October 14, 1904.] 



SCIENCE. 



495 



taken too much time with a matter which 

 is aside from my main purpose. Before 

 leaving this topic I must add, however, that 

 I have used the phrase 'Avogadro's law' 

 advisedly in spite of the fashion set by 

 some chemists ,of calling it Avogadro's 

 hypothesis.* 



I remarked, a few moments ago, that the 

 facts which have been outlined almost com- 

 pel us to the acceptance of van't Hoff's 

 hypothesis in some form. It is of the ut- 

 most importance for us to recognize, how- 

 ever, that we are here at the very confines 

 of our present knowledge and that we 

 must, at every step, bring ourselves back 

 to the rigorous test of experimental fact. 

 In accepting the hypothesis we are not com- 

 pelled to consider molecules as set pieces of 



position of two compounds AB and BG has been 

 determined, the composition of a series of com- 

 pounds between A and C can be predicted and a 

 compound which does not belong to this series 

 has never been discovered. A still more general 

 statement of the law, and one which includes, by 

 implication, all of those facts which are used in 

 tlie selection of atomic weights, is given above. 

 In that form it is more properly called the law of 

 atomic weights. 



* Two reasons may be given for this usage. 

 My own view is that we have, by a process of in- 

 ductive reasoning, acquired such positive knowl- 

 edge of the existence of atoms and molecules that 

 the expression ' Avogadro's law ' is fully justified. 

 But even if we admit the contention of those who 

 think that the atomic theory must always remain 

 an unproved hypothesis, it is possible to frame a 

 definition of the word molecule which would be 

 merely a generalized statement of those empirical 

 facts which lie at the basis of our atomic and 

 molecular theories. Such a generalized, empirical 

 definition must, of course, be very complex but 

 it would not include the concept of discrete part- 

 icles. Yet it will be still true of these empirically 

 defined molecules that equal volumes of gases 

 contain equal numbers under the same conditions 

 of temperature and pressure. For instance, the 

 term gram-molecule may be considered as a purely 

 empirical generalization and it is true that a 

 gram-molecule of one gas occupies the same 

 volume as a gram-molecule of any other. But this 

 is, in essence, Avogadro's Law. 



mechanism ; on the contrary, there is strong 

 reason for thinking that the positions as- 

 sumed by the atoms are positions of dy- 

 namic and not of static equilibrium. While 

 there have been many speculations in the 

 matter, we have no strong reason for as- 

 suming, as yet, any definite shape for the 

 carbon atom, nor even that there are within 

 it definite points of attraction for other 

 atoms. All that seems to be thoroughly 

 established is that for their position of 

 most stable equilibrium the four atoms or 

 groups attached to a given carbon atom are 

 arranged in approximate symmetry around 

 its center. I say approximate symmetry 

 because the existence of compounds con- 

 taining rings of three and four carbon 

 atoms demonstrates that the symmetry is 

 not always absolute, and makes it probable 

 that in cases where the four atoms or 

 groups are unlike the symmetry is also im- 

 perfect. So far as I am aware, no fact in- 

 consistent with this fundamental concep- 

 tion is known, while very many facts about 

 optically active and cyclic compounds find 

 in this conception the only satisfactory ex- 

 planation which has thus far been given. 

 It is true, also, that many facts with re- 

 gard to optically active compounds indi- 

 cate that when one group is exchanged for 

 another the exact configuration is often 

 retained, or, in other words, the entering 

 group takes the same position with regard 

 to the other three atoms or groups as was 

 held by the group which was displaced. 

 The manner in which it has been possible 

 to work out, consistently, the complex re- 

 lations between a considerable number of 

 sugars, gives a very strong experimental 

 basis for this statement. On the other 

 hand, it is well known that such reactions 

 often give racemic mixtures, which indi- 

 cates that a shifting of groups with re- 

 gard to a central carbon atom takes place 

 much more easily than the shifting of a 

 group from one carbon atom to another, at 



