"There is a proportion of keen designers and constructors always on the lookout for 'new worlds to conquer', to whom old-fashioned simplicity and ease of construction make an inadequate appeal, and some of these feel an exhilarating urge to pass over ordinary reflectors and wrestle with the troubles of Cassegrainian and newer types. They undoubtedly have hard and adventurous jobs before them, but these are precisely what they want.

"So, first, regarding the aperture, a inches, of an ordinary Cass RFT: If this is less than 4", the convex and the hole are likely to rob the main mirror of more than 20 percent of the light, and that is rather too much compared with the 9 percent of the 4'' Newtonian. If, on the other hand, the aperture exceeds 11", the constructor may need an eyepiece more than about 3" in diameter. This really should not be allowed to matter, but 3" is about the limit of what some seem to like or think practicable in ordinary instruments.

"Having settled the aperture, a inches, the mirror's focal length is made c times a inches, where c is the focal ratio. It is advisable to have c equal to about 4; for, if c is greater, the area of mirror put out of action by obstruction and by the hole is unduly increased, while if c is less the mirror and the convex are not easy to make of a quality to give good definition.

"With a and c both settled, and so of course with F=ca inches (Figure 1), the proper distance of the convex within the primary focal point, or the distance d, is found from inches. Then 2r, the diameter of the convex and of the hole in the main mirror is given by inches.

"The focal length of the convex, or , is given by inches, though perhaps a 5 percent error in making it, especially 5 percent less, need not be worried about. As to the eyepiece, it is to be made identical with one which would suit a plain refractor RFT of focal length equaling the F" of the main mirror, but of aperture equaling only 2r, the inches diameter of the convex mirror. Its particulars may then be arranged by methods like that outlined in 'ATMA,' but the extra diameter of the field lens, mentioned at the end of the foot note on page 633 and amounting to F/50d² inches (where a is now and here the diameter of the convex may not have to be considered 'negligible'. The eye distance, too, may often be rather larger, at about inches, where the convex diameter is again inserted for a, as the 'virtual aperture' in the Cass eyepiece calculations.

"There is an alternative graphical way of solving these problems of the Cass RFT, and it sometimes has advantages over mere inflexible formulas, and nearly always helps. It is illustrated in Figure 1, in its application to a 6" aperture of 24" focal length, for which, of course, c=24/6=4. The method is as follows: From Z draw ZA horizontally, equal, to scale, to the 24" focal length of the main mirror. Again from Z draw ZY vertically, equal, to a much larger scale, to the 3" radius of the mirror. Then from A draw AX equal, on the same larger vertical scale, to the radius of the main focal RFT image, or to F lOa, which in this case is 24/60, or 0.4". Join XY, to tell the needed radius of the convex mirror for any distance within the main focal point. From Z draw the 45 degree line shown. Now from A draw the 'triangular spiral ABCDE (by a little easy trial and error), having CD exactly equal to AX and DE exactly parallel to AB, and having its finishing point E on CB and also exactly on the line XY.

"Then we have found at C the proper place for the convex mirror, 17.6" from the main mirror; and in CE we have found the proper radius of the convex mirror, 1.10", and of the resultant field image, 1.10", and of the hole to be made in the main mirror, 1.10"-and, within about 1/8", the larger radius of the field lens of the eyepiece. As to the focal length, f of the convex mirror, by drawing a 45 degree line from C till it joins BA produced in H, and noticing how far H is horizontally and to scale to the right of C, the focal length needed, or f, is found to be 10.12"; and that is 10.12/2.20, or 4.60, times the convex's diameter.

"Making the eyepiece according to the settled rules, as for a 2.2" refractor of 24" focal length, the field lens is 2.4" diameter. The eye lens may be 3/4 of that, or 1-3/4", but it will suit if not less than 1.4". The lenses' distance apart, the usual c/4-that is, F/4a inches-is 2-3/4", and the eye distance will be about 1.4" according to the formula before given.

"It might be asked: 'Why not design the convex an inch or more farther from the main mirror and so have the convex only 0.99" or less in radius?' The answer of the triangular spiral is that the resultant field image like CE, and therefore the hole in the main mirror, would swell up to 1.37" or more in radius (see the dotted curve through E), so that no advantage could be reaped. Then, it may be oppositely asked: 'Why not design the convex an inch or more nearer the main mirror, and so have the resultant field image and hole only 0.90" or less in radius (see the dotted curve through E)?' The answer of the XY line is that the obstructive convex needed would itself swell up to 1.21" or more in radius, so that again no advantage could be reaped.

"The only real remedy both ways is to have a very short main focal length, say 9", so as to have a delightfully small convex and hole, and the whole instrument as small and portable as a silk hat; but, at the present day, such short-focus remedy is more easily spoken about than put into practice, especially seeing that the convex needs to be similarly shortened in focal length and be formed like too much of the end of an egg.

"It is useful to notice that this graphical method equally well solves the problem of any ordinary Cass of 40 degrees fully illuminated apparent field, even if not an RFT, provided we draw AX, the radius of the primary field image, 0.35 F/pa inches long, where p is the lowest power per inch of aperture which it is proposed to use.

"To the right of point A in Figure 1 is drawn the similar graphical solution for the corresponding 6" Gregorian RFT, if only to show how unsuitable this type seems to be for RFT construction, for it should be noticed how large the concave mirror and the hole have to be. For this reason and because the diagram is similarly lettered to the Cass diagram (using slanting capitals, detail description is unnecessary; moreover, the chief formulas are written at the right of the drawing. In the Gregorian the eyepiece has to be arranged the same as for a common refractor RFT, of focal length equaling the F" of the main mirror but of virtual aperture assumed to be only ad (F+ d) inches diameter.

"At the top of the diagram is drawn, entirely to the horizontal scale, the sectional arrangement of the 6" Cassegrain RFT, which certainly has the virtue of shortness; and at the bottom of the diagram is drawn to the same scale the 6" Gregorian RFT, which certainly has more than the one defect of length. But, whatever defects either is here seen to have as described, these defects may easily be the longed-for challenges to the clever and energetic and further discovering constructors before referred to, each acting on his belief that difficulties are only made to be met with and be triumphed over. So far as there is success there is again the reward, of the richest and loveliest views of the heavens yet seen by man, using the given apertures."

AS Kirkham showed here last month, the very simple RFT calls for a better-than-simple eyepiece-ideally an achromatized and costly Ramsden but at least a plain but very good Ramsden. However, when the market was canvassed it turned out that there was no wholly suitable eyepiece to be had if the rather ideal specifications-f.l. 1.12", .92' diam. field lens, as in "ATMA," 636 were considered. However, one dealer is making up a special lot having approximately these specifications. At the same time comes a letter from Walkden containing his own impressions regarding eyepieces for RFT. First, he says: "If a telescopist thinks of employing a certain eyepiece of stated focal length f", he should pay great regard to the caution in 'ATMA,' page 645, footnote 5, making quite sure, as by test, that he knows the actual focal length f of the eyepiece." In this he is quite right for, as Ellison has pointed out, many eyepieces differ quite widely from the focal length designated on them. He then continues: "Now the RFT is really a simple telescope of the lowest possible power of about 3.5 per inch of aperture, and its proper, fully illuminated apparent field of view is considered to be about 40 degrees, as obtainable by a usual type of Ramsden eyepiece. From all this there follow certain consequences, one of which is that the field lens of the suitable eyepiece of f" focal length should have approximately the diameter of 0.70 X f inches and, indeed, could be about 1/10" larger than that, because the lens is a little on this side of the field image. If the field lens is much smaller than that, the apparent field of view is likely to be correspondingly less than 40 degrees in diameter and even then have the stars rather dim toward the margin of the field. The fault closely resembles that of the too-high-powered Galilean field-glass or telescope with small eyepiece.

"The diameter of the field lens being satisfactory, the eye-lens' diameter should be about one quarter less. Though 0.6 times the diameter of the field lens is not in every case too small, it is usually a little in doubt. On no account should the eye-lens fail to be a good deal wider than 0.3", since that is about the width of the pupil of the eye.

"The eye-hole should be 0.4" to 0.5" in diameter and he at a proper distance from the eye-lens, but those things are easily enough set right in the completed instrument.

"Speaking generally, RFT eyepieces are confined to the range of l" to 5" f.l. Ramsdens of about 1-1/4" f.l. are called for chiefly by the Newtonian RFTs of moderate apertures. Ramsdens of about l-3/4" f.l. are called for by the small, short refractor RFTs. Ramsdens of about 2-1/2" f.l. can convert the moderate length refractors into RFTs and Ramsdens of about 3-1/2" f.l. can convert the ordinary long refractors into RFTs. The Ramsdens of 2-1/2" to 4" f.l. can also help to complete Herschelian RFTs of moderate apertures, to which variety of RFT too little attention has hitherto been given." [Later we shall publish Walkden's specifications for several Herschelian RFTs, calling for eyepieces with field lens diameters all the way up to five full inches! Needless to say, no reasonable telescope maker can ask dealers to stock all these freak eyepieces-if, indeed, he stocks any that are larger than about 1.14", so the would-be owner will probably have to take off his coat and maybe his shirt and make his own gill, pint, and quart eyepieces.-Ed.]

Continuing with regard to ordinary and medium sized RFT eyepieces, Walkden adds: "In all these cases the main focal length F", of aperture a", made to suit the eyepiece, is given by F = 3.5 X a X f inches, just as f = 0.286 X F/a inches, and F/f = 3.5 a; and for the Newtonians, an eyepiece focal length within about 15 percent of that of the table on page 636 of 'ATMA.' with the flat recalculated to suit the mirror and its actual focal length F", will not result in any material increase in the flat obstruction. In effect, it evidently interests some correspondents that a = 0.286 X F/f, and, indeed, that a is not greater than 0.285 X F/f inches, where 'not greater than' stands for 'cannot get used greater by the human eye than,' due to anatomical limitations."

SOMEONE-amateur, dealer or manufacturer-ought perhaps to canvass carefully the question whether it would not be profitable to put on the market, not for telescope makers or necessarily for real amateur astronomers alone, but for a larger market among that part of the public which has a less scientific but more emotional interest in astronomy, a compact, fool-proof RFT, probably a refractor, designed with studied care on the basis of the fixed anatomical and optical optimums stated in the chapter on the RFT in "ATMA" and in the January 1938 Scientific American. The American people are known to be especially susceptible to "mosts"-things that are the most this and the most that-and the RFT, showing as it does the most stars it is possible for any human being to see at one view, not even excluding a view with 200" telescope ought easily to be dramatized and caused to be desired by far more than the few hundred dyed-in-the-wool amateur telescope makers who are dealing with it now.

LAST month Alan R. Kirkham showed in these columns that the old, conventional Cassegrainian telescope, with its hyperbolical secondary which was diabolical to figure, can be supplanted by a spherical secondary Cass with elliptical primary, which will be far less of a headache to make. A copy of Kirkham's article was sent to Walkden and in an immediate reply the latter points out that Kirkham's spherical secondary Cass also kills another bird, making practicable at last the short RFT Cass. The Cassegrainian, he points out, can beat the Newtonian RFT in illumination only by being very short, but this has previously meant figuring hyperboloidally, with much difficulty, that "end of an egg" mentioned above in his article. Now, however, with a merely spherical end-of-an-egg needed, we may go the whole hog, and Figure 2, redrawn from a rough sketch sent hurriedly by Walkden, is one example. One trouble with this stubby, chubby and intriguing little Cass might be that, in the poor light of night, the owner's neighbors might think, as they watched him holding it aloft against the skyline, that he was tipping up a large bottle of some liquid, and might come to wonder about "this astronomy." "Altogether," Walkden writes, "many thanks are due to Kirkham for this well-timed help that places the amusingly short Cass RFT quite on the map."

Credit for putting back on earth the spherical secondary Cassegrainian idea which appears to have been described years ago but so far as is now known was never actually embodied in a telescope at that time, is shared by Kirkham and Dall, as mentioned last month. We discover that the little Cassegrainian shown on page 447 of "ATM" was Dall's first spherical secondary Cass. In the February 1932 Scientific American, where the same photograph first appeared, Dall described it as a "modified Cassegrainian. "

WAX coating laps, Everest's method: "My method was to draw strips of tissue paper through smoking hot beeswax, cut these into squares after cooling, scrub the dry pitch lap with a clean rag slightly moistened with turp', lay the squares on the facets of the lap (channeled in the regular manner) and roll them down with a rubber roller in order to eliminate air pockets. However, I have discarded wax coating for figuring precision surfaces. It gives a beautiful visual polish, free from sleeks and scratches, but I have never seen the optical qualities in wax-polished surfaces that

I have been able to produce with plain pitch. HCF is several times faster than plain wax, so I prefer to use it to produce a perfect visual preliminary polish and then take the necessary care to preserve this visual polish while figuring on pure pitch."

We occasionally hear from workers who complain that HCF leaves its marks on the figure. It does; but, as has often been pointed out, Everest does not recommend HCF for figuring ("ATM," 4th edition, page 149). For this he uses pitch, and states that the HCF marks disappear in about 20 minutes.

Everest makes his own pitch. Formerly he used the old rosin-turpentine mixture but found that laps made of this soon became "case hardened." To remove this shell the turpentine rag was used. The immediate effect of this was great stickiness. This disappeared some 24 hours later, after the surplus turps had evaporated off. From then on, and lasting a week or so, the lap worked splendidly until the turps had evaporated, when case-hardening became evident again and the same cycle had to be repeated. It now appears that turpentine in laps may be one of those blunders which have been perpetrated for years for the simple reason that someone back in the Dark Ages started the procedure-just as with the hyperboloidal secondary Cassegrain. Everest learned that castor oil would go into perfect solution with melted rosin and that the resulting mixture would be stable since the oil does not evaporate. "And we now make our pitch of rosin," he states. "It is first boiled hard to remove all traces of natural solvent and then is tempered with castor oil."

ON August sixth, which is a Saturday, the Thirteenth Annual Convention of amateur telescope makers from everywhere will be held at Stellafane, near Springfield, Vermont. Any person having an interest in telescopes is welcome. People begin arriving late Saturday morning, the afternoon is taken up with mutual and informal conversation, also with the examination of telescopes (bring your own), and there is a dinner at six, for which a dinner price is charged. Following this there are speeches for about two hours and then more informal "visiting." The majority leave during the evening but a few enthusiasts stay the night to use the telescopes. Those who remain meet Sunday morning for breakfast and by noon all are flown home. It all provides a fine chance to meet and talk with other "folks." Feminine family members can escape from telescoptical boredom by talking with other non-telescoptical family members who always come. It's a combination of convention, sewing circle, old home week and a three-ring circus Places to camp if you wish to camp. Plenty of parking space. R. J. Lyon, 252 Summer St., Springfield, Vt., is the Secretary.

TO obtain data for compiling a relative rating of the general opinion regarding telescope supply dealers, the editor invites all readers to give confidential reports based on their experiences, good or otherwise. Please name the dealers.

The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds.