Laws of Molecular Force, 215 



The critical volume of ethyl oxide is between 5 and 4 ; so 

 that if "dpfaT does become variable with temperature below 

 the critical volume, the values of Rvf(v) and v 2 4> (v) , calcu- 

 lated for volumes below 5, on Ramsay and Young's assump- 

 tion that even below the critical volume 'dp/'dT is independent 

 of temperature, will be affected with an error of more or less 

 importance ; they may therefore be regarded as a first approxi- 

 mation only and are added for comparison. 



The first point to notice in these numbers is that ~Rvf(v) 

 increases steadily from its limiting value *842 in the perfect 

 gas state to double that amount near the critical volume, while 

 at the same time v' 2 cf?(v) diminishes from its limiting value in 

 the gaseous state to the half of it near the critical volume. 

 This result would seem at once to contradict the law of the 

 inverse fourth power ; but we shall see in the sequel that, in 

 compression down to the critical region, there is a process of 

 pairing going on among the molecules and producing this de- 

 parture from the requirements of the law of the inverse fourth 

 power, uncomplicated by such a process. 



It is to be noted that the limiting value of v 2 cj>(v) is diffi- 

 cult to determine experimentally, because (j)(v), the quantity 

 measured, tends to the limit zero. But while below volume 4, 

 Rvf(v) increases with increasing rapidity, v 2 <fi(v) remains 

 almost stationary, it dips a little and then increases ; but 

 remembering that its values count only as first approxima- 

 tions, we may assume that v 2 <f)(y) attains near the critical 

 volume a value which remains constant in the liquid state, 

 and is about half of the limiting value for the gaseous state. 

 Thus there is discontinuity in the passage from the region 

 above the critical volume to that below (or, more briefly but 

 less accurately, during liquefaction). We must note carefully 

 that in the range of volume from 4 to 1*9, which is a large 

 liquid range, v 2 cjj(y) remains constant, as it should according 

 to the law of the inverse fourth power, now that the process 

 of pairing is completed. 



To represent Uvf(v) I found the form R{1 + 2k/(v + k)\ to 

 be efficient ; it gives the limit 2R to the function when v = k; 

 and as *842 is the known value of R, each of the above 

 tabulated values of Rr/(v) yields a value of k, the mean value 

 4*066 having been adopted by me. The other function, 

 v 2 <j>(v), proved no less amenable to simple representation, the 

 form found to fit it being lv/(v-{-k), which attains the value 

 l)'l when v — k-, and as the value of k is known, we can calcu- 

 late from each tabulated value of i' 2 (/>(r) a value of /, and 

 again adopt the mean value 5514. Hence down to near the 



