126 ON THE THEORY OF TYPES IN CHEMISTRY. 
expansion, (homogeneous differentiation.) In metagenesis, on the 
contrary, unlike species may unite, and by a subsequent heterogene- 
ous differentiation give rise to new species, constituting what is 
called double decomposition, the results of which, differently inter- 
preted, have given origin to the hypothesis of radicals and the notion 
of substitution by residues, to express the relations between the 
parent bodies and their progeny. The chemical history of bodies 
is then a record of their changes; it is in fact their genealogy, and 
in making use of typical formulas to indicate the derivation of 
chemical species, we should endeavour to show the ordinary modes 
of their generation. (See On the Theory of Chemical Changes, 
Am. Jour. Sci. xv. 226, L. E. & D. Phil. Mag. (4) v. 526, and Chem. 
Centralblatt, 1853, p.849. Also Thoughts on Solution, Am. Jour. 
Sct. xix. 100, and Chemical Gazette, 1855, p. 92. 
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,O,. Mr. Wurtz, 
seven years later, (in 1855) put forth a similar view. He supposes 
a monatomic radical PO’, a diatomic radical P’O,, and a triatomic 
radical PO”, replacing respectively one, two and three atoms of hy- 
drogen in H,O,,H,0,, and H,O,, thus (PO’,H) O,(PO",H,)O, 
and (PO”,H;)O,. These radicals evidently correspond to PO, 
which has lost one, two and three atoms of oxygen in reacting upon 
the hydrogen of the water type, and these acids may be accordingly 
represented as formed by the substitution of the residue PO,—O 
for H, ete. 
To this manner of representing the generation of polybasic acids 
we object that it encumbers the science with numerous hypothetical 
radicals, and that it moreover fails to show the actual successive 
generation of the series of acids in question. When phosphoric 
anhydrid, P,O,,=(PO,),0., is placed in contact with water it 
combines with one equivalent, H,O,. The union is followed by 
homogeneous differentiation, and two equivalents of metaphosphorie 
result, (PO,),0,+H,O, =2(PO,H)O,. Two equivalents of 
this acid with one of water at ordinary temperatures are slowly 
transformed into two of pyrophosphorie acid, by a reaction pre- 
cisely similar to the last. 2 (PHO,)=(PHO,),0, + H,O,= 
2(PHO,H)O,, and two equivalents of pyrophosphoric acid when 
