672 SCIENCE PROGRESS 



The ratios which have been given in the above tables are 

 indications of the changes in the physical states simply, and are 

 independent of the nature of the substances. They show the 

 increases in the vibration spaces from one physical condition to 

 another. 



If the space were a molecular vibration space, there is no 

 reason why it should be practically constant. Indeed, it would 

 be likely to diminish with increasing complexity, because the 

 greater molecular weight of the more complex compounds 

 would tend to diminish the amplitudes of the vibrations and so 

 diminish the co-volumes. The constancy of the ratio must 

 therefore be connected with the atomic vibrations, which show 

 similar amplitudes of vibration under similar physical conditions. 



B 



After tracing the Law of Coincident States in the two states — 

 the Solid and the Liquid — we are led to a Second Regularity. 

 This refers to the relations between the volumes of the com- 

 pounds under particular physical conditions. 



Since it is likely that the effects of differences in constitution 

 would show themselves in the ratios, care must be taken to 

 compare chemically similar substances. Suppose the conditions 

 be equal or reduced pressure p. 



Then for a number of substances which are structurally 

 similar and which form a homologous series or one characterised 

 by some constant difference in composition : 



(V m = V [i + *(p)] ) 

 At pressure) V' m = V' [i + *(p)] L. , ,, ,„ 



P V'WUx-^p)] [Since*-*-* = 



Comparing the volumes of the second and the third with the 

 first we find : 



fV' m _V' o [i + *(p)]__V 



At pressure 

 P 



V m V [i + *(p)] V, 



V^ V' 



v V 



v m 



V"' v 



i + nx 

 = i + (n + i)x 



2 = i + (n + 2)x 



V m V 

 (Regularity II.) 



x being some difference and n a number which is usually unity. 



