things being presupposed (says Ber noulli), I thus construct a perpetual motion. Let there be taken in any (if you please, in equal) quantities two liquids of different densities mixed together (which may be had by hyp. 4), and let the ratio of their densities be first determined, and be the heavier to the lighter as G to L, then with the mix ture let the vase AD be filled up to A. This done let the tube EF, open at both ends, be taken of such a length that AC:EF>2L:G+L; let the lower orifice F of this tube be stopped, or rather cov ered with the filter or other material sep arating the lighter liquid from the heavier (which may also be had by hyp. 5) ; now let the tube thus prepared be immersed to the bottom of the vessel CD; I say that the liquid will continually ascend through the orifice F of the tube and overflow by the orifice E upon the liquid below.
Bernoulli then proceeds to apply this theory to explain the per petual rise of water to the mountains, and its flow in rivers to the sea, which others had falsely attributed to capillary action—his idea being that it was an effect of the different densities of salt and fresh water.
One really is at a loss with Bernoulli's wonderful theory, whether to admire most the conscientious statement of the hypothesis, the prim logic of the demonstration, so carefully cut according to the pattern of the ancients, or the weighty superstructure built on so frail a foundation. Most of our perpetual motions were clearly the result of too little learning; surely this one was the product of too much. (G. CO The foregoing article by the distinguished mathematician George Chrystal, who died in 1911, is devoted to a delusion which is still distressingly prevalent. A certain number of weak heads genu inely succeed in deceiving themselves with the old fallacies, and often spend money which they can ill afford in taking out patents for patent absurdities. No man of science who has any suscepti bilities can receive their communications without a certain com passion. On the other hand we have the conscious charlatans, who prey upon a class of people, by no means extinct, which pos sesses great cupidity, some money, a dangerous smattering of science and no sense. The form under which the perpetual motion is presented for the benefit of the credulous and affluent has been modified of recent years, to keep pace with the march of science.
Whereas formerly the perpetual motion engine was usually a me chanical arrangement of weights, wheels and water-buckets, or such like, which did work without a supply of energy, to-day the form under which the invention is presented is usually an elec trical one. Frequently the vendor or inventor makes no claim to create energy out of nothing, a point to which he directs special attention, admitting that this is known to be impossible by such shrewd and learned men as the prospective purchaser of shares, but states that his machine takes in a certain amount of electrical energy and turns out a greater amount of energy—a steady supply of 2o kilowatts is turned into an output of 37.5 kilowatts, say. The popular confusion between work and power, and between volts and amperes and electrical energy renders it easy to delude the self-satisfied victim, and the plausible denial of any creation of something out of nothing makes the creation of much out of little seem comparatively reasonable.
The latest scientific invention is often made the basis of a per petual motion claim, in more or less good faith. For instance, shortly after the liquid air machine became a commercial suc cess, claims are put forward—not by the inventor of the ma chine, of course—that part of the air liquefied by such a machine could be made to furnish a source of motive power which would run the machine itself, so that a continuous and increasing supply of liquid air could be produced without input of energy, once the machine was started.
The kind of perpetual motion which has been considered in Professor Chrystal's article is against all the ordered experience which is embodied in the first law of thermodynamics. This law states the equivalence of heat and work as alternative forms of energy, and denies that energy can be created. There is, how ever, nothing in the first law of thermodynamics against the fol lowing line of argument : Heat is equivalent to work. It is possible to build machines which turn heat into work. Therefore it must be possible to build a machine which will take heat from some ordi nary body at atmospheric temperature, say a pond, and turn it into work. The pond will, of course, grow colder, but this need not disturb us, as for a very slight cooling we should obtain a large amount of work. For instance, a pond 200 yards across and of an average depth of 6 feet, cooling I° centigrade, would yield 75,00o horse-power-hours if the heat lost could all be turned into work. It is usual to speak of a machine which could convert the heat of surrounding bodies into work as effecting a perpetual mo tion of the second kind, perpetual motion of the first kind being that which creates energy out of nothing. A perpetual motion of the second kind involves no creation of energy, but a conversion of energy under certain conditions.