# Did George Biddell Airy write a paper "On Certain conditions under which a Perpetual Motion is possible"?

George Biddell Airy was an English mathematician. He was Astronomer Royal from 1835 to 1881

According to the Bessler Wheel web-site (a site dedicated to investigationg perpetual motion machines, Airy wrote the paper titled On certain Conditions under which a Perpetual Motion is possible, published in Cambridge Philosophical Transactions, December 14, 1829. They provide scans of the paper:

It is well known that perpetual motion is not possible with any Laws of force with which we are acquainted. The impossibility depends on the integrability per se of the expression Xdx + Ydy + Zdz: and as in all the forces of which we have an accurate knowledge this expression is a complete differential, it follows that perpetual motion is incompatible with those forces.

But it is here supposed that, the law of the force being given, the magnitude of the force acting at any instant depends on the position, at that instant, of the body on which it acts. If however the magnitude of the force should depend not on the position of the body at the instant of the force's. action, but on its position at some time preceding that action, the theorem that we have stated would no longer be true. It might happen that, every time that the body returned to the same position, its velocity would be less than at the preceding time: in this case the body's motion would ultimately be destroyed. On the contrary it might happen, that the body's velocity in any position

I am skeptical that this was originally written by Airy because of its impenetrable style and it is apparently nonsense.

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– Jamiec
Commented Jun 5, 2020 at 10:04

The claim that George Biddell Airy wrote a paper titled “On certain Conditions under which Perpetual Motion is possible” which was published in the Transactions of the Cambridge Philosophical Society is true. The full text of the (short) paper can be read on Google Books.

The claim that this is a “rigorous mathematical proof of the theoretical possibility of perpetual motion” is a stretch. Airy's paper is an investigation into a mathematical model. Airy does not claim that perpetual motion is physically possible. He merely investigates under what conditions one particular mathematical model would lead to a situation where a “machine might move with uniform velocity, and might at the same time do work: which is commonly understood to be the meaning of the term perpetual motion”.

Note that this isn't exactly what perpetual motion means in modern terms: perpetual motion is about creating energy. Airy's definition only takes some forms of energy into account (kinetic energy in the motion of the machine, and the “work” performed by the machine, but not necessarily, for example, electromagnetic forces).

Airy analyses a physical system and states that it obeys a certain mathematical equation. He analyses the possible solutions and concludes that, under a certain assumption (“on the supposition that g is small”)

I shall only remark that if c√e be less than π, the arc of vibration increases continually.

Airy does not claim that it is physically possible for c√e to be less than π and that this would be compatible with the assumption that g is small.

Furthermore, even if the arc of vibration increases continually, this might not be perpetual motion. It is possible that the analysis was missing some of the forces through which energy can be transferred. Airy does not clearly state whether he believes that the analysis of forces is complete.

• "Airy does not claim that perpetual motion is physically possible." As I expected... But the style of the paper is (I will say it again) impenetrable. And the “rigorous mathematical proof of the theoretical possiblity of perpetual motion” is... [insert here some appropriate adjective]. Commented May 27, 2020 at 10:49
• @Martín-Blas Pérez Pinilla: "Impenetrable style" is perhaps an artifact of the reader. I find the quoted excerpt quite clear, at least as academic writings go. Commented May 27, 2020 at 16:28
• @Martín-BlasPérezPinilla how many academic papers from ~1830 have you read? Academic writing tends to be dense even today, and going further back in time tends the make the language even more flowery/dense/odd Commented May 27, 2020 at 18:10
• @mbrig, none! See my comment -> Nate Eldredge. Commented May 27, 2020 at 18:13
• The c√e assumption is not so remarkable, and it is mostly saying that the driving force does not depend on something too far into the past (assuming a periodic-ish solution, that it only looks up to a half of a cycle in the past). The much bigger assumption is that there is a way for a system to have a force proportional to a previous position -- likely it takes external energy to apply a force like this through time. I have a short analysis over at physics.stackexchange.com/a/555549/265876 Commented May 28, 2020 at 23:10

Airy's official autobiography, edited by his son Wilfrid and published in 1896, contains an appendix listing every paper that Airy ever published, along with when and where he published them.

On certain Conditions under which a Perpetual Motion is possible is listed partway down page 374:

So yes, George Biddell Airy really did write that paper. This doesn't mean that he believed perpetual motion was actually possible - he said as much at the start of the section you quoted:

It is well known that perpetual motion is not possible with any Laws of force with which we are acquainted.

By "certain conditions", he's referring to hypothetical changes to the Laws of forces, not to any actual real-world force.

• Looking at the excerpt quoted in the question, it is entirely possible that the paper is abn investigating in to the mathematical forms of laws that could lead to perpetual motion, rather than a claim that any such laws actually exist or are possible. I don't know what the paper actually says, but a conclusion of "perpetual motion requires forces with these properties, and electromagnetism doesn't have those properties, so you can't get perpetual motion using electromagnetism" could well be consistent with the title. Commented May 27, 2020 at 7:46
• Thanks for your effort. I will accept the other answer because is more focused on my doubts. Commented May 27, 2020 at 14:50
• @PhillS actually electromagnetism has these kinds of forces (only the backreaction prevents perpetual motion). Commented May 28, 2020 at 12:06
• Note that Airy does not claim that perpetual motion is possible - it seems he's just having a bit of fun playing with the math to see what would have to happen to allow perpetual motion. Commented May 29, 2020 at 12:42
• I must confess that I didn't actually read the paper - it wasn't necessary to do so in order to establish whether Airy wrote it, which was OP's primary concern. I've heavily revised the last section of my answer to properly address its contents, as per your comments. Commented May 29, 2020 at 12:52