466 THEORY OF TYPES IN CHEMISTRY. [XX. 



use of typical formulas to indicate the derivation of chemical 

 species, we should endeavor to show the ordinary modes of 

 their generation. [See the preceding papers XVI. and XVIII.] 



Keeping this principle in mind, let us now examine the theory 

 of the formation of acids. As we have just seen, I taught in 

 1848 that the monobasic, bibasic, and tribasic acids are derived 

 respectively from one, two, and three molecules of water, H 2 2 . 

 Mr. Wurtz, seven years later, put forth an analogous view. He 

 however supposes a monatomic radicle P0' 4 , a diatomic radicle 

 PCX's, and a triatomic radicle P0'" 2 , replacing respectively one, 

 two, and three atoms of hydrogen in H 2 2 , H 4 4 , and H C 6 ; 

 thus (PO' 4 H)0 2 , (PO" 3 H 2 )0 4 , and (PO"' 2 H 3 )0 6 . These radicles 

 evidently correspond to P0 5 , which has lost one, two, and three 

 atoms of oxygen in reacting upon the hydrogen of the water- 

 types, and the acids, may be accordingly represented as formed 

 by the substitution of the residues PO S for H, P0 5 2 

 for H 2 , and P0 5 3 for H 8 . 



To this manner of representing the generation of polybasic 

 acids we object that it encumbers the science with numerous 

 hypothetical radicles, and that it moreover fails to show the 

 actual successive generation of the series of acids in question. 

 When phosphoric anhydride is placed in contact with water, 

 it combines with one equivalent. The union is followed by 

 homogeneous differentiation, and two equivalents of metaphos- 

 phoric acid result. Two equivalents of this acid with one of 

 water at ordinary temperatures are slowly transformed into two 

 of pyrophosphoric acid, by a reaction precisely similar to the 

 last; while two equivalents of pyrophosphoric acid when heated 

 with a third equivalent of water yield, in like manner, two of 

 tribasic phosphoric acid. The generation of the three acids 

 may be represented as follows : 



2(P0 6 ) or (P0 4 ) a O a + H a O a = 2(P0 4 H)0 2 or 2(PH0 6 ) 

 2(PHO e ) or (PH0 6 ) a O a -f H a O a = 2(PH0 6 H)O a or 2(PIL< ).) 

 2(PH a O T ) or (PH a O.),O a + H 3 O a = 2(PH 2 6 H)0, or 2(PH 8 O e ) 



Gerhardt long since maintained that we cannot distinguish 

 between polybasic salts and what are called sub-salts, v.-hich 



