Figure 1 shows J. E. Myers, 1519 Olin Ave., Omaha, Neb., holding a 5-5/8", f/4 RFT. Figure 2 is a photograph of Frank Wickenburg, Theosophical Headquarters, Point Loma, Calif., with a 5", f/4 RFT which gives a full 2 degree field. "It is packed full of thrills," he says, "and at a recent meeting of our club in San Diego it stole the show." Figure 3 is a 4", f/3.4 RFT made by George R. Harrington, Jr., 4031 Vernon Road, Drexel Hill, Pa. He writes: "It astonishes me what this scope picks up-I'll give Mr. Walkden a vote of thanks." Figure 4 is from Willard R. Harer, 311 Rodman Ave., Jenkintown, Pa., who says, "The results with it are highly gratifying, giving me the most beautiful sights I've ever seen with a telescope. It surpassed my expectations."

The remainder of the account is by Mr. Walkden, and the reader will discover that the chapter in ATMA merely scratched the surface of this subject. Whenever the abbreviation RRFT is used, this means 'richest, richest-field telescope," a sort of superlative superlative, if this is possible.

ADOPTING the accessible data it becomes evident that, if the observer uses an 11th magnitude RFT, perhaps of about 2" aperture, he may obtain the most star-crowded average field of view with respect to the zone of the Milky Way all round the sky, on which account such an RFT had better be distinguished as the general-purpose RRFT, and, though small, be regarded as the most important instrument (Figure 5).

"Suppose, then, that instrument is directed upon an average star-cloud at average distance of about 3000 light-years, upon which cloud the RFT is acting as the proper RRFT because of just revealing that critical star, here of the 11th magnitude, at which the stars of the cloud stop increasing in numbers faster than they grow fainter (ATMA, pages 631-633). Now let the aperture be made times greater. Of course the aperture area is times greater, and so it can reveal the critical star if times as faint. That will occur if the whole star-cloud and its critical star is placed times farther away. Any doubt as to whether the critical star remains the same individual star may be easily dispelled, on realizing that distance fades all the stars similarly, without altering the relative brightness of one star compared with another. (Each cloud is supposed to have only a moderate depth, compared with its distance.)

"Now the ability just to reveal the critical star exactly defines the RRFT condition, and so it comes about that an RFT of any aperture inches can become a special region RRFT on our finding for it a star cloud at distance 3000 light-years. Since 3000x÷ is practically 1000, we may say that every RFT can become a special-region RRFT for a star cloud distant about 1000 1ight-years per inch of aperture. The rate of proportionality, 1000 light-years per inch of aperture, will be further justified, later, on the basis of what the critical star really is.

"Then there is the question of the numbers of stars in the fields of view. As in the third line of page 63l, ATMA, the rule for the number of stars seen in the field of a standard RFT is

(The final term of this equation was misprinted in ATMA with . The 102.6 is the square degrees area of the actual field of view of a standard 1" RFT of 40 degrees apparent field diameter; so the is the square degrees area of the actual field of a standard RFT of a" aperture. Finally, of course, the multiplication by at once finds N which for the general-purpose, ", RRFT becomes

stars, as stated on page 636, ATMA.

"When, now, the star-cloud is pushed x times farther away, and is followed up by the x times larger aperture, so that the aperture becomes inches and the star density becomes, by a natural perspective effect, , then

stars,

precisely as at first, aperture and distance having had no effect whatever.

"Yet it is the case that the larger sizes of instruments do offer opportunities for showing much more star-crowded fields of view, and there are reasons for this being so. If, while looking at an average cloud at the average distance, we turned to another cloud at the same distance, and found it gave a field of view b times more crowded, we should have to conclude this second cloud had b times the of the first, in fact a star-density of 25.4b. But, looking at the cloud even with the naked eye, we should notice it also had b times the surface brightness or shine of the first cloud, because there would be b times as many stars per square degree to help the surface brightness or shine. Thus b, the brightness or shine compared with the average, becomes an exact measure of the of the cloud for a view at the average distance. The shine of the cloud is not affected by distance, for while at x times the distance the stars are all faded x² times there are, to compensate, x² times as many stars per square degree acting to make the shine. Accordingly, a brightness or shine of a cloud b times the average tells us the cloud has a star-density, at average distance, of 25.4b, so that if the cloud is actually at x times the average distance then, by the rule,

stars.

"This all becomes very simple; it enjoins looking at the star-clouds which are distant as many thousand light-years as there are inches in the RFT aperture used, and then preferring the brightest of these clouds

"But the problem is to know the distances. What can usually be done is to judge on the basis of results or experience. The nearer clouds, such as the Cygnus clouds, are recognizable by soon resolving into stars on a darkening background, even with quite small RFT apertures: but the farther and farther clouds want larger and larger RFT apertures, before a decidedly stellar field replaces the powdery appearance and there is a substantial darkening of the milky luminous background.

"(Note: So far as the star-clouds contain the Eddingtonian kind of stellar mixture to be referred to later on, the following method can estimate by calculation, and closely enough, the RRFT aperture required for a simple spot of cloud. First, look at the cloud through a refracting test telescope of T" aperture, of low power though not necessarily as low as an RFT, and count the stars in the field of view. Then cut down the aperture to 60 percent of the full diameter, by a cardboard stop, and again count the stars, and find the quotient, Q, of the first number of stars divided by the second. The RRFT aperture needed is then simply about inches diameter, so long as Q is kept within the limits of 5 and 2 by the use of a suitable size of test aperture, T". A 3" will be found to test up to 15" aperture, a 4" up to 20" aperture, and so on in proportion. The quotient Q is always about , or 2.9, when the telescope in use is already the proper RRFT; and so far as the cloud is distant 1000 1ight-years per inch of RRFT aperture the method also estimates the distance of the star-cloud. The reflector RRFT has generally to be of about 50 percent larger aperture, and it may show about 25 percent smaller number of stars. The method is based on our knowing how far we are from the peak of a known arched curve, as soon as the slope near where we are now has been made to reveal itself.)

"However, it is clear why the larger apertures can show more crowded fields. A small 2" RFT acting as an RRFT performs upon star-clouds distant only about 2000 light-years, and such clouds are few to select from and not particularly bright ones. Perhaps 300 stars may be expected. But a 20" RFT acting as an RRFT performs upon clouds distant about 20,000 light-years where there are a hundred times as many to select from (chiefly a surface matter, depending quite on the square of the distance), and several really very bright specimens. Where b = 6, N = 345 X 6, and about 2000 stars may be expected in the field of view.

"(Note: Since the actual field of a special-region RRFT is 11.43/a degrees in diameter, and 1 degree at 1000 1ight-years is 17.5 light-years, and since the distance at which the instrument operates is about l000a light years, the actual field of view is, very curiously, always about (17.5/1000) X l000a X 11.43/a, or 200 light years diameter in the proper star-cloud. A tube of 100 light years radius and of D light-years depth is of volume , cubic light-years, which is the volume of the field in the star-cloud. If S is the number of stars per million cubic light-years of the cloud (down to the critical star), then the number of stars in the field is the volume X S÷1,000,000, and that is to say that N = 0.0314 X D X S. This alternative formula for N is of little more use than again to advise finding deep and congested clouds to operate on with the proper apertures-the clouds distant and bright, like those about 30,000 light years away near the hub of the galaxy and needing apertures of about 30" for their RRFT's. The special" region RRFT for a particular star-cloud is, by the way, very agreeably more sharply defined than is the general purpose RRFT designed for the whole round of the Milky Way, for reasons of a kind not very hard to perceive.)

"Practical Applications: In the application of what has been explained, a 1" RFT could be a special region RRFT if the nearest clouds in Cygnus were at half their distance of 2000 light-years, to bring their critical star within the grasp of so small an aperture. But, used upon those clouds as they are, there may be seen about 200 stars in the field of view, and though not very bright the view is recommended as quite cheerful for so tiny an instrument. A 2" can really start being a special-region RRFT upon those clouds of Cygnus, exhibiting bright and charming views of about 300 stars. The important 3" RFT is a special-region RRFT for the further clouds of Cygnus, as well as being the general-purpose RRFT for the whole Milky Way, as several times explained. It shows about 350 stars per average view. The 6" RFT, as the special-region RRFT for the 6000 light-year, nearer clouds of Scorpio, is able to select brighter clouds, and 600 or 700 stars per view may be expected (probably parallelled by the special-region, rich-field observations described by Mr. Tombaugh on page 640, ATMA).

"The 12" and larger are special-region instruments for the big clouds near the hub of our galaxy, in Scorpio and Sagittarius, and have much bright material from which to select. Fields quite as rich as 1000 or 2000 stars may be found in places, and appear very magnificent. A 100" RFT, which should be the proper special-region RRFT for the Greater Magellanic Cloud, which is very bright in places, may be expected to produce superbly magnificent fields of view of surpassing grandeur, containing thousands, perhaps nearly 10,000 stars, with several, perhaps, as bright-looking as Sirius, and one or two, perhaps, as bright-looking as Venus or even brighter -much brighter if a naked-eye foreground star can be caught in the view.

"The Real Critical Star: Turning to the sublime meaning of these views, few users of the RFT's as regional RRFT's are likely ever to forget that these marshalled hosts of heaven, delicately colored like sparkling jewels, from red to blue, and drifting across like snow at every move of the telescope, are really the magnificent suns of our universe. Estimates have been made of the relative numbers of stars of different sun-powers in an average sample of the stellar mixture that seems to prevail everywhere in space. One estimate is in Vol. 21, page 320, of the 14th or latest edition of the Encyclopaedia Britannica (Sir Arthur Eddington's article on Stars). For every 200,000 stars of the same power as our own sun, there are said to be 42,000 ten times as powerful, 3300 one-hundred times as powerful, 90 one thousand times as powerful, and one ten thousand times as powerful, and of course there are vaster multitudes less powerful than our sun, all of which, strangely enough, we shall not have to regard. The important thing is that, when these figures are examined by means of a curve on squared paper (a curve of the numbers of stars, 1, 91, 3391, 45,391, and 245,391 against the sun-powers, 10,000, 1000, 100, 10, and 1, preferably done on double logarithmic paper or by plotting logs both ways on plain squared paper, carefully noticing the point of 45 degree slope), it is found to be at about sun-power 15 that the stars stop increasing in number faster than they grow fainter. Of course, this tells us what our critical star really is at close quarters. It is really a sun of about 15 times the power of our own splendid sun, and other disclosures easily ensue. Since the special-region size of RRFT is determined by just perceiving the critical star and none fainter, it astonishingly follows that these gloriously rich fields are made up of stars all more than 15 times as powerful as our sun. Indeed, if all the stars less powerful than that were blotted out of existence the fields might look still finer, gaining by contrast with a darker background between the lucid countable stars. Other facts emerging are that the average power of those stars in the field of view must be about 27 times the power of our sun, and out of every 350 stars in the field there is one likely to be over 1000 times as powerful as our sun. Of course there are stray stars between us and the star-cloud, and some of these within one quarter of the distance of the cloud- the square root of 15 is about 4-may be no more powerful than our sun, but they are only a casual few, and not in the cloud.

"Our own sun, we know, looks like a 10th-magnitude star at 326 light-years distance. Therefore, it would look 2.512 times brighter and of the 9th magnitude at , or 206 light-years distance. So the critical star of 15 sun-power would also looks like a 9th magnitude star-which is supposed just perceivable with 1" of aperture-at or 797 light-years distance. This-with some disrespect for exactness of the data or respect for better eyesights-is going to be rounded off to about 1000 1ight-years for each inch of aperture. And so we find confirmed the rule, easy to remember and already used in the earlier part, that an RFT proves to be an RRFT, for star-clouds distant about 1000 light-years per inch of aperture.

"There is, accordingly, good reason for an observer having not only the little general-purpose RRFT, but another of as large an aperture as he finds possible, this second one for use on to-be-discovered special regions of the Milky Way and giving views magnificent according to the aperture. The observer need not first ascertain the cloud distances-small star magnitudes and the powderiness of the fields can suggest the distances-he only needs to discover and exult in the brightest and richest spots, which he knows are findable here and there.

"The Special-Object RRFT: The possessor of an RFT soon notices the vivid views it gives of some objects which are not definitely star-clouds. Since a standard RFT has an actual field of about 11.43/a degrees in diameter (see footnote, page 633), it always performs splendidly on objects which look their best in fields of about 12/a degrees diameter, or, with reasonable latitude, in fields from about 18/a to 8/a degrees diameter. In this way a 2", with field of about 6 degrees diameter, may be found to be a special-object RRFT for viewing the bright groupings in the prominent constellations of Orion, Taurus, Cygnus and many others. A 4" is still more delightful in the same way, and for viewing the Hyades and Pleiades and open clusters, and especially for most beautifully viewing the Andromeda Nebula as a complete whole. A 12" gives most dazzling (perhaps too dazzling) views of the moon, three-quarters filling the field when a power of 5 per inch of aperture is used; the bright light contracts the eye's pupil to about 1/5th inch. A 24", of field about half a degree, takes its place for viewing most brilliantly the globular clusters, especially the great Hercules Cluster; but it also gives a remarkable view of the whole spread of Jupiter and his satellites, the latter looking like first-magnitude stars. It is as well in these instruments to have spare eyepieces of about 3/4, 2, and 3 times the strict richest magnifying power, to help some objects to occupy the apparent field in the best possible manner, since a separate RFT for each of the many sizes of objects is rather out of the question.

"The Spiral-Nebulae RRFT: Just as the 4" RFT is found to be about the best size for observing the Andromeda Nebula as a whole, so also would the 8", 12", 16", etc., RFT's be the best sizes for observing the same nebula if it went away to 2, 3, 4, etc., times its present distance of about 1,000,000 light-years, for of course, the nebula would shrink to 1/2, 1/3, 1/4, etc., of its present apparent size, by such recessions. Evidently an RFT suits the observation of such spiral nebulae at a distance of about 1,000,000 light-years for each four inches of its aperture. The number of nebulae so observable, each in its entirety and nicely filling the field, must, of course, be roughly proportional to the square of the distance, and that means to the square of the aperture. The great 200" therefore, if completed as a visual RFT, would show a few thousand nebulae, just as the one in Andromeda appears so beautifully in the field of a 4" RFT. For the tens of thousands of such nebulae much nearer, the 200" is too large to show more of each one than a small patch, which, however, in the case of the Andromeda it self, may be richly filled with 1000 or more of stars, each one at least 400 times as powerful as our sun, and these seen against the irresolvable luminous haze of all the rest."

THIS ends Mr. Walkden's contribution on the RRFTs for various special uses, and the reader will have observed that, just as the common or garden variety of RFT enhanced the view many times, compared with a conventional telescope, so the special-purpose RRFTs, used on their appropriate objects, enhance even this a goodly number of times. Every amateur has had the experience of showing the stars to non-astronomical persons and slyly noting their disappointment at not seeing something quite striking; they go away thinking their telescope-making friend "isn't so much, after all." If, however, they are shown some RRFT views, they may go away vastly impressed.

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