general law has been established. Several functions have been proposed to express the elastic force of the vapour as depending on the temperature. The first form is that of Young, namely F = ( a + b t ) m , in which a , b , and m are unknown quantities to be determined by observation. Roche proposed, on theoretical grounds, a complicated formula of an exponential form, and a third form of function is that of Biot, as follows—log F = a + b α t + c β t . I mention these formulæ, because they well illustrate the feeble powers of empirical inquiry. None of the formulæ can be made to correspond closely with experimental results, and the two last forms correspond almost equally well. There is very little probability that the real law has been reached, and it is unlikely that it will be discovered except by deduction from mechanical theory.
Much ingenious labour has been spent upon the discovery of some general law of atmospheric refraction. Tycho Brahe and Kepler commenced the inquiry: Cassini first formed a table of refractions, calculated on theoretical grounds: Newton entered into some profound investigations upon the subject: Brooke Taylor, Bouguer, Simpson, Bradley, Mayer, and Kramp successively attacked the question, which is of the highest practical importance as regards the correction of astronomical observations. Laplace next laboured on the subject without exhausting it, and Brinkley and Ivory have also treated it. The true law is yet undiscovered. A closely connected problem, that regarding the relation between the pressure and elevation in different strata of the atmosphere, has received the attention of a long succession of physicists and was most carefully investigated by Laplace. Yet no invariable and general law has been detected. The same may be said concerning the law of human mortality; abundant statistics on this subject are available, and many hypotheses more or less satisfactory have been put forward as to the form of the curve of mortality, but it seems to be impossible to discover more than an approximate law.
It may perhaps be urged that in such subjects no single invariable law can be expected. The atmosphere may be divided into several variable strata which by their unconnected changes frustrate the exact calculations