466 THi: POPULAR SCIENCE MONTHLY. 



raarkable as to outweigh many times over all seeming variations. All 

 this evidence is, however, inadequate in one respect : the relations 

 thus far pointed out cannot be simply expressed in figures. Are there, 

 then, any numerical relations connecting tlie elements ? This question 

 may be answered, partly by studying their atomic weights, and partly 

 by an examination of their specific volumes. 



The regularities which connect the elementary atomic weights 

 have been examined and discussed by many investigators from widely 

 differing points of view. Some chemists have contented themselves 

 with the naked facts ; others have considered the bearing of those 

 facts upon chemical theories ; and a third class, with less caution than 

 ignorance, have speculated upon them in the wildest and most reck- 

 less manner. Of course a full summary of the whole subject, however 

 interesting it might prove, would be out of place in a condensed argu- 

 ment like this. All we can do here is to glance at a few of the many 

 relations known, and afterward consider them in their connection with 

 our main subject. The general reader who cares to go deeper into 

 the question will do well to consult the original papers of Dumas, 

 Gladstone, J. P. Cooke, Kremers, Mendelejeff, and others. 



Of the relations now under consideration, the one most frequently 

 cited is as follows : Many elements are most naturally arranged in 

 threes, of which the middle member has an atomic weight very nearly 

 a mean between the atomic weights of the other two. Thus we have 

 calcium, atomic weight, 40 ; strontium, 87.5 ; and barium, 137. Here, if 

 the value of strontium were 88.5, it would be an exact mean. Again, 

 chlorine has the atomic weight 35.5 ; bromine, 80 ; and iodine, 127 ; the 

 second being almost precisely midway between the first and third. A 

 still closer agreement with theory is furnished by lithium, sodium, and 

 potassium, whose values are respectively 7, 23, and 39.1. A fourth 

 example is afforded by potassium, 39.1 ; rubidium, 85.4; and caesium, 

 133 ; while a fifth case is offered by phosphorus, 31 ; arsenic, 75 ; and 

 antimony, 122. To be sure, these illustrations afford only an approxi- 

 mation to regularity ; but then the variations are themselves some- 

 what regular. In each of these twos the middle term is just a little 

 too low to be an absolute mean between its associates ; that is, the 

 variations from theory are all in one direction. It is hardly possible 

 at present to say whether this means anything, or is only ascribable 

 to accident. One more example of regularity among atomic weights 

 is worth noting, namely, the relation which connects the members of 

 the oxygen group. Here we have oxygen, 16 ; sulphur, 32 ; selenium, 

 79.5 ; and tellurium, 128. These higher numbers are simple multiples 

 of the lowest ; there being only a variation of half a unit (minus) in 

 the case of selenium. Since these elements are very similar in their 

 chemical relations, this regularity is extremely significant. Can it be 

 due to chance, and void of real meanins;'? 



But all these relations ^iroye nothing they merely suggest. Stand- 



