18 PROCEEDINGS OF THE AMERICAN ACADEMY 



as tetratomic or hexatomic. In what follows I have adopted the latter 

 hypothesis, partly because the hexatomic character of tungsten is well 

 marked in various compounds, as for example in WC1 C , and partly 

 because the graphical representations are, on the whole, simpler. More- 

 over, if we consider tungsten to be tetratomic in the normal series, we 

 obtain a reason for the existence aud peculiar character of the meta 

 series, by supposing that in this the metal is hexatomic. We may, to 

 begin with, represent sodic metatungstate, 4 W0 3 . Na 2 0, as follows : 



wo 2 = wo 2 



■ v- 



o 



1 I 



Na - - W0 2 = WO, - O - Na 



The next term in the series, 6 W0 3 . 2 Na 2 0, will then be 

 W0 2 = W0 2 



o o 



I I 



Na - - WO, — W0 2 - - Na 



i i 



o 



1 I 



Na - O - W0 2 = W0 2 - - Na 



The third term, 8 W0 3 . 3 Na 2 0, may be represented by the graph- 

 ical formula 



W0 2 = W0 2 



■ v- 



Na - - W0 2 — W0 2 - - Na 



i i 



o 



1 I 



Na - - WO, — W0 2 - - Na 



i " i 



o 



1 I 



Na - O - W0 2 = W0 2 - - Na 



and so on for the other known terms, the highest, 14 W0 3 . 6 Na 2 0, 

 being represented by the expression 



