86 
WA TORE 
| May 27, 1886 
construction of telescopic objectives by a short historical account 
of what has been attempted and achieved in the past, but time 
will not permit. 
A very few words, however, on the history of glass manu- 
facture are necessary. 
As I pointed out last Saturday afternoon, Dollond’s brilliant 
discovery, which afforded a means of achromatising objectives, 
rendered possible their construction of greater size and perfec- 
tion than formerly, provided suitable material could be obtained. 
But the chromatic errors being removed, faults in the material 
hitherto masked by them were detected, and it was not until 
after many years that Guinand, a lowly but gifted Swiss peasant, 
succeeded in producing glass disks of a considerable size and 
free from these defects. 
The secrets of his process have been handed down in his own 
family to M. Feil, of Paris (one of his descendants), and also 
through M. Bontemps, who for a time was associated with 
Guinand’s son, and afterwards accepted an invitation from Messrs. 
Chance bros. and Co., of Birmingham, to assist them in an 
endeavour to improve that branch of their manufacture. Only 
these two houses, so far as I am aware, have succeeded in 
manufacturing optical disks of large size. 
Testing of Optical Glass.—Let me here say a few words re- 
specting the testing of optical glass; I mean of the material of 
the glass, quite apart from the optician’s work in forming it into 
an objective. When received from the glass manufacturer it is 
sometimes in this state, roughly polished on both sides, and 
sometimes in this, in which as you see there are small windows 
only, facets as they are called, polished on the edges. In case 
of lenses for telescopic objectives, it is always well to have them 
roughly polished on the sides, to avoid the chance of having to 
throw away a lens after much trouble and labour has been spent 
on it. 
There are only three distinct points to be looked to in the 
testing of optical glass: (1) general clearness and freedom from 
air-bubbles, specks, pieces of ‘dead metal,” &c. ; (2) homo- 
geneity ; (3) annealing. 
The first is the least important, and needs no instructions for 
detection of defects, any one can see these. The second ismuch 
more important, and much more difficult to test. 
The best test for homogeneity is one somewhat equivalent to 
Foucault’s test for figure of concave mirrors. 
The disk of glass should be either ground and polished to 
form a convex lens, or if that be not convenient, it should be 
placed in juxtaposition with a convex lens of similar or larger 
size, and whose excellence has been established by previous 
experience, 
The Jens or disk is then placed opposite some small 
brilliant light, a small gas flame generally suffices, and at such a 
distance that a conjugate focus is formed at other side and at a 
convenient distance. When the exact position of this focus is 
found, the eye is placed as nearly as possible so that the image 
of flame is formed on the pupil. On looking at it with the 
eye in this position, the whole lens should appear to be ‘full of 
light”; but at the slightest movement to one side the light will 
disappear and the lens appear quite dark. If the eye be now 
passed slowly backwards and forwards between the position 
showing light and darkness, any irregularity of density will be 
most easily seen. 
Of course, like everything else, some experience is neces- 
sary. 
The rationale of this is very obvious. When the eye is placed 
exactly at the focus of a perfect lens, the image formed on the 
pupil is very small, and the slightest movement of the eye will 
cause the light to appear and disappear. If the eye be not at 
the focus, the pencil of light will be larger, and consequently it 
will require a much greater movement of the eye to cause the 
light to disappear. Now if any portion of the lens be of a dif- 
ferent density to the general mass, that portion will have a longer 
or a shorter focus ; consequently while the light flashes off the 
general area of the lens quickly, it still remains on the defective 
portions. 
By imitating this arrangement and substituting a camera for 
the eye and forming the focus of a small point of light on the 
stop of the lens, Ihave succeeded in photographing veins in 
glass, and sometimes have found this useful as a record. 
The third point—that of proper annealing—is easily tested by 
the polariscope. 
For small disks the usual plan is to hold them between the 
eye and a polarising plane, such as a piece of glass blackened at 
back or a japanned surface, and look at them through the facets, 
| using as an analyser a Nicol prism. 
Larger sizes, which are polished on the surfaces, can be more 
easily examined. It is difficult to describe the appearances, but 
I will put a few disks into the lantern polariscope and endeavour 
to point out what amount of polarisation may safely be permitted 
in disks of glass to be used for objectives. 
The composition of metallic mirrors of the present day differs 
very little from that used by Sir Isaac Newton. Many and dif- 
ferent alloys have been suggested, some including silver or nickel 
or arsenic ; but there is little doubt that the best alloy, taking 
all things into account, is made with 4 atoms of copper, and 1 
of tin, which gives the following proportions by weight : copper, 
252, tin, 117°8. 
Calculation of Curves. —Vaving now obtained the proper 
material to work upon, the first thing necessary is to calculate 
the curves to give to the lenses, in order that the objective, 
when finished, may be of the required focus, and be properly 
corrected for the chromatic and spherical aberrations. 
As this lecture is intended to deal principally with the tech- 
nical details of the process, I do not intend to occupy your time 
for more than a few moments on this head, nor indeed is it at 
all necessary. In my lecture last Saturday I explained the 
principles of achromatism, and in many published works full 
and complete particulars are given as to the calculation of the 
curves—particulars which are sufficient, and more than sufficient, 
for the purpose. 
Much has been discussed and written concerning the calcula- 
tion of curves of objectives, and much care and thought has been 
bestowed by mathematicians on this subject, and, so far as the 
actual constructors are concerned, a certain amount of veil is 
thrown over this part of the undertaking, as if there were a 
secret involved, and as if each had discovered some wonderful 
formulze by which he was enabled to calculate the curves much 
more accurately than others. 
I am sorry to have to dispel this illusion. Practically the 
case stands thus. The calculation of the curves which satisfy 
the conditions of achromatism and desired focus is a most simple 
one, and can be performed by any one having a very slight alge- 
braical knowledge in a few minutes, provided the refractive in- 
dices and dispersive power of the glass be known. Both Messrs. 
Chance and Feil supply these data quite sufficiently accurately 
for small-size objectives. | Speaking for myself, I am quite con- 
tent to take the figures as given by these glass manufacturers for 
any disk. up to 10 inches indiameter. If over that size, I grind 
and polish facets on the disk and measure the refractive and 
dispersive powers myself. 
The calculations of the curves required to satisfy the condi- 
tions of spherical aberration are very troublesome, but fortu- 
nately these may be generally neglected. 
Some years ago the Royal Society commissioned one of its 
members to draw up tables for the use of opticians, giving the 
curves required to satisfy the conditions of both corrections for 
all refractive and dispersive indices. 
A considerable amount of labour was expended on this work. 
but in the end it was abandoned, for it was found that the caleu- 
lation of these curves was founded on the supposition that all 
surfaces produced by the opticians were truly spherical ; while 
the fact is, a truly spherical curve is the exception, not the rule, 
The slightest variation in the form or figure of the curve will 
produce an enormous variation in the correction for spherical 
aberration, and it was soon apparent that the final correction for 
spherical aberration must be left to the optician and not to the 
mathematician. Odyect-glasses cannot be made on paper. When 
I tell you that a sensible difference in correction for spherical 
aberration can be made by half an hour’s polishing, correspond- 
ing probably to a difference in the first place of decimals in radii 
of the curves, you will see that it is practically not necessary to 
enter upon any calculation for spherical aberration, We know 
about what form gives an approximate correction ; we adhere 
nearly to that, and the rest is done by figuring of the surface. 
To illustrate what I mean. I would be quite willing to under- 
take to alter the curves of the crown or flint lens of any of my 
objectives by a very large quantity, increasing one and decreas- 
ing the other so as to still satisfy the conditions of achromatism, 
but introducing theoretically a large amount of positive or 
negative spherical aberration, and yet to make out of the altered 
lens an object-glass perfectly corrected for spherical aberration. 
I am now speaking of ordinary sizes. For very large sizes it 
is usual to go more closely into the calculations ; but I may 
———— 
