AS A RESULT of the recent sale of a large number of war-surplus Pyrex telescope blanks with the uncommonly large diameter of 16 inches, 16 inch telescopes should soon become fairly common among amateurs. With smaller sizes it is customary to grind the mirror disk against a tool disk of equal diameter; but to stroke one 50-pound, 16-inch disk across another requires more brawn than many possess.

Dr. Robert E. Smith of Sacramento, Calif., has devised a simple, workable way to reduce the weight of the disk any desired amount by means of a variable counterweight. As shown in the illustration at left, the counterweight is a receptacle suspended from a steel cable over two pulleys at ceiling height. It is attached to the mirror by suction cups of the kind used to fasten skis to automobile tops.

"When dampened with glycerine these cups really stay put," Dr. Smith reports, "yet they are easily removed with a knife blade." Just above the cups is an attachment for the cable, consisting of a ball-and-socket joint and a small tapered pin to facilitate detachment. Above this is a swivel, and then the cable. On the counterweight side of the cable is a scale for measuring the weight put into the receptacle beneath it. "My idea works," Dr. Smith declares. "I can handle the 16-inch disk as easily as I can an eight-inch in the ordinary way."

In further description of the illustration, he adds, "The man seated at the grinding pedestal is Harold Simmons, president of our Sacramento Valley Astronomical Society. A small motor near his feet slowly rotates the pedestal, so that he or I can grind in comfort."

Instead of standing and walking around the grinding pedestal, Lyle A. Ellis of Spokane, Wash., enjoys the sybaritic luxury of the mechanism shown in the illustration at right. "You sit," he writes, "on the embroidered feather pillow at the end of the jib arm, and kick yourself around the pedestal, which is a length of three-inch pipe set deep in the earth. To the top of the pedestal is welded a 15-inch pipe flange to receive the pipe fittings of the grinding tool (and of the mirror, whenever it is desired to shallow the curve by working with the tool on top). Surrounding the central pipe, beneath the pan for catching drippings, is a length of five-inch pipe. This rides on a large ball bearing at its bottom. The lateral thrust forces due to the worker's weight are transferred to the central pipe member through slots in the outer pipe, by means of two pairs of ball bearings that are mounted on stub shafts welded to the outer pipe."

W. H. Newman of Ditchling, England, accomplishes the occasional rotation of the tool by mounting it on top of a vertical spindle that has a broad wooden disk near floor level which is turned occasionally with the feet.

The relatively simple arrangement shown at left, a sketch by the late Russell Porter, is used by James J. Pflaum of Dayton, Ohio. It enables the mirror maker to sit in a chair with his work on another chair or a box and grind as good a mirror as if he stood up and walked round a pedestal, though he loses the fun of building a more elaborate rig. If now and then he unhooks the spring rod and rotates the mirror, he will get good results.

Rotating the mirror or "walking round the barrel" can be greatly overdone, though no harm will result and the worker may even gain needed exercise. Until last-stage grinding neither component motion need scarcely be thought of. Of the two, the rotation of the mirror is the more important. So long as no deliberate pains are taken to replace the mirror always in the same position, accident alone will rotate it enough, just in the way it happens to be picked up and replaced on the tool. Increased care may be taken toward the end of grinding, and again of polishing. to ensure that it is rotated fairly often.

Now consider the tool. Suppose that it were never rotated at all. and that the worker did not walk around it. As a result of the uneven application of pressure, it would grind too low on one side, but no great harm would be done. Devices for turning the mirror by exact angular fractions of 360 degrees have sometimes been devised. These tend simply to defeat the randomness of the rotation when no thought is given to the matter.

Some workers have taken the "ring-a-round-a-rosy" principle of grinding so seriously as to perform a kind of dance taking one step around the pedestal for each stroke of the hands. This is mostly superfluous, but it may keep the worker's weight down. During most grinding and polishing the author takes about 16 strokes at each position without bothering to count the strokes. Even this is fewer than need be, but it changes the scenery.

An interesting contribution to the lore of telescope making might be made by some inquiring mind. First he would rotate neither mirror nor tool, and see just how astigmatic the mirror would come out. Then he would rotate the mirror but not the tool, and measure the runover-heel effect on the tool.

WHOEVER seeks to learn the best magnifying powers for telescopes should be prepared to do much scattered reading, find varying and contradictory statements and in the end not find the concise, unqualified answer he probable had hoped for. A correspondent of this department writes that he has been through all this, has waded through the literature, found it vague and confused, but has finally found terra firma. "This confusion,' he states, "is surprising, since there is a very simple mathematical formula, based on elementary physics and the anatomy of the human eye. The answer is clear and definite. The problem involves only two factors, the resolving power of the objective and the acuity of the eve.

"The resolving power of the normal eye is one minute of arc. The best power of a telescope is attained by the combination of objective and eyepiece focal length that causes the resolving power of the objective and eye to match. To determine this we merely divide the 60-second resolving power of the eye by thc 4.56 seconds per inch of aperture of the familiar Dawes formula for separating power. There is only one definite answer. The best power is seen to be 13.16 times the aperture of the telescope in inches."

The return to terra firma is indeed concise, and free from encumbering modifications of the kind that irritate the tidy mind. If we examine the literature of observing, however, we find that observers have been using magnifications far in excess of this rule-as high as 35 or 40 diameters per aperture inch of the telescope for planetary observation, and even higher, 50 or even 70 diameters per inch, for double star observation.

Something must be wrong. It is this: the satisfying rule just stated refers only to the magnification that fully exhausts the objective's resolving power-its power to bring out all the detail in the image it forms. This is explained in D. H. Jacobs' Fundamentals of Optical Engineering, where the same figure, 13 diameters, is reached. While this is not the figure at which we shall finally arrive, it is well worth remembering-provided we also remember, first, that it is valid only for point objects having equal brightness, and second? that many astronomers do not accept the one-minute resolving power of the eye, which appears to be based on ideal data obtained in the laboratory by physiologists and ophthalmologists.

The textbooks tell us that any magnification beyond this 13 diameters per inch of aperture is "empty": it brings out no new details of the image, no matter how much higher it is raised. The word empty has a certain connotation of the unworthy, and has sometimes been used in a derisive sense. For example, a proposal received years ago by this department, to compound 10 compound microscopes and thus magnify a billion diameters, brought forth derision, for this was empty magnification at its very worst

Nevertheless, the whole experience of observing astronomers goes to prove that empty magnification of already resolved images needs no apology, but is even a necessity, up to the point where atmospheric conditions cause the image to lose more by blurring than it gains by increased ease of vision-which is the kernel of the whole matter. The blurring point varies with the seeing conditions and somewhat with the aperture of the telescope. For amateur-size telescopes and ordinary atmosphere it runs from two to four times the resolving magnification of 13. A formula for useful magnification quoted in L. Bell's The Telescope is 140 times the square root of the aperture. This would be 35 diameters per inch of aperture on a 16-l inch telescope, 47 on a nine-inch and 70 on a four-inch. This is not a rule, but an abstraction from the reports of expert double star observers who had set the magnification empirically wherever they found it best. Your own "rule," similarly, is wherever you get the best results.

In The Binary Stars, Director Robert G. Aitken of Lick Observatory emphasizes: "Use the highest power the seeing will permit." For the planets, the astronomer Bernard Lyot found at Meudon near Paris that in a refracting telescope the minimum magnification to show the finest details accessible on the best nights was 37 per inch on a four-inch, 35 on an eight-inch, 27 on a 12-inch and 20 on a 24-inch. In Arizona's atmosphere, on an 18-inch refractor, Percival Lowell most commonly used 24 to 34 diameters per inch on planetary work. Lyot says that for planetary details, which generally show low contrast, the limits used on double stars are a bit too high.

In this connection a statement by Dr. W. H. Steavenson of Cambridge, England, in The Journal of the British Astronomical Association is of interest: "Very few textbooks point out that the Dawes formula is not applicable to planetary detail, or give the reason for this. Cassini's division in Saturn's ring and the shadows of Jupiter's satellites, both visible with apertures between two and three inches, are well-known examples of the relatively superior resolving power of a telescope when applied to planets. Experiments have often been made on terrestrial objects also, and give similar results. Recently I have myself found that a black dot on a white ground is visible when subtending an angle about one third of that corresponding to the Dawes formula, and I find that Sir William Herschel obtained a similar result in 1804. For a dark line, visibility is attained at an angle something like one fifth of the Dawes limit. The reason for the apparent discrepancy is, in the main, the low intensity of the illumination of planetary surfaces, each element of which has consequently a relatively small spurious disk."

INVITED to contribute his experiences in observational work to the present discussion, Rolland R. LaPelle of Longmeadow, Mass., a well-known amateur astronomer, writes:

"In estimating the resolving power of a telescope most of us tend to fall back on the classic expression of Dawes, an empirical formula relating the resolving power of its objective to its diameter thus: R = 4.56/D, where R is the resolving power of the objective for moderately bright double stars expressed in seconds of arc of separation, and D is the diameter of the objective in inches.

"Actually this expression is correct for stars of only one color, the yellowish type G, similar to the sun. The expression may also be taken to represent the diameter of the spurious disk which is the stellar image, out to the center of the dark space midway between the disk and the first bright ring. The spurious disk will, however, be much larger, by a factor of at least two, for very red stars of type M and later, and smaller by an almost equal factor for very blue stars of type B. Further, the diameter of the spurious disk, as the eye perceives it, will be greater, because of irradiation, for very bright stars' and smaller, because of the lack of light, for very faint stars. Hence for very bright blue, or moderately bright or very bright red stars, we cannot expect to reach Dawes' limit, while for moderately bright blue stars (but not for faint ones, because of the deficiency of light) we may do considerably better than Dawes' limit.

"If we assume Dawes' limit as a median value, however, we may then ask what power will be necessary in our eyepiece to render the two stars visible. This factor again is uncertain, since the resolving power of the human eye is a much-disputed question. It is said that the ophthalmologists base their charts upon the assumption that the eye can resolve objects separated one minute of arc. This may be true for nearby bright objects, but a search of astronomical textbooks yields a somewhat different result. J. C. Duncan's Astronomy states that the astronomical resolving power of the eye is between three minutes and three minutes, 80 seconds, and uses a value of three minutes. Bell, in a quite thorough discussion in The Telescope, states that those of fairly keen vision can distinguish the two stars of Epsilon Lyrae, separated three minutes and 27 seconds, while he has never known anyone who could separate the two components of Asterope, two minutes and 80 seconds apart. He then uses a value of five minutes in his calculations.

"From my observations with a six-inch telescope, I believe my own constant is between two minutes, 30 seconds, and three minutes. It is important to state the diameter of the objective, since with a larger instrument having greater resolving power less magnification is required. Thus, while the closer pair in the double-double, Epsilon Lyrae, requires at least 75X in my six-inch, giving them a separation of 75 X 2.6 seconds or 195 seconds (three minutes and 15 seconds), they are readily perceived in a 10-inch at a power of only 48X. This illustrates the well-known impossibility of setting up an absolute constant for all sizes of objective, even though the constant supposedly refers only to the eye of the observer.

"If, however, we are dealing with stars separated by Dawes' limit for the particular size of objective in use, then the spurious disks will be of the same diameter, regardless of the objective size. If we assume that the average human eye, under these conditions, requires 200 seconds of separation for stars of median brightness and of yellow color, then the power required will be 200/(4.56/D) or 44 D. That is, to split stars at Dawes' limit of resolution to a point where they may readily be perceived by the normal eye, the magnifying power must be 44 per inch of objective diameter.

"How does this check with the practice of skilled observers? In The Telescope Bell summarizes the findings of a paper by T. Lewis, published in The Observatory, in which that author tabulated the most often used power of a large group of professional observers. With telescopes of moderate size powers around 50 per inch of aperture were usual, and now and then on special occasions up to 70 per inch were used. These were trained professional observers, most of them doing double star work, and using excellent equipment.

"In my own work with a six-inch f10 reflector, I find myself using powers of 30 and 44 diameters per inch consistently for close double stars and for Mars and Saturn. For star clusters, except globulars, and on nebulae, I generally use a power of 34X, but these are not objects that require high resolving power, and the nebular and extragalactic objects cannot be resolved anyway. For globular clusters, however, where it is desired to resolve the individual stars, and where the brightness of the stars is such as to make this possible with a six-inch telescope, the higher powers are of course desirable.

"Double star observing demands training of the eye; nevertheless, power may sometimes be substituted for training. At the Stellafane convention in 1948 I tried to show several visitors a double star of one-second separation, Zeta Herculis. This was perfectly clear to me at 130 diameters (30X per inch), but my visitors could not see it. I then raised the power to 46X per inch, whereupon all those who had observational experience had no difficulty in seeing it.

"Another experience with the same six-inch telescope may be of interest with regard to Dawes' limit. Yellow or blue stars of one-second separation may readily be split when the seeing is reasonably good and the star within 45 degrees of the zenith. Alpha Capricorni, a wide double-double very low in the south even at culmination, shows four stars very readily. One of these four, of 10.5 magnitude, is itself a double, consisting of two stars of 11.2 and 11:5 magnitude, separated only 1.2 seconds. They are both yellow. This proved perhaps the most difficult object I ever attempted to separate, and was seen only with the greatest difficulty on a very good night and at a power of 46X per inch.

"At the other extreme is Gamma-Two Andromedae, the blue star of a wide yellow-blue pair. This fifth-magnitude star is itself a double, consisting of two stars, both blue, of about equal brightness at 5.4 magnitude, and separated only between .5 and .6 second. I have clearly seen this star as a double on at least three occasions, when it was near the zenith on good nights. At the same time the spurious disk of the third-magnitude yellow star Gamma-One Andromedae fell within the field of view and had an apparent diameter greater than the two blue stars together. This demonstrates the effect of brightness and color on the size of the spurious disk seen by the eye of the observer. It also shows, as Bell and others remark, that for small instruments under good conditions, and for moderately bright blue stars, the resolving power may be much better than that indicated by Dawes' limit, which would be about .77 second for a six-inch objective.

"My belief is that much of the distrust of the amateur for high powers is due to incorrect selection of eyepiece equipment. Most amateurs use Ramsden eyepieces, which not only have a small field of view and very poor eye relief, but also have considerable color aberration, which absolutely prevents sharpness at high powers. I have standardized on orthoscopic eyepieces with a 45-degree field of view, which are available at a moderate price, using the coated variety to eliminate 'ghosts' and light loss. For high powers I use an achromatic, coated Barlow lens in conjunction with an orthoscopic eyepiece of 5/8-inch focal length. The combination gives high power without ghosts, and with the same eye relief normally obtained with an orthoscopic eyepiece of this focal length. In addition, the emergent pencil of rays is larger than would be the case with an eyepiece of short focal length, say, .22-inch, which would be needed to obtain equivalent power without the Barlow lens.

"In sum it seems, from both theory and practice, that to use the maximum theoretical resolving power of an objective a power of 40 to 45 per inch of objective diameter is required, to enable the eye of the average observer to perceive that which the objective is able to resolve. In my own experience and that of professional observers as well, such high powers do serve a useful purpose in observing double stars and also Mars and Saturn. Under certain favorable conditions, small telescopes may be made to perform considerably better as regards resolving power than is indicated by Dawes' limit, although, as an average value for all types of stars, this limit probably represents a fairly accurate measure of resolving power in a well-constructed reflector used with adequate magnification."

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