524 Mr. W. Sutherland on the Viscosity 



cent, of that due to collisions ; with rising temperature and 

 diminishing pressure, that is with nearer approach to the 

 gaseous state, this difference ought to diminish towards as 

 a limit ; in the case of the esters the reverse of this appears 

 to hold, but the experiments are perhaps at fault. For the 

 complete elucidation of this part of the subject further ex- 

 periments are required, in which the various values of the 

 viscosity of a substance are followed from the one limit when 

 it is a gas to other limits when it is a saturated vapour. The 

 theoretical investigation of this part of the subject would not 

 be difficult, though it might be tedious, and not very interesting 

 unless hand in hand with experiment. 



The other main properties of a gas besides viscosity which 

 depend on the molecular free path or number of collisions 

 are the coefficient of diffusion into other gases, the thermal 

 conductivity and the characteristic equation, in all of which 

 molecular attraction plays as fundamental a part as in vis- 

 cosity, and in the theory of which molecular attraction can 

 be taken account of on the same simple principle as has been 

 applied to viscosity, namely, imagine the molecular spheres 

 to have their sections increased in the proportion (1 + C/T) : 1, 

 and then proceed with the theory of them as if they were 

 forceless. 



The difficulties that confront us in diffusion and conductivity 

 arise entirely from the fact that the theory of these pheno- 

 mena, even for forceless molecules, is incomplete ; in the case 

 of diffusion chiefly on account of mathematical difficulties, 

 and in that of conductivity because it is not known what 

 provision there is for the transmission of other forms of 

 molecular kinetic energy besides that of translatory motion. 

 However, this much may be said in general terms, that ex- 

 periment has shown that if theory and experiment were 

 brought into harmony for viscosity they would be in as good 

 harmony for diffusion and conductivity as could be expected 

 in the confessedly incomplete state of theory. In the case of 

 diffusion the question is still further complicated by the fact 

 that we have to deal with the attractions of unlike molecules, 

 a subject which will yet become of great importance, but too 

 large to open in this paper, so it must suffice to repeat that, 

 assuming the attractions of unlike molecules to be of about 

 the same strength as those of like, then the experiments of 

 Loschmidt and Obermayer show that when the temperature- 

 variation of viscosity is correctly explained by theory the 

 temperature-variation of diffusion must also be correctly ac- 

 counted for. A complete theoretical discussion of diffusion 

 would come in more naturally in connexion with a general 



