316 



SCIENTIFIC THOUGHT. 



By drawing curves on paper which correspond to the 

 thermal properties of various substances, the conditions 

 have been defined beforehand under which gaseous bodies 

 like oxygen, hydrogen, nitrogen, or common atmospheric 

 air can be reduced to liquid and solid bodies, upsetting 

 the notions of the last generation, which looked upon 

 these substances as permanent gases. 1 If the mathe- 

 matical formula has killed, or failed to grasp, the true 

 life of nature, that which to the poet and the philosopher 

 will always be the feature of supremest interest, it has on 

 the other side given birth to that new life of ideas which 

 in our reasoning minds serve as the images of things 



example of a purely mathematical 

 quantity which, suggested originally 

 by a formula, acquired later a physi- 

 cal meaning, is that of the potential 

 function, used first by Lagrange as 

 a simplification in calculating the 

 forces of a disturbing planet, and 

 termed by Laplace ' ' a cause de son 

 utilite, une veritable de"couverte" 

 ('Mec. eel.,' v. livre xv. chap, i.) 

 This function, which has the pro- 

 perty that by a simple differentia- 

 tion the component of the force in 

 any direction is found, acquired a 

 physical meaning as the quantity, 

 the change of which measures the 

 work required to move a unit of 

 matter from one point to another 

 (see Thomson and Tait, ' Natural 

 Philosophy,' vol. i. 2, p. 29). Other 

 examples of purely mathematical 

 quantities which reveal physical 

 properties are Hamilton's " char- 

 acteristic function " (see Tait, 

 "Mechanics," 'Ency. Brit.,' 9th 

 ed., p. 749), Rankine's "Thermo- 

 dynamic function," called by Clau- 

 sius "Entropy" (see Maxwell, 

 ' Heat,' pp. 162, 189) : it measures 

 the unavailable energy of a system. 

 1 Thomas Andrews (1813-85) took 

 up the experiments begun by Cag- 



niard - Latour in 1822, and ex- 

 plained how it comes about that a 

 gas remains incondensable however 

 great the pressure may be, pro- 

 vided the temperature exceeds 

 what he termed the " critical tem- 

 perature," which is different for 

 different gases. He accompanied 

 his statements, which were first 

 published in the 3rd edition of 

 Miller's Chemical Physics, by curves 

 representing the behaviour of at- 

 mospheric air and of carbonic acid, 

 the latter being a condensable gas, 

 and he suggested in 1872 that the 

 so-called permanent gases had a 

 critical point far below the lowest 

 known temperatures, and that this 

 was the reason why their lique- 

 faction had not yet been achieved. 

 Two physicists, Cailletet and Pictet, 

 took up these suggestions ; after 

 various trials they succeeded inde- 

 pendently in 1877 in liquefying 

 several of the permanent gases, 

 notably oxygen and nitrogen. 

 These have been followed by all 

 the other permanent gases, includ- 

 ing atmospheric air, of which large 

 quantities can now be prepared in 

 a liquefied form. 



