500 THE PRINCIPLES OF SCIENCE. [CHAP. 



Yet no incontestable general law has been established. 

 Several functions have been proposed to express the 

 elastic force of the vapour as depending on the tem- 

 perature. The first form is that of Young, namely 

 F = (a + b ) m , in which a, I, and m are unknown quan- 

 tities to be determined by observation. Roche proposed, 

 on theoretical grounds, a complicated formula of an ex- 

 ponential form, and a third form of function is that of 

 Biot, 1 as follows log F = a + 6a* + c fp. I mention 

 these formulae, because they well illustrate the feeble 

 powers of empirical inquiry. None of the formulae 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 dis- 

 covery 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 investiga- 

 tions 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 im- 

 possible 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 



1 Jamin, Court de Physique, vol. ii. p. 138. 



