May 27, 1886] 
NAMES RE 
39 
subsidence depending of course on the pressure placed upon it. 
Now, if we reduce the size of the squares in any zone while 
retaining the same distance from centre to centre of squares, 
we increase at first the pressure per unit of area on the pitch 
squares in that zone, and consequently the subsidence will be 
greater, and the action will not be so tight or severe on that zone. 
I know of no substance but pitch and a few of the resins 
which possesses this peculiar quality except perhaps ice, and it is 
curious to think that the same quality which in ice allows of 
that gradual creeping and subsidence and consequent formation 
of glaciers with their characteristic moraines, &c., will in pitch 
help us to produce accurate optical surfaces. 
Polishing-Machines.—Vhe two best-known polishing-machines 
arethose of the late Earl of Rosse and the late Mr. Lassell, the 
general forms of which were shown in these diagrams. Time 
will not permit me to enter into a minute description of their 
working, nor is it necessary, as both have been often described. 
A few words, however, as to the different character of the 
strokes given by these machines may be interesting. The stroke 
of Lord Rosse’s machine may be imitated in hand-work by the 
operator traversing the polisher or mirror in a series of nearly 
straight strokes, of about one-third the diameter of the glass, to 
and from himself, at the same time that he keeps walking slowly 
round the post, and instead of allowing the centre of polisher 
to pass directly over the ceatre of mirror, each stroke that he 
gives he slides a little (about one-tenth diameter) to one side 
and then a little to the other. 
Mr. Lassell’s stroke may be imitated by causing the polisher 
to describe a series of nearly circular strokes a little out of the 
centre, walking round the post at the same time; thus the 
centre of polisher will deseribe a series of epicycloidal or hypo- 
cycloidal curves on the speculum. 
Many years ago my father devised a machine, figured and 
described in Nichols’s ‘‘ Physical Science,” by which either of these 
motions could be obtained. He appeared to have got better 
results with Mr. Lassell’s strokes, for he afterwards devised a 
machine which gave the same character of stroke, but over which 
the operator had greater control, and this machine has been used 
for many years with great success. Like all machines, however, 
which give a series of strokes constantly recurring of the same 
amplitude, it is apt to polish in rings It is impossible to 
obtain absolute homogeneity in the pitch patches, and if any 
one square be a shade harder than the general number, and 
that square ends its journey at each stroke at the same dis- 
tance from the centre of speculum or glass, there will almost 
surely be a change of curvature in that zone. To avoid this I 
have made a slight modification in the machine, which has in- 
creased its efficiency to a great extent. I will now place in the 
lantern a model of this machine, and first draw you a few curves 
with the machine in its old state, and afterwards in its improved 
state. 
In order to convey some idea of the relative quantities of 
material removed by the various processes, I have placed upon 
the walls a diagram which will illustrate this point in two dis- 
tinct ways. 
The diagram itself represents a section of a lens of about 
8 inches aperture and 1 inch thick, magnified 100 times, and 
shows the relative thickness of material abraded by the four 
processes. 
The quantity removed by the rough grinding process is repre- 
sented on this diagram by a band 25 inches wide, the fine grind- 
ing by one 58; inch wide, the polishing by a line ;'5 inch wide, 
while the quantity removed by the figuring process cannot be 
shown even on this scale, as it would be represented by a line 
only zp40~ inch thick. 
I have also marked on this diagram the approximate cost of 
abrasion of a gramme of material by each of the four processes, 
viz. <— 
b Sch 
Rough grinding, about 0 oO I per gramme. 
Fine grinding, oe) Om .ON 174. rs 
Polishing, jy) POTION. 0 op 
Figuring, m Ce &) © ” 
Figuring and Testing.—By the figuring process I mean the 
process of correcting local errors in the surfaces, and the bring- 
ing of the surfaces to that form, whatever it may be, which will 
cause the rays falling on any part to be refracted in the right 
direction. When an objective has undergone all the processes 
I haye described, and many more which are not so important, 
and with which I have not had time to deal, and when the 
objective is centred and placed in its cell, it is, to look at, as 
perfect as it will ever be, but to look through and use as an 
objective it may be useless. The fact is that when an objective 
has gone through all the processes described, and is in appear- 
ance a finished instrument, I look upon it as about one-fourth 
finished. ‘Three-fourths of the work has probably to be done 
yet. True, sometimes this is by no means the case, and I have 
had instances of objectives which were perfect on the first trial ; 
but this is, I am sorry to say, the exception and not the rule. 
This part of the process naturally divides itself into two 
distinct heads :— 
(1) The detection and localisation of faults—what may, in 
fact, be termed the diagnosis of the objective. 
(2) The altering of the figures of the different surfaces to cure 
these faults. This may be called the remedial part. 
It may be well here to try to convey some idea of the quanti- 
ties we have to deal with, otherwise I may be misunderstood in 
talking of great and small errors. 
L have before mentioned that it is possible to measure with the 
spherometer quantities not exceeding ;shy, Of an inch, or with 
special precaution much less even than that ; but useful as this 
instrument is for giving us information as to the general curves 
of the surface, it is utterly useless in the figuring process ; that 
is, an error which would be beyond the power of the sphero- 
meter to detect, would make all the difference between a good 
and a bad objective. 
Take actual numbers and this will be evident. Take the case 
of a 27-inch objective of 34 feet focus; say there is an error in 
centre of one surface of about 6 inches diameter, which causes 
the focus of that part to be ;4; of an inch shorter than the rest. 
For simplicity’s sake, say that its surface is generally flat ; the 
centre 6 inches of the surface therefore, instead of being flat, 
must be convex and of over 1,050,000 inches radius. The 
versed sine of this curve, as measured by spherometer, would 
be only about sposo0, 4 millionths of an inch, a quantity 
mechanically unmeasurable, in my opinion. 
If that error was spread over 3 inches only instead of 6 inches, 
the ver-ed sine would only be about z55}yay- Probably the 
effect on the image of this 3-inch portion of 34; inch shorter 
focus would not be appreciable on account of the slight vergency 
of the rays, but a similar error near edge of objective certainly 
would be appreciable. Until, therefore, some means be devised 
_of measuring with certainty quantities of 1 millionth of an inch 
and less, it is useless to hope for any help from mechanical 
measurement in this part of the process. 
If, then, no known mechanical arrangement be delicate 
enough to measure these quantities, how, it may be asked, are 
these errors detected ? 
The answer to this is, that certain optical arrangements enable 
us to carry our investigations far beyond the limits of mechanical 
accuracy. ‘Trials of the objective or mirror as a telescope are 
really the crucial test, but there are various devices by which 
defects are detected and localised. 
The best object to employ is generally a star of the third or 
fourth magnitude, when such is available, but as it frequently 
occurs that no such object is visible, recourse is had to artificial 
objects. The minute image of the sun reflected from little 
polished balls of speculum metal, or even a thermometer bulb is 
a very good object ; polished balls of black glass are also used 
with good effect ; but as the sun also is of somewhat fickle 
disposition in this country, we have frequently to have recourse 
to artificial light. Small electric lamps, such as this, with their 
light condensed and thrown on a polished ball are very useful. 
In fact, I am never without one of them in working order. 
For the detection and localisation of errors it is very useful 
to be provided with sets of diaphragms which leave exposed 
various zones of the surface, the foci of which can then be 
separately measured, but a really experienced eye does not need 
them. 
For concave surfaces, Foucault’s test is useful. I shall not 
trespass on your time to explain this in detail, as it is described 
very fully in many works, in none better than in Dr. Draper's 
account of the working of his own reflecting telescope. ‘This 
diagram will give an idea of the principle of the system, which 
is really the same as what I have described as useful for detect- 
ing want of homogeneity in the substance of the glass. 
This system is extremely useful for concave spherical surfaces, 
but is not available for convex surfaces, and only partially avail- 
able for concave parabolic surfaces. 
The really crucial test is, as I said before, the performance ol 
