semblance between Jupiter and our earth, we may safely (so far as our inquiry is concerned) proceed on the assumption that the atmosphere of Jupiter does not differ greatly in constitution from that of our earth. We may further assume that, at the upper part of the cloud-layers we see, the atmospheric pressure is not inferior to that of our atmosphere at a height of seven miles above the sea-level, or one-fourth of the pressure at our sea-level. Combining these assumptions with the conclusion just mentioned, that the cloud-layers are at least 100 miles in depth, we are led to the following singular result as to the pressure of the Jovian atmosphere at the bottom of the cloud-layer: The atmosphere of any planet doubles in pressure with descent through equal distances, these distances depending on the power of gravity at the planet's surface. In the case of our earth, the pressure is doubled with descent through about 3 miles; but gravity on Jupiter is more than 2 times as great as gravity on our earth, and descent through If mile would double the pressure in the case of a Jovian atmosphere. Now, 100 miles contain this distance (If mile) more than seventy-one times; and we must therefore double the pressure at the upper part of the cloud-layer seventy-one successive times to obtain the pressure at the lower part. Two doublings raise the pressure to that at our sea-level; and the remaining sixty-nine doublings would result in a pressure exceeding that at our sea-level so many times that the number representing the proportion contains twenty-one figures.[1] I say would result in such a pressure, because in reality there are limits beyond which atmospheric pressure cannot be increased without changing the compressed air into the liquid form. What those limits are we do not know, for no pressure yet applied has changed common air, or either of its chief constituent gases, into the liquid form, or even produced any trace of a tendency to assume that form. But it is easily shown that there must be a limit to the increase of pressure which air will sustain without liquefying. For the density of any gas changes proportionately to the increase of pressure until the gas is approaching the state when it is about to turn liquid. Now, air at the sea-level has a density equal to less than the 900th part of the density of water; so that, if the pressure at the sea-level were increased 900 times, either the density would not increase proportionally, which would show that the gas was approaching the density of liquefaction, or else the gas would be denser than water, which must be regarded as utterly impos-
- ↑ The problem is like the well-known one relating to the price of a horse, where one farthing was to be paid for the first nail of 24 in the shoes, a half-penny for the next, a penny for the third, two pence for the fourth, and so on. It may be interesting to some of my readers to learn, that if we want to know roughly the proportion in which the first number is increased by any given number of doublings, we have only to multiply the number of doublings by 3⁄10ths, and add 1 to the integral part of the result, to give the number of digits in the number representing the required proportions. Thus multiplying 24 by 3⁄10ths gives 7 (neglecting fractions); and therefore the number of farthings in the horse problem is represented by an array of 8 digits.
