These three celebrated problems have received the attention of mathematicians in every age and country, and led to many learned discussions, and controversial writings. But in point of litigiousness the Squarers of the Circle most decidedly carry off the palm, having frequently laid and lost heavy wagers, and even appeared in a Court of Justice to settle their monetary disputes. They are renowned for their pamphlets, in which philosophers of every class are charged with prejudice, conceit, and ignorance, and denounced for their want of candour and consistency in not giving audience to the projector of the last best demonstration.
PERPETUUM MOBILE.
To conclude this Lecture we shall offer a few remarks on Perpetuum Mobile, or the search for a means of obtaining a mechanical perpetual motion. As a mathematical problem it dates back some 2000 years or more, but we know nothing of any actual attempt earlier than the 14th century to construct a machine intended to be self motive, by containing within itself the means of continually overbalancing. External motive agency such as the tides, magnetism, and the like are not included; the only admitted agent being gravity.
If we considered wear and tear the question would be settled at once, but this is allowed as the single exception, and therefore any machine constantly renewing the means that first moved it might be deservedly called a perpetual motion.
Until a history of the schemes invented by numerous ingenious mechanics was published in 1861, inventors of this class were continually though unconsciously reproducing obsolete contrivances, from taking up the ordinary idea that a wheel may be kept constantly over-weighted on one side, so as to raise the next weight which is to perform the same miracle of art. It is singular to observe this particular coincidence of the inventive faculty of man, and it shows next to a demonstration, that if all mechanical inventions were swept from the face of the earth they would be reproduced in some remote age.
A common error with those who toil at perpetual motion machinery is their aiming to produce a bottled-up power; or to apply the principles of the ordinary scale or balance to a wheel, overlooking the simple facts of friction on one side acting against their most ingenious contrivances, and of non-production on the other. Sooner or later, however, they discover the inertia of matter, that a pound will not raise a pound, and that they cannot invent mechanism to move independently of the laws of action and reaction.
A ball descending a semicircular path, as suggested by Dr. Henderson, will only rise to the same height as that from which it fell; and will afterwards gradually diminish in velocity until it rests at the centre. If it would ascend to a height greater than that from which it descended, then indeed an inclined path might return the ball to repeat such evolutions until quite worn out.
And as regards the weighted wheels, it is always overlooked that they come to rest from the same fact, that the vertical line of descent and that of ascent are equal, however much the weights may on one side recede from the centre, while on the other side the weights are approaching the centre. (See [Plate 6], Fig. 1.)
The most famous perpetual motive schemes were those of the Marquis of Worcester made 1630-41; (See [Plate 6], Fig. 2,) and of Bessler, better known as Orfyreus, between 1712-19.
The Marquis gives a brief notice of his plan, in his "Century of Inventions," a curious catalogue of his several ingenious schemes.