This blog post is based on some early experimental writing that was done for my Falling Felines and Fundamental Physics book that was cut from the final draft! As you will see, it was much too long and too much of a digression to include in the book, so I’ve posted it here sorta as a preview of not-quite-the-book!

Some of the most fascinating physics demonstrations are some of the oldest. In my office, I have several versions of a device known as a Crookes radiometer, including both quality display pieces as well as a cheap plastic version.

A Crookes radiometer looks very much like a four-armed weathervane, each arm of the vane having a white side and a black side, or a glossy side and a matte side. The entire vane is contained within a thin glass (or plastic) case. When direct light, from the sun or a flashlight, is shined upon the device, it begins to rotate: it is a device whose movement is entirely powered by light!

Though the radiometer is simple in design, its discovery resulted in an epic 50 year history of physicists attempting to adequately explain the origin of its motion. The device would attract the interest of some of the most famous scientists of its time, and provoke lively scientific arguments. It is, in fact, a good illustration of how the solution of problems in physics can often be trickier than they first appear to be!

The radiometer is named after its discoverer, the British chemist and physicist William Crookes (1832-1919). Like many scientists of his era, the London-born Crookes spurned the desires of his family, who wanted him to be an architect, and instead enrolled in the Royal College of Chemistry in 1848, working under one Professor Hofmann. He evidently made excellent progress, as he became an assistant in the college in 1850 and held the position until 1854. From there, he became the Superintendent of the Meteorological Department at the Radcliffe Observatory for a short time, and then a Lecturer in Chemistry at Chester Training College in 1855.

Were it not for twists of fate and Crookes’ temperament, he might have been famous in a very different field of study. He was born in the era of rapid progress in photography, and he developed a love for the science and application of the technology. His enrollment in the Royal College of Chemistry was motivated by the desire to learn more about the chemistry of photography, and together with a classmate he engaged in photographic experiments through his entire time there. By 1855, he was suitably well-known in the field to serve as a witness in a trial over the patents of the groundbreaking photographer William Henry Fox Talbot. In 1857, the War Department was interested in improving artillery by studying the flight of shells photographically, and Crookes successfully took on the task, making him an early pioneer in high-speed photography, ahead of the masters of the field Edweard Muybridge and Etienne-Jules Marey.

However, Crookes needed to make a living, and he supported himself as the editor of photographic journals. He began in 1857 as the editor of the London Photographic Society, but was fired a year later due to a dispute over whether their journal should emphasize the art or science of photography; Crookes, clearly, was in favor of science, but he lost to the more artistic members of the society. He moved to the editorship of a new journal, the Photographic News, that same year, and in 1859 started his own journal, Chemical News, to supplement his income. The latter act, however, led Crookes to put the best articles on photography in his own journal, which in turn led the proprietors of the Photographic News to fire him in 1860. Crookes sued his former employers, to no avail; after that, he was for a time supported by his own journal.

The story of the radiometer begins in an unlikely place: the processing of a quantity of raw ore. In 1850, Crookes obtained about 10 lbs. of ore from Professor Hofmann, with which he worked to extract a quantity of the element selenium for chemistry experiments. This study, in fact, resulted in Crookes’ first published scientific work, which appeared in 1852. The processing of selenium from the ore left behind a small amount of leftover residue that Crookes suspected contained a quantity of the element tellurium; the thrifty Crookes put aside this residue for further study.

He did not return to it for a full decade. In 1861, however, needing tellurium for some other experiments, Crookes attempted to extract it from the residue. To test for the presence of the tellurium, he turned to the technique of spectrum-analysis. Every atom and molecule has characteristic frequencies, or colors, of light at which they emit and absorb radiation, a sort of “optical fingerprint” that uniquely identifies them. By burning an unknown substance, it is sometimes possible to deduce the constituent parts from the colors of the light emitted in the combustion; a device called a spectroscope can be used to spatially separate the colors on a screen, where they appear as isolated bright lines. When Crookes did this with his sample, what followed was unexpected and momentous; in his own words [1],

A portion of the residue, introduced into a blue gas-flame, gave abundant evidence of selenium; but as the alternate light and dark bands due to this element became fainter, and I was expecting the appearance of the somewhat similar, but closer, bands of tellurium, suddenly a bright green line flashed into view and as quickly disappeared. An isolated green line in this portion of the spectrum was new to me.

What Crookes had inadvertently discovered was a previously unknown metallic element, which would be given the name thallium. Today, thallium is used in optics, electronics, and medicine; in Crookes’ time, its most practical application was vaulting him into scientific celebrity status almost overnight. In short order, Crookes displayed his new element at the 1862 world’s fair known as the Great London Exhibition. His work appeared alongside other impressive discoveries such as the electric telegraph, the first man-made plastic, one of the earliest refrigerators, and parts of Charles Babbage’s analytic difference engine; even in this formidable company, Crookes won an award for his discovery. By 1863 he was elected a Fellow of the Royal Society, a remarkable twist for a person who essentially did science as an amateur occupation.

In the discovery of a new element, one of the most important properties to measure is the element’s atomic weight. Crookes set himself upon this task with admirable diligence and thoroughness, and only presented his results over a decade later, in 1873, in a paper [2] with the to-the-point title, “On the atomic weight of thallium.” He used two different techniques to weigh the substance and found the results of the two agreed sufficiently well to remove any doubt as to their accuracy.

In his work, Crookes used a pair of balances, one which functioned in air and one which functioned in a vacuum; both were designed to weigh exceedingly small quantities of material, and were highly sensitive. In working with the vacuum balance, Crookes found a very unusual result, which he noted only briefly in this paper.

In particularly describing the vacuum-balance, I have one peculiarity to note in relation to the effect of heat in diminishing the weight of bodies. That a hot body should appear to be lighter than a cold one has been considered as arising from the film of air or aqueous vapour condensed upon or adhering to the surface of the colder body, or from the upward currents of air caused by the expansion of the atmosphere in the vicinity of the heated body. But neither hypothesis can be held when the variation the force of gravitation occurs in a vacuum as perfect as the mercurial register, and under other conditions which I am now supplying, and which embodying in a paper to be submitted to the Royal Society during a subsequent session.

In short: researchers had long been aware that the weight of objects can appear to change in the presence of heat or cold, and this had been taken to be the effect of thermal motion of the air. But Crookes found these effects still existed even in a vacuum, where no air currents should be present. What, then, was causing the weight change, or force, on the objects?

 

Crookes immediately set out on a series of experiments [3] to find out. He designed a novel balance consisting of two pith balls of equal mass on either end of a balance arm, contained entirely in a glass tube which could be evacuated. One of the balls could be brought into contact with a heated or cooled mass within the tube, allowing for any apparent change of weight of the ball to be observed by a change in the tilt of the balance arm. The initial results were somewhat curious: when in air of ordinary density, the ball appeared to be repelled by a cold mass and attracted by a hot mass; when in a vacuum, the ball appeared to be attracted by a cold mass and repelled by a hot mass. To Crookes, this seemed to indicate that air currents played a role in the former case, but that some new fundamental force related to temperature was dominant in the latter. He even tentatively speculated that this new force might be some alternative manifestation of gravity.

Crookes made his first demonstration of his discovery at the annual soirée of the Royal Society on April 22, 1874. By placing a candle underneath one end of his vacuum balance, he could get the balance to tilt and show that hot objects apparently cause repulsion. The public display was a sensation, but it also led to the first challenge of Crookes’ work, from soirée attendee Professor Osborne Reynolds. At the soirée, Reynolds noted that the balance seemed to oscillate continuously when exposed to a steady flame. But objects exposed to a steady force, like a pendulum under the influence of gravity, eventually settle into a non-moving position; the fact that Crookes’ radiometer did not do so suggested to Osborne that it was still being subjected to thermal forces due to heating and cooling. He speculated that the motion of the pith balls used in Crookes’ demonstration was due to condensed water on their surface evaporating when exposed to heat; this flight of molecules from the surface would cause the balls to recoil, producing the observed effect. In quite a rapid turnaround, Reynolds presented his results [4] to the Royal Society on May 16, 1874, less than a month after the soirée.

Crookes presented a rebuttal in August of 1874 [5]. From the text, it appears that he was somewhat offended that anyone might imagine that he could be so careless as to not have considered and eliminated evaporation as a possible cause:

It does not appear that Professor Reynolds has tried more than a few experiments; and he admits that they were in reality undertaken to verify the explanation above quoted. I have worked experimentally on this subject for some years; and the last experiment recorded in my notebook is numbered 584.

Crookes argued that he had, in fact, carefully flushed all the moisture out of his tubes in a variety of ways, and with a variety of gases. In the same paper, he also presents arguments against the simple “air currents” explanation, and against the possibility that subtle electrical forces might be playing a role.

Thus satisfied, Crookes continued his experiments, presenting part II of his series of papers on April 22, 1875 [6]. At this stage, the word “attraction” disappeared from the titles of Crookes’ papers, coinciding with his new view that everything could be explained by the direct pressure of radiation upon the balance itself. The attraction created by a cold body, in Crookes’ eyes, was the result of the cold object cutting off the influx of heat-rays from that side of the pith ball, making the pressure on the opposite side greater.

By this time Crookes had come to the conclusion that the forces he was observing were the direct result of the momentum of light. In formulating his famous set of equations demonstrating the existence of electromagnetic waves in 1861, James Clerk Maxwell had also shown that such waves must carry momentum, and consequently exert a pressure on anything they illuminate. When you stand outside in the sun, the sunlight is exerting a force on you; this force is so small, however, that it does not cause any noticeable effect in daily life. For the tiny balance that Crookes was using, however, it was reasonable to think that he might be seeing, for the first time, direct experimental evidence of this force.

Crookes himself was unusually coy in his explanations, however, for reasons which will be suggested later. At the end of his paper, he simply notes,

Facts tested and verified by numerous experiments, but scarcely more than touched upon in the present paper, are, I think, gradually shaping themselves in order, in my mind, and will, I hope, aid me in evolving a theory which will account for all the phenomena. But I wish to avoid giving any theory on the subject until I have accumulated a sufficient number of these facts. The facts will then tell their own tale; the conditions under which they invariably occur will give the laws; and the theory will follow without much difficulty.

At last, on February 10, 1876, in the third part of his series of presented papers [7], Crookes officially introduced the first form of his radiometer, and gave it its name. His original figure is illustrated below; he also referred to it, for obvious reasons, as a “light-mill.” The device had already been previewed to the scientific community at another Royal Society soirée in mid-1875, where it received international attention and acclaim.

With the view that radiation was driving his device, Crookes had painted alternate sides of the radiometer vanes white and black to enhance the effect. When a particle of light hits the black surface of the vane, it is absorbed and transfers all of its momentum to the vane; when a particle of light his the white surface, however, it is reflected back, and by conservation of momentum it transfers twice as much momentum to the vane. The radiometer should therefore spin in the direction that the dark sides of the vanes are facing.

But there was a problem with interpreting the radiometer’s rotation as the result of radiation pressure: it was spinning in the wrong direction! If it were truly light pressure that was driving the device, the black surfaces should have been leading the white surfaces; in actual operation, the opposite was seen.

Crookes, remarkably, tried to explain this with a complete confusion of energy and momentum. In his own words,

Light falls on the black and white surfaces of a radiometer, or other similar instrument. That which falls on the white surface is nearly all reflected back again. Were the surface perfectly white all the force which went into the bulb would be reflected out again; the incident ray would contain in itself a certain amount of potential work; but as the emergent beam would come out with no loss of intensity, no work could have been done on the reflecting surface…

But in the case of light falling on the lampblacked surface the result is very different. Here, practically, the whole of the light is quenched by the lampblack. Force is poured into the bulb, but none comes out. When, then, becomes of it? It is changed into motion, and becomes evident in the strong repulsion which is exerted on the black surface.

Crookes seems to have confused absorption of energy with absorption of momentum, and argues that because the black side absorbs more energy, there is more force upon it, when in fact the opposite is true.

Confusion or no, the question of “radiation pressure or air pressure?” was definitively put to rest by Arthur Schuster of Owens College, who on March 23, 1876 presented the results [8] of his own ingenious experiments to determine the origin of the force on the radiometer. Schuster placed a radiometer in a bed of oil, so that the glass case, as well as the vanes, could rotate somewhat freely. Schuster’s reasoning was as follows. If light rays were directly making the vanes move, then as they started to turn, they should convey some of that rotation to their axis through friction, and the case should rotate in the same direction as the vanes. If it is in fact an effect of air currents making the vanes move, then by conservation of angular momentum the air currents should circulate in the opposite direction as the vanes, partially transfer some of this circulation to the case through friction, and the case should rotate in the opposite direction as the vanes. Schuster found the latter situation to be true: somehow, air currents were driving the motion of the radiometer.

To Crookes’ credit, he seems to have quickly recognized his mistake, and he rapidly followed up with a new experiment [9] very similar to Schuster’s to verify the results; this work was received March 30, 1876. Crookes floated his entire radiometer in a vessel of water, which would allow the glass case to rotate as well as the vanes of the radiometer. Crookes used a magnet to turn the vanes of the radiometer; he found that the case ended up counter-rotating at the same time. Apparently, though he had originally thought that his radiometer was operating in a vacuum, there was sufficient air remaining to be pushed around by the moving radiometer vanes and, through friction, to cause the surrounding glass case to move. Though Crookes had originally ruled out air currents as having any effect on his device, clearly that conclusion was mistaken.

One possible way that air could still be affecting the radiometer had already been proposed, almost as an afterthought, by Osborne Reynolds in his 1874 paper. On March 23, 1876, he presented his thoughts in more detail [10] to the Royal Society. The reasoning he presented is roughly as follows. When illuminated with light, the black side of each vane will absorb more energy than the white side, and the black side will consequently be hotter than the white side. Each side of the vane is constantly being bombarded with the residual gas molecules in the radiometer, and those molecules can pick up some of the thermal energy from the vane during a collision. Molecules hitting the black side will on average gain more energy than those hitting the white side, and recoil with more momentum; there will consequently be a stronger force pushing the black side than the white side. The radiometer is predicted to rotate with the white faces leading, in agreement with what is actually observed.

This explanation was considered quite satisfying by most scientists of the era, including Crookes himself, and some still use it in modern times as an explanation of the operation of the radiometer. Unfortunately, it is also wrong! The first hint at a problem had already been proposed [11] in 1875 by the prominent Scottish theoretical physicist Peter Guthrie Tait and the Scottish chemist James Dewar. The latter scientist is familiar to many chemistry students as the inventor of the Dewar flask; other people unknowingly use this same invention to keep their favorite beverages hot or cold in the form of a thermos.

Tait and Dewar noted, somewhat obliquely, that the faster-moving molecules rebounding off of the hot surface of a vane are consequently more effective at stopping additional particles from hitting the surface in the first place. The hot molecules act as a sort of “molecular artillery barrage” that reduces the number of impacts on that face. The result is that the pressure on the black face of a radiometer vane is in fact not much different than the pressure on the white side, and the difference is not enough to account for the observed rotation of the radiometer.

Ironically, though Osborne Reynolds was the one who suggested that the imbalance of pressures was causing the radiometer to move, he would eventually argue against his own hypothesis. In a lengthy paper published in 1879, Reynolds imagined [12] a pair of plates of infinite size, parallel to one another, as illustrated below. If Reynolds’ original argument holds, one would expect that the hot plate would feel more pressure than the cold plate, and that the pair of them would experience a spontaneous net motion to the left. But, because the plates are infinite, the gas between them would be trapped and also move to the left; there would be nothing moving to the right, and the system would violate the conservation of momentum.

Reynolds noted that the same argument would not necessarily hold for plates of finite size. His argument was recognized as significant by none other than James Clerk Maxwell who, in 1879, added an appendix to one of his own papers [13] noting that the edges of the vanes of a radiometer must be where all the force is directed.  Roughly speaking, the “molecular artillery barrage” would not function along the narrow edges of the vanes, allowing air molecules to pick up energy and provide the kick needed to turn the device.

These arguments did not convince everyone. Crookes held onto Reynolds’ interpretation, having been impressed by an incorrect argument [14] by G. Johnstone Stoney from 1876, in which he argued that the “artillery barrage” of particles recoiling off of a hot surface was not effective at sufficiently low pressures. Crookes also was too busy trying to find practical uses for his invention to bother properly explaining it: in his 1876 patent publication, Crookes suggests, for example, that a radiometer stationed in photographic darkrooms could be used to detect any harmful light leaking within.

After this, discussion of Crookes’ radiometer settled down for a while, as other fundamental discoveries in physics caught the attention of the scientific community, such as radioactivity, X-rays, quantum physics, and special relativity. It was not until the 1920s that researchers would return to the problem and tackle it with some rigor. Albert Einstein himself got into the debate, making simple and elegant arguments [15] that all of the force on the radiometer must be applied at the edges.  But how could this be proven?

In 1925, H.E. Marsh, E. Condon and L.B. Loeb confirmed the edge hypothesis [16], and more or less provided the final, satisfactory explanation of the radiometer with an ingenious experiment. They designed a collection of radiometer vanes with edges of different length but similar surface areas, as illustrated below. If the radiometer force arose primarily from the surface of the vanes, then the different vanes should have turned at same same rotation speed.  If the radiometer force instead arose primarily from the edges of the vanes, then each vane should turn at a different rotation speed for the resulting radiometers; this latter result was in fact found to be the case.

Overall, then, though most of the work on Crookes’ radiometer occurred in a flurry of activity between 1873 and 1876, it took over fifty years total for the question “how does a radiometer work?” to be answered satisfactorily. For me, this is an illustration of an interesting issue in physics. Physicists often attempt to understand a physical phenomenon by forming a simple hypothesis and then designing an experiment to isolate and test that hypothesis. But in some real-world systems, like Crookes’ radiometer, the phenomenon can resist a simple explanation, and it can take quite a bit of time to build a model sophisticated enough to explain everything that is observed.

Muddying the Crookes radiometer waters even further, so to speak, is that it is in fact possible to make a Crookes-type radiometer which is turned entirely by the radiation pressure of light! This was successfully achieved in 1901 by P.N. Lebedev [17], using newer and more advanced vacuum pump technology to eliminate all air effects from the device.  Such a radiometer turns in the direction you would expect, with the black sides leading the white sides.

One interesting footnote to this whole strange story: what drove Crookes to study the radiometer so thoroughly in the early years of its discovery, and why was he so coy in his explanation of its operation? In 1869, after the death of a beloved brother, Crookes became involved in the spiritualism fad that had swept the western world at the time, presumably to make contact with his departed relative. By 1870, he had decided to subject the spirit mediums he was interacting with to the same scientific scrutiny with which he was investigating the weight of thallium, and this would be a passion that would drive — and haunt — him for the rest of his life.

In the operation of his vacuum balance, he evidently saw a way to explain and even quantify the motion of objects by unseen spirits in seances. In an article [18] he wrote in 1870 in defense of his supernatural research, “Spiritualism viewed by the light of modern science,” he practically proclaims a connection between the spirit world and his new discovery,

The spiritualist tells of bodies weighing 50 or 100 lbs. being lifted up into the air without the intervention of any known force; but the scientific chemist is accustomed to use a balance which will render sensible a weight so small that it would take ten thousand of them to weigh one grain; he is, therefore, justified in asking that a power, professing to be guided by intelligence, which will toss a heavy body up to the ceiling, shall also cause his delicately-poised balance to move under test conditions.

Note that he is explicitly drawing a parallel between the forces on his delicate balances and the motion of bodies by spirits! Though he would quickly put aside his supernatural explanation of the radiometer in favor of more physical ones, he would continue to study — and be duped — by spiritualists for the rest of his life… but that is a story for another time!

Crookes himself, though he was subjected to significant criticism and attacks from the scientific community due to his beliefs, nevertheless managed to thrive. His work on the Crookes radiometer led him to study the motion of molecules through highly evacuated glass tubes, which became known as Crookes tubes. These Crookes tubes were used to investigate mysterious particles known as “cathode rays,” later identified as electrons, and the collision of cathode rays with the walls of the glass tube led to the inadvertent discovery of X-rays by Röntgen in 1895. That same year, Crookes would correctly identify the first known terrestrial sample of helium gas. Furthermore, in 1903 Crookes would invent another remarkable physics demonstration device, that allows one to observe the individual decays of radioactive atoms — the spinthariscope!

In the end, in spite of his failings as an investigator of spirits, Crookes was simply too good a scientist to be ignored, dismissed, or disparaged altogether.  And his radiometer showed that even the best scientists could be baffled at times by seemingly mundane phenomena!

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[1] W. Crookes, “On the existence of a new Element, probably of the Sulphur Group,” Phil. Mag.  21 (1861), 301–305.

[2] W. Crookes, “On the atomic weight of thallium,” Phil. Trans. Roy. Soc. Lond. 163 (1873), 277–330.

[3] W. Crookes, “On attraction and repulsion resulting from radiation,” Phil. Trans. Roy Soc. Lond. 164 (1874), 501–527.

[4] O. Reynolds, “On the forces caused by evaporation from, and condensation at, a
surface,” Proc. Roy. Soc. Lond. 22 (1874), 401–407.

[5] W. Crookes, “On attraction and repulsion accompanying radiation,” Phil. Mag. 48 (1874), 81–95.

[6] W. Crookes, “On repulsion resulting from radiation,” Phil. Trans. Roy. Soc. Lond.  165 (1875), 519–549.

[7] W. Crookes, “On repulsion resulting from radiation – Parts III. & IV,” Phil. Trans. Roy. Soc. Lond. 166 (1876), 325–376.

[8] A. Schuster, “On the nature of the force producing the motion of a body exposed to
rays of heat and light,” Phil. Trans. Roy. Soc. Lond. 166 (1876), 715–724.

[9] W. Crookes, “On the movement of the glass case of a radiometer,” Proc. Roy. Soc. Lond. 24 (1875-1876), 409–410.

[10] O. Reynolds, “On the Forces Caused by the Communication of Heat between a Surface and a Gas; And ona New Photometer,” Phil. Trans. Roy. Soc. Lond. 166 (1876), 725-735.

[11] P.G. Tait and J. Dewar, “Charcoal vacua,” Nature 12 (1875), 217.

[12] O. Reynolds, “On certain dimensional properties of matter in the gaseous state.
Part I. Experimental researches on thermal transpiration of gases through porous plates and on the laws of transpiration and impulsion, including an experimental proof that gas is not a continuous plenum,” Phil. Trans. Roy. Soc. Lond.  170 (1879), 727–845.

[13] J.C. Maxwell, “On stresses in rarified gases arising from inequalities of temperature,” Phil. Trans. Roy. Soc. Lond. 170 (1879), 231–256.

[14] G. Johnstone Stoney, “On Crookes’s radiometer,” Phil. Mag. 1 (1876), 177–181.

[15] A. Einstein, “Zur Theorie der Radiometerkräfte,” Z. Phys. 27 (1924), 1–6.

[16] H.E. Marsh, E. Condon, and L.B. Loeb, “The theory of the radiometer,” J. Opt. Soc. Am. 11 (1925), 257–262.

[17] P.N. Lebedev, “Untersuchungen über die Druckkräfte des Lichtes,” Ann. Phys.  6 (1901), 433–458.

[18] W. Crookes, “Spiritualism viewed by the light of modern science,” Q. J. Sci. 7 (1870), 316–321.