Among those intrigued by the demon's alleged capture was George O. Smith of Highlands, N.J. Smith writes: "The 19th century British physicist James Clerk Maxwell made many deep contributions to physics, and among the most significant was his law of random distribution. Considering the case of a closed box containing a gas, Maxwell started off by saying that the temperature of the gas was due to the motion of the individual gas molecules within the box. But since the box was standing still, it stood to reason that the summation of the velocity and direction of the individual gas molecules must come to zero. In essence Maxwell's law of random distribution says that for every gas molecule headed east at 20 miles per hour, there must be another headed west at the same speed. Furthermore, if the heat of the gas indicates that the average velocity of the molecules is 20 miles per hour, the number of molecules moving slower than this speed must be equaled by the number of molecules moving faster.

"After a serious analysis of the consequences of his law, Maxwell permitted himself a touch of humor. He suggested that there was a statistical probability that, at some time in the future, all the molecules in a box of gas or a glass of hot water might be moving in the same direction. This would cause the water to rise out of the glass. Next Maxwell suggested that a system of drawing both hot and cold water out of a single pipe might be devised if we could capture a small demon and train him to open and close a tiny valve. The demon would open the valve only when a fast molecule approached it, and close the valve against slow molecules. The water coming out of the valve would thus be hot. To produce a stream of cold water the demon would open the valve only for slow molecules.

"Maxwell's demon would circumvent the law of thermodynamics which says in essence: 'You can't get something for nothing. 'That is to say, one cannot separate cold water from hot without doing work. Thus when physicists heard that the Germans had developed a device which could achieve low temperatures by utilizing Maxwell's demon, they were intrigued, though obviously skeptical. One physicist, Robert M. Milton, investigated the matter at first hand for the U. S. Navy.

"Milton discovered that the device was most ingenious, though not quite as miraculous as had been rumored. It consists of a T-shaped assembly of pipe joined by a novel fitting, as depicted in the accompanying illustration [left]. When compressed air is admitted to the 'leg' of the T, hot air comes out of one arm of the T and cold air out of the other arm! Obviously, however, work must be done to compress the air.

"The origin of the device is obscure. The principle is said to have been discovered by a Frenchman who left some early experimental models in the path of the German Army when France was occupied. These were turned over to a German physicist named Rudolf Hilsch, who was working on low temperature refrigerating devices for the German war effort. Hilsch made some improvements on the Frenchman's design, but found that it was no more efficient than conventional methods of refrigeration in achieving fairly low temperatures. Subsequently the device became known as the Hilsch tube.

"The Hilsch tube in the illustration is constructed as follows. The horizontal arm of the T-shaped fitting contains a specially machined piece, the outside of which fits inside the arm. The inside of the piece, however, has a cross section which is spiral with respect to the outside. In the 'step' of the spiral is a small opening which is connected to the leg of the T. Thus air admitted to the leg comes out of the opening and spins around the one-turn spiral. The 'hot' pipe is about 14 inches long and has an inside diameter of half an inch. The far end of this pipe is fitted with a stopcock which can be used to control the pressure in the system. The 'cold' pipe is about four inches long and also has an inside diameter of half an inch. The end of the pipe which butts up against the spiral piece is fitted with a washer, the central hole of which is about a quarter of an inch in diameter. Washers with larger or smaller holes can also be inserted to adjust the system.

"Three factors determine the performance of the Hilsch tube: the setting of the stopcock, the pressure at which air is admitted to the nozzle, and the size of the hole in the washer. For each value of air pressure and washer opening there is a setting of the stopcock which results in a maximum difference in the temperature of the hot and cold pipes. When the device is properly adjusted, the hot pipe will deliver air at about 100 degrees Fahrenheit and the cold pipe air at about -70 degrees (a temperature substantially below the freezing point of mercury and approaching that of 'dry ice'). When the tube is adjusted for maximum temperature on the hot side, air is delivered at about 350 degrees F.

"Despite its impressive performance, the efficiency of the Hilsch tube leaves much to be desired. This perhaps explains why no one has mathematically analyzed its operation. Indeed, there is still disagreement as to how it works.

"According to one explanation, the compressed air shoots around the spiral and forms a high-velocity vortex of air. Molecules of air at the outside of the vortex are slowed by friction with the wall of the spiral. Because these slow-moving molecules are subject to the rules of centrifugal force, they tend to fall toward the center of the vortex. The fast-moving molecules just inside the outer layer of the vortex transfer some of their energy to this layer by bombarding some of its slow-moving molecules and speeding them up. The net result of this process is the accumulation of slow-moving, low-energy molecules in the center of the whirling mass, and of high-energy, fast-moving molecules around the outside. In the thermodynamics of gases the terms 'high energy' and 'high velocity' mean 'high temperature.' So the vortex consists of a core of cold air surrounded by a rim of hot air.

"The difference between the temperature of the core and that of the rim is increased by a secondary effect which takes advantage of the fact that the temperature of a given quantity of gas at a given level of thermal energy is higher when the gas is confined in a small space than in a large one; accordingly when gas is allowed to expand, its temperature drops. In the case of the Hilsch tube the action of centrifugal force compresses the hot rim of gas into a compact mass which can escape only by flowing along the inner wall of the hot pipe in a compressed state, because its flow into the cold tube is blocked by the rim of the washer. The amount of the compression is determined by the adjustment of the stopcock at the end of the hot pipe. In contrast, the relatively cold inner core of the vortex, which is also considerably above atmospheric pressure, flows through the hole in the washer and drops to still lower temperature as it expands to atmospheric pressure obtaining inside the cold pipe.

"Apparently the inefficiency of the Hilsch tube as a refrigerating device has barred its commercial application. Nonetheless amateurs who would like to have a means of attaining relatively low temperatures, and who do not have access to a supply of dry ice, may find the tube useful. It will deliver a blast of air 20 times colder than air which has been chilled by permitting it simply to expand through a Venturi tube from a high-pressure source. Thus the Hilsch tube could be used to quick-freeze tissues for microscopy, to chill photomultiplier tubes, or to operate diffusion cloud chambers. But quite apart from the tube's potential application, what could be more fun than to trap Maxwell's demon and make him explain in detail how he manages to blow hot and cold at the same time?"

In August it was stated in this department that if a rectangle is cut into strips, its area, as found by multiplying its length by its width, is not changed when the strips are pushed over to make a parallelogram. Many readers have asked why this should be so. The explanation is that the strips merely slide over one another and the pushing does not alter the sum of their widths [see illustration right]. Some readers were also puzzled by the fact that the resulting parallelogram was shown in the August issue with straight sides instead of the stepped edges depicted here. When the rectangle is sliced into strips of infinitesimal thickness, and has been pushed over, the ends of the strips form a row of mathematical points, which by definition constitutes a straight line. The notion of angular edges changing into straight lines when the number of strips reaches infinity appears to offend common-sense, and has baffled generations of students. But once the concept is grasped the battle with the calculus is half won.

Tarry Simpson of West Lafayette, Ind., submits a simple method of using the pocket-knife planimeter, also described in the August issue. One first draws a straight reference line from the center of the unknown area. The rounded edge of the big blade, fully opened, is put on the line. The point of the small blade at the other end of the knife is opened to make a right angle with the handle, and is placed on the end of the reference line inside the unknown area. The point of the small blade is used to trace the reference line to its intersection with the boundary, around the boundary, and back to the starting point. This action causes the big blade to take a zigzag path over the paper. It comes to rest at a perpendicular distance from the reference line which depends on the size of the unknown area. The handle of the knife then makes an angle with the reference line. Instead of computing the unknown area in terms of this angle, as described in the August issue, Simpson achieves substantially the same result by multiplying two lengths. "The area," he writes, "is approximately equal to the distance between the point of the little blade and the point at which the big blade touches the paper, multiplied by the perpendicular distance between the reference line and the point at which the big blade touches the paper after the figure has been traced. For relatively small angles between the knife handle and the reference line the error introduced by this additional approximation is small enough to neglect."

Most novices who set out to build a telescope select an instrument of the Newtonian type for their first project because of its simplicity and ease of construction. The Newtonian employs only three optical parts: the parabolic objective mirror which brings celestial objects to focus, a small diagonal mirror (or prism) which bends the converging rays at a right angle so the image can be viewed without obstructing the objective, and an eyepiece for examining the image. The performance of all telescopes depends primarily on the quality of the optical parts, particularly of the objective, which should not depart more than a fraction of a wavelength of light from the desired curvature. But performance is also affected by the design of the mounting-the structure which holds the optical elements in alignment and keeps them trained on the stars.

Every part of the mounting contributes to one or more aspects of the instrument's performance: the ease with which a desired star can be brought into the field of view and kept there, the steadiness of the image and its sharpness and freedom from distortion. It is relatively easy to design a mounting to maximize a given aspect of performance, such as steadiness of the image. Steadiness, for example, can be achieved by using heavy parts. But usually a gain in one aspect of performance is bought at some cost to another aspect, such as portability. As a consequence no two amateur instruments are precisely alike.

One disadvantage of nearly all reflecting telescopes is the necessity of supporting the diagonal mirror or prism in the aperture of the telescope. In this position the diagonal blocks part of the light entering the telescope. Moreover, rays which graze the diagonal err route to the objective are diffracted, or bent slightly, an effect which detracts from the sharpness of the image. It is possible to tilt the objective mirror somewhat and thus move its focal point outside the aperture without introducing a diagonal mirror into the optical system, but even a small tilt introduces serious distortion. Thus most amateurs use a diagonal, as Isaac Newton did, and support it by an assembly of sheet-metal arms attached to the inner wall of the telescope's main tube. The supporting arms, frequently assembled as a three-legged "spider," are set edgewise with respect to the entering rays to minimize the loss of light.

The spider arrangement leaves much to be desired as a support for the diagonal, however. Any bar which sticks into the aperture introduces diffraction and causes a streak of light to cross all bright star images Three bars make three streaks. When these are spaced 120 degrees apart, as in the conventional spider, bright stars have six long points. A spider of four bars set at right angles makes only four points, which might seem preferable to six. But the streaks of opposite pairs of bars fall on top of each other and reinforce the total light. Hence the designer must make a choice between six relatively dim streaks and four bright ones.

Under certain circumstances the presence of the streaks can prove useful. Brilliant stars appear as relatively large, diffuse disks on a photographic plate made with the unobstructed refracting telescope, and their centers are difficult to establish accurately. The streaks provide the astronomer with a convenient set of coordinates which aid in locating the star. But more often than not the streaks are a nuisance, as when one wishes to view the faint companion of a bright star such as Sirius or Polaris, and discovers that the position of the telescope is such that the faint star is lost in a bright streak. To solve the difficulty, the French astronomer A. Couder devised a set of specially shaped- masks to cover the four bars of his spider. They had the effect of dividing the telescope into four proportionately smaller instruments, each with an unobstructed aperture. This expedient eliminated the streaks, but at some cost in the sharpness of the images. Photographs made with the masks showed star images slightly more diffuse than those made without the masks.

Rene A. Wurgel of Union City, N.J., submits a diagonal support which also minimizes diffraction effects as well as the amount of light blocked off by the diagonal. "Neither reading the literature on telescope-making nor experimenting on one's own account assures that this is the best way to support a diagonal," he writes, "but in my experience it is clearly superior to the conventional three-arm spider.

"The support substitutes a short brass cylinder sandwiched between a pair of rings for the conventional spider arms [see illustration in Figure 3]. The rings are rigidly attached to the main tube by screws. Another set of screws fastens the inner side of the rings to the cylinder. One end of the cylinder is turned down, split and threaded to clamp a quarter-inch shaft which passes through the center. The lower end of the shaft screws into one end of a fiber cylinder, the other end of which is cut off at an angle of 45 degrees as a backing for the diagonal. The threaded portion of the shaft is locked into the fiber cylinder with a nut as shown. All adjustments of the mirror are made by means of sliding or rotating the shaft.

"The support includes no obstruction with a diameter greater than the minor axis of the diagonal mirror. This was achieved by the unorthodox method of taping the diagonal to the fiber cylinder. I used No. 810 Permanent Mending Tape, sold by the Minnesota Mining and Manufacturing Company. Do not try this with Scotch tape, or attempt to cement or glue the diagonal in place. Repeated trials proved to me that cement warps the mirror when it sets.

"Although the amount of light conserved by this arrangement is doubtless negligible, it is still satisfying to know that maximum light reaches the objective The real advantage of the system becomes apparent during the observation of double stars. With a run-of-the-mine eyepiece, a diagonal corrected to 1/8 wavelength, and a six-inch objective corrected to 1/12 wavelength, my instrument easily splits double stars with a separation of 7/10 second of arc and a difference in brightness amounting to one magnitude."

In these days of inexpensive surplus parts amateurs without access to machine tools can still have telescope mountings with most of the features found in professional instruments Such a mounting was built by Charles N. Fallier, Jr., of Hicksville, N.Y. [see illustration above]. "As mountings go," writes Fallier, "this one boasts nothing particularly noteworthy with the possible exception of the mechanism for driving the telescope in right ascension. This portion of the assembly is from a surplus panoramic telescope which had a 360-degree rotation and a 32 to 1 worm-and-gear drive with an attached circle calibrated in 100-mil divisions, all totally enclosed. For a clock drive a 48 to 1 reduction gear is substituted for the right-ascension knob and driven by a one-revolution-per-minute motor. The driving rate is not quite sidereal but close enough for casual observation. The gears came from the tuner of a surplus radio transmitter."

Bibliography

AMATEUR TELESCOPE MAKING-BOOK ONE. Edited by Albert G. Ingalls. Scientific American, Inc., 1957.

AMATEUR TELESCOPE MAKING-ADVANCED. Edited by Albert G. Ingalls. Scientific American, Inc., 1957.

AMATEUR TELESCOPE MAKING-BOOK THREE. Edited by Albert G. Ingalls. Scientific American, Inc., 1957.

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