together they will,- as 
may be supposed, tend to keep spherical; for the spherical is 
the only curve which is the same radius every part of its surface. 
If fine dry abrading powder be used between, the same result 
will be obtained ; but, if wet powder be used, the surface will 
no longer continue spherical, but will abrade away more on the 
centre and edge than in the zone between. It was to meet this 
difficulty that the late Mr. A. Ross devised the idea of the dis- 
tributing grooves. The fine grinding process is the first of the 
series which calls for any skill on the part of the operator. 
That the modus operandi of the grinding be the more easily 
__ understood, let me explain the principle of the process in a few 
words. 
When two surfaces of unequal hardness are rubbed together 
with emery powder and water between the two, each little 
particle of the powder is at any given moment in either of these 
conditions: (a) embedded into the softer surface ; (4) rolling 
between the two surfaces; (c) sliding between the two 
surfaces. 
Those particles which become embedded in the softer material 
do no work in abrading it, and but little in abrading the harder. 
__ They generally consist of the finer particles, and are kept out of 
action by the coarser which are rolling or sliding between the 
surfaces. Further, those that are purely rolling do little or no 
work. The greater part of the work is performed by those 
particles which are facetted and which s/ide between the two 
surfaces. 
As the grinder is always of a much softer material than 
the glass, there is much more friction between the grinder and 
these particles than between the glass and the same particles, 
and therefore they partially adhere to the grinder and are carried 
by it across the face of the glass. This being so, it is now easy 
to perceive what the best conditions for rapid grinding are. Not 
too little emery, for then there will not be enough of abrading 
particles ; not too much, for then the particles will roll on each 
other and tend to crush and disintegrate each other instead of 
abrading the glass, but just sufficient to form a single layer of 
particles between the grinder and the glass surface. 
In the grinding of the small lenses, I mean up to 5 or 6 
inches diameter, it is usual to carry out the entire grinding pro- 
cesses by hand ; above that size by machinery. Surfaces up to 
12 or even 15 inches can be ground by hand; but the labour 
becomes severe, and for my part Iam gradually reducing the 
size for which the hand grinding is used, as I find the machine 
work more constant in its effects. 
' The machinery used is the same as that employed for the 
polishing operation, and I shall describe it under that head 
further on. 5 
In the fine grinding operation by hand, the glass is usually 
cemented on to a holder of this form, having (for smaller sizes) 
three pieces of cork, to which the lens is attached, and this 
holder being screwed to a spud or nose on top of a post screwed 
to the floor. The operator, having applied the proper quantity 
of moist emery powder between the grinder and the glass, pro- 
ceeds to work the former over the latter in a set of peculiar 
‘strokes, the amplitude and character of which he varies accord- 
ing to circumstances, at the same time that he changes his 
position round the post every few seconds... . 
Although, as I have shown, the harder material is abraded 
very much more than the softer, yet the softer (the grinder) 
suffers considerable abrasion as well as the glass, and the skill 
of the operator is shown by the facility with which he is able to 
bring the glass to the curve of the grinder without altering the 
curve or figure of the latter. 
It is even possible for a skilled operator to take a lens of one 
curve and a grinder of, say, a deeper curve, and by manipulation 
to produce a pair of surfaces fitting together, and of shallower 
curves than either. 
Measurement of the Curves.—In the early stages of grinding, 
gauges of the proper radius, cut out of sheet brass or sheet steel, 
are used for roughly testing the curves of the lenses ; but when 
we get to the finer grinding process it is necessary to have 
something much more accurate. 
For this purpose a spherometer is used. It is made in various 
forms, generally with three legs terminating in three hardened 
steel points, which lie on the glass, and a central screw with fine 
thread, the point of which can be brought down to bear on the 
centre of the glass. In this way the versed sine of the curve for 
a chord equal to diameter of circle formed by these points is 
measured, and the radius of curve can be easily calculated from 
this. 
I do not find the points satisfactory for regular work. They 
are apt to get injured or worn, and for ground surfaces are a little 
uncertain, as one or other of the feet may find its way intoa deep 
pit. This particular spherometer has three feet, of about half 
an inch long, which are hardened steel knife-edges forming three 
portions of an entire circle. In using this it is laid on the surface 
to be measured, and the screw with micrometer head is turned 
till the point is felt to touch the surface of glass. This scale and 
head can then be read off. The screw in this instrument has 
fifty threads to the inch, and the head is divided into roo parts, 
so that each division is equal to 55 of an inch. With a little 
practice it is easy to get determinate measures to 75 of this, 
or satca Of an inch, and by adopting special precautions even 
more delicate measures can be taken, as far probably as 
soters OT gscsaa Of an inch, which I have found to be prac- 
tically the limit of accuracy of mechanical contact. 
To give an idea of the delicacy of the instrument, I bring the 
screw firstly into contact with the glass. Now the screw is in 
good contact ; but there is so much weight still on the three feet, 
that, if I attempt to turn it round, the friction on the feet oppose 
me, and it will not stir except I apply such force as will cause 
the whole instrument to slide bodily on the glass. Now, how- 
ever, I raise the whole instrument, taking care that my hands 
touch none of the metal-work, and that the screw be not dis- 
turbed. I lay my hands for a moment on part of the glass 
where centre screw stood, and thus raise its temperature 
slightly, and on laying the spherometer back in the same place, 
you now see that it spins on the centre screw, showing how 
easily it detects what to it is a large lump, caused by expansion 
of the glass from the momentary contact of my hand. 
Flexure.—One of the greatest difficulties to be contended 
with in the polishing of large lenses is that of flexure during 
the process. 
It may appear strange that in disks of glass of such consider- 
able thickness as are used for objectives, any such difficulty 
should occur; but a simple experiment will demonstrate the 
ease with which such pieces of glass can be bent, even under 
such slight strain as their own weight. 
We again take our spherometer and set it upon a polished 
surface of a disk of glass of about 7} inches diameter and 3 inch 
thick. I set the micrometer head as in the former experiment 
to bear on the glass, but not sufficiently tight to allow the instru- 
ment to spin round. ‘This has now been done while the glass, 
as you see, is supported on three blocks near ils periphery. I 
now place one block under the centre of disk and remove the 
others thus, and you see the instrument now spins round on 
centre screw. 
It is thus evident that not only is this strong plate of glass 
bending under its own weight, but it is bending a quantity easily 
measurable by this instrument, which, as I shall presently show, 
is quite too coarse to measure such quantities as we have to deal 
with in figuring objectives. 
After this experiment no surprise will be felt when I say that 
it is necessary to take very special precautions in the supporting 
of disks during the process of polishing, to prevent danger of 
