Such measurements are too delicate to be made with mechanical devices. Instead, a special kind of weightless and inflexible indicating pointer is used-rays of light. The drawing at the left shows in principle how such refined curves are measured. The following explanation is addressed not to telescope makers, who already understand its substance, but to general readers. For simplification some corners can be cut without harm.

Of the three arrangements shown side by side in the drawing, only the central one need be noted at first. The three disks in the background may be ignored for the present.

In the drawing, rays of light are directed at the mirror from in front of it; for simplicity these rays are not shown. If the mirror is spherical, i.e., if a large sphere would fit against it, these rays will all be reflected to cross one another at some single point in space. The method used to determine this is to locate representative reflected rays by means of a movable feeler. For this a razor blade on a little pedestal serves about as well as would more complicated apparatus. This "knife-edge" is slowly moved by hand from left to right, cutting off ray after ray, each of which is thus identified with the part of the mirror from which it is reflected. At a distance of a few feet these pointers of light greatly multiply the mirror's irregularities. Thus a millionth-of-an-inch change of angle on the mirror deflects the light-ray pointer an easily detectable hundredth of an inch at knife-edge distance.

One deviation from the sphere that is actually desirable is the paraboloid. The mirror maker knows that he has deepened his sphere the few millionths of an inch needed to make it a paraboloid when the rays reflected from the inner part of the mirror (left-hand mirror) cross one another nearer the mirror than those reflected from the outer part (right-hand mirror) by a distance r²/R, where r is the half-diameter of the mirror and R is the radius of its curvature. The actual distance involved is seldom more than a fraction of an inch. The scale of things near the knife-edge is exaggerated in the drawing.

An auxiliary method used by mirror makers for keeping track of the curve between spells of work is to set the mirror up on edge, as shown in the representations in the background, place the eye close behind the knife-edge, and move the knife-edge partly across the reflected rays. A paraboloidal mirror will then show over its surface a pattern of lights and shadows like the one in the central representation. The origin of this peculiar pattern-new moon on the left, oval on the right, with subtle intergradations-will be seen if the six typical rays shown are traced from the mirror to the knife-edge. Some rays are cut off by the knife-edge, and the corresponding areas on the mirror look dark. Other rays, swung farther right by a slightly . different angle on another part of the mirror, pass the knife-edge and enter the eye, making the corresponding part of the mirror appear bright. The patterns of shadows that are found on telescope mirrors as polishing progresses, some of them indicating excellent shape, others indicating evil shapes too numerous to mention, soon become as familiar to the worker as his own features.

This exquisite and most revealing method is the "Foucault test" invented by the French physicist and telescope maker Leon Foucault, who described it in 1859. It has been said that the Foucault test changed mirror making from an art to a science. This is true, but the remainder of the present article will show that mirror makers before Foucault were not so much in the dark as such a statement might imply.

IN 1773, 86 years before Foucault revealed his knife-edge test, William Herschel began making mirrors of speculum metal and of glass, ending about 1789 with a 40-inch mirror. Constance A. Lubbock, in The Herschel Chronicle, tells how Herschel tested his mirrors. Placing them temporarily in a telescope, he successively isolated three zones with masks and located the focus of each. He then figured the mirror till all three zones had an equal focal length. In 1924 the British amateur telescope maker W. H. Steavenson tested a dozen of these old mirrors that had been preserved by Herschel's descendants in the family home at Slough, 20 miles west of London. Steavenson's tests, made by the Foucault method, which was of course wholly unknown to Herschel, show that while Herschel sometimes grossly overcorrected his mirrors, he often obtained K proper correction. Steavenson's findings on 12 of Herschel's mirrors revealed the following conditions:

Speculum mirror, 9-inch f7 Gregorian. Figure very even; one high zone.

Speculum mirror, 7-inch f11 Gregorian. Figure very even, except for a narrow shallow zone.

Speculum mirror, 6-inch f5.6. Figure only very slightly uneven, but 414 per cent correction.

Glass mirror, 6 1/2-inch f13. Good polish. Even figure so closely spherical that no zonal test was made.

Glass mirror, 8 1/2-inch f14. Figure very even, except for three narrow zones. Too nearly spherical for zonal test.

Glass mirror, 6 1/2-inch f13.5. Even figure, except for two narrow zones, but 1,015 per cent correction.

Speculum mirror, 5-inch f3.6. Figure even; no zones. Parabolic shadow, but too short a focus for testing apparatus.

Speculum mirror, 9-inch f8. Very even, regular figure. Too nearly spherical for zonal test.

Speculum mirror, 8.85-inch f14. Very smooth, nearly spherical and regular, except for a deep, broad zone spanning 40 per cent of the mirror's radius.

Glass mirror, 9-inch f13, 1/3-inch thick. Too violently distorted when stood on edge to permit testing.

Speculum mirror, 8.8-inch f13. Very even, except for three zones. No zonal test made because of nearness to sphericity.

Speculum mirror, 6.1-inch fl3.9. A beautifully smooth curve from center to edge without sign of zones or other irregularities. Correction 62 per cent.

In his book The Telescope, Louis Bell mentions Herschel's so-called "7-foot" (Herschel designated telescopes by their focal length), a

Newtonian reflector with which he discovered Uranus. The drawing on the right depicts a Herschel 7-foot now at Oxford University. Steavenson tested and used another Herschel 7-foot which he found among the mirrors, 30 elliptical Newtonian flats, 9 Gregorian secondaries, 48 eyepieces, 10 micrometers and 33 miscellaneous pieces of apparatus preserved at Slough. ( Later he described them all in the Transactions of the Optical Society, Volume 26, pages 210-236.) The last mirror in the list above, the one with 62 per cent correction and "a beautifully smooth curve," was the one in the 7-foot tested by Steavenson. "This," Steavenson writes, "is the only complete instrument in the collection. It stands in the entrance hall of Observatory House, and is in good condition and fair working order. Both tube and mounting are of mahogany, the former being of octagonal section, like all Herschel's smaller telescopes. Both mirror and flat were much tarnished, the cover of the former being far from airtight, and the latter being without a cover of any kind. A good deal of the tarnish on both was removed by means of lemon juice, and a useful proportion of the original reflectivity was thus restored.

"The large speculum, of diameter 6.2 inches and focal length 7 feet 2 3/4 inches, was removed from the tube and subjected to a Foucault test. The latter showed the figure to be beautifully regular, without a trace of rings. A measurement of the zones suggested the presence of a very slight degree of undercorrection, the test being made under conditions of constant temperature. The mirror was then replaced in the tube and the whole telescope taken out of doors for actual testing on celestial objects. For this one of Herschel's own eyepieces was used, a single biconvex lens giving a power of 361. No observations were made until the telescope had stood in the open air for several hours; but even with this precaution the effect on the mirror of a steadily falling temperature was very marked, for whereas the figure had appeared slightly but definitely undercorrected at a constant temperature, it was now found to have passed through the paraboloid to a state of slight overcorrection. However, definite rings were visible in the expanded images of stars on both sides of the focus, while at the latter itself there was nothing to indicate any departure from perfect correction.

"Apart from the inevitable color and loss of definition in the peripheral portions of the field (due to the form of the eyepiece), the performance of the telescope was most admirable. Of course the light grasp was deficient, owing to tarnish, but it did not seem inferior to that of a S-inch refractor, the companion of the Pole Star being easily seen. The detail on the Moon was as fine as that shown by any modern reflector or refractor of similar aperture. The shape of the second peak in Tycho was well made out and the third peak, to the west of it, could just be seen. The central craterlet in Plato was clearly seen as such, and one or two of the minute craterlets on the west half of the floor of Clavius were definitely visible. This is about as much, as regards detail, as a modern 6-inch refractor will do. Venus and Jupiter were exquisitely defined. Arcturus showed a neat disk with diffraction rings, which is more than is brought out by many modern reflectors.

"It has often been suggested that Herschel's instruments, though marking a great advance on previous efforts, would not be accounted good according to present-day standards. Anyone holding such an opinion would, I think, feel inclined to revise it after a glance through this beautiful 7-foot telescope."

Now we drop back a third of a century. In his Compleat System of Opticks, published at Cambridge, England, in 1738 (the year Herschel was born), Robert Smith gave instructions for speculum making that were destined to be the beginner's guide for Herschel the amateur 35 years later. To find the center of curvature of a speculum Smith's method was to set it on edge opposite a candle. Selecting a tiny pinhole near the edge of the tin, he shifted candle and tin until he could simultaneously focus in the eyepiece the edge of the tin and the image of the pinhole reflected from the speculum. How he then tested the speculum is described in his book thus:

"You will now also judge of the perfection of the spherical figure of your metal by the distinctness with which you see the representations of the holes, with their raggedness, dusts and small hairs sticking in them; and you will be able to judge of this more exactly and likewise to discover the particular defects of your speculum, by placing the eyeglass so as to see one of the smallest holes in or near its axis; and then by turns shoving the eye-glass a very little forward towards the speculum and pulling it away from it by turns, letting the candle and plate stand still in the mean time. By this means you will observe in what manner the light from the metal comes to a point, to-form the images, and opens again after it has past it. If the area of the light, just as it comes to or parts from the point, appears not round but oval, squarish, or triangular &c. it is a sign that the sections of the specular surface, through several diameters of it, have not the same curvature. If the light, just before it comes to a point, have a brighter circle round the circumference and a greater darkness near the center, than after it has crossed and is parting again; the surface is more curve towards the circumference and flatter about the center, like that of a prolate spheroid round the extremities of its axis; and the ill effects of this figure will be more sensible when it comes to be used in the telescope. But if the light appears more hazy and undefined near the edges, and brighter in the middle before its meeting than afterwards, the metal is then more curve at its center and less towards the circumference; and if it be in a proper degree, may probably come near the true parabolic figure. But the skill to judge well of this must be acquired by observation.

"In performing the foregoing examination, the image must be reflected back as near the hole it self as the eye's approach to the candle will admit of; that the obliquity of the reflection may not occasion any sensible errors: in order to which the eye should be screened from the candle; and the glaring light which may disturb the observation may be still more effectually shut off, by placing a plate, with a small hole in it, in the focus of the eye-glass which is next the eye. A is the speculum, B the candle and plate with the small holes, C the cell with the eye-glass and plate behind it.

"Instead of the flame of the candle and plate with small holes, I sometimes made use of a piece of glass thick stuck with globules of quicksilver, strained t}.rough a leather and let to fall on it in a dew; placing this glass near a window and the speculum at a distance on the side of the room, being it self and every thing about it as much in the dark as can be. The light of the window reflected from the globules of mercury, appearing as so many stars, serves instead of the small holes, with this advantage, that the reflection from the metal may be very near at right angles."

ANOTHER example of pre-Foucault methods of testing telescope mirrors is from the Philosophical Transactions of the Royal Society of London, Volume 130, Part 2 (1840), in which Lord Oxmanton, the third Earl of Rosse, born William Parsons, describes his method of testing as used on a 36-inch speculum. The dial plate of a watch is suspended from a high tower, face downward. At the bottom of the same tower is the speculum, face up on its machine. Lord Rosse used masks "as Mudge did."

How Mudge used masks was described in the same periodical, Volume 67, page 335, in a paper that Mudge delivered in March, 1777. He placed a separating mask having one eighth the diameter of the mirror opposite a zone midway between the center and the edge, and tested first the inner zone and then the outer one both for definition and for coincidence of focus. If the two images were equally sharp and of equal focus "the speculum," he said, "is perfect and of true parabolic curve."

Foucault described his test in 1859. Two years later William Herschel's son Sir John, in his Encyclopaedia Britannica article on the telescope, reprinted as a book, The Telescope, in 1861, briefly outlines Foueault's "peculiar method." But he prefers the diffraction-ring test (Amateur Telescope Making, page 428), supplemented by his father's test of matching-three zones for focus on the stars, and the watch-dial test of Lord Rosse. Thus the older mirror makers did not rush at once to use Foucault's test. In 1887 With, the English professional, wrote the following about a mirror: "Among my choicest of the choicest, I find one recorded thus: '8lh focus 5 feet 3 inches. Absolute Perfection; Not for Sale.'" F. J. Hargreaves, Britain's foremost optician, who was once an amateur, states in the Journal of the British Astronomical Association that With had no knowledge of Foucault's knife-edge test. Hargreaves found in 1941 that this mirror "gave images as nearly perfect as any I have ever seen, even with a magnification of 500 diameters." He tested it by the Foucault method and found that it "showed no imperfection, apart from a narrow turned-down edge."

Hargreaves' article was shown in 1941 to Russell Porter, who jotted on the page, "Anderson judges the 200-inch mirror by inspecting image of pinhole as much as by knife-edge test."

Nothing said above may be taken as in any sense derogatory to the knife-edge test, best of all tests. The evidence assembled may, however, show that workers before Foucault's time were not so much in the dark as we sometimes assume.

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