113 DIRECT PROPEKTIES OF MOLECULES 313 



doubts may be raised even against Kopp's laws, although 

 the molecular volumes of all liquids that had then been 

 investigated with sufficient exactness could be so well cal- 

 culated by them as to agree excellently with experiment. 

 For there remains the very grave objection that by these 

 rules one and the same volume is not always to be ascribed 

 to one and the same atom. Thus, for instance, the volume 

 of the oxygen atom has to be now 7'8, now 12'2 ; the 

 nitrogen atom has to have a different volume in ammonia 

 and analogous compounds from what it has in cyanogen 

 compounds, and a third different volume in nitro-compounds. 



A further objection is that the molecular volumes cal- 

 culated for gaseous bodies cannot be represented by the 

 atomic volumes given by Kopp for the liquid state, for this 

 seems to contradict the assumption that the atoms are to 

 be looked upon as invariable. But in order to obtain agree- 

 ment between calculation and experiment, Lothar Meyer 

 was obliged to assign, both to nitrogen and hydrogen, a 

 different atomic volume in gaseous compounds than in 

 liquid ones. 



The variation in the occupation of space by the atoms 

 which we should have to assume in accordance with these 

 investigations can only mean this, that we have not at all 

 to do with the actual dimensions of the atoms and mole- 

 cules, but with the smallest space which these particles 

 at least require for themselves under the given circum- 

 stances. This space may really alter with circumstances. 

 As is almost obvious, it alters with the temperature, 

 because this determines the motion of the atoms. But the 

 shape of the molecule and the grouping of its atoms may 

 also have an influence on the space required by it as a 

 minimum. A flat molecule with its atoms grouped together 

 nearly in a plane will require more room, when turning 

 with its motions that depend on the temperature, than a 

 spherically shaped molecule with its atoms all crowded 

 together. It is thus explicable, from the differences between 

 molecules that have been described, that different extensions 

 in space may be ascribed to the atoms according to their 

 location in the molecule. 



