OF ARTS AND SCIENCES. 89 



The case of an acid containing for twenty-four atoms of tungstic 

 oxide six atoms of hydroxyl may easily be deduced from the above, 

 upon the principle explained in the first example cited. Without again 

 writing the cumbrous formula, it may easily be seen that the cases 

 of acids containing more than twelve atoms of hydroxyl, if such really 

 exist, are embraced in the above-given structural formula, and that in 

 such cases there will be two variations in the mode of combination of the 

 hydroxyl, similar to the two which occur when there are six or twelve 

 atoms of hydroxyl. The structural formula given would explain sim- 

 ply and naturally the trihasic character of all known phospho-molyb- 

 dates and phospho-tungstates containing twenty-four atoms of metallic 

 oxide, since in these all the hydroxyl may be united with phosphorus 

 exclusively, or with tungsten exclusively. It only remains to consider 

 the case of the compounds having for one atom of phosphoric or arsenic 

 oxide an uneven number of atoms of metallic oxide, as, for instance, 

 the 5 : 1 and 7 : 1 series. In these cases also there exists, as has been 

 shown, a second and derived series, of which the successive terms are to 

 be regarded as formed from those of the first series by doubling the mo- 

 lecular weight and dropping an atom of fixed base. Thus, we have 



5 M0O3 • PA • 3 H2O and 10 M0O3 . 2 Vf^, . 5 Kp . H^O + 19 aq 



7 M0O3 • ^s.Ps . 3 H2O 14 WO3 . 2 P2O5 . 5 Nap . Hp -f 42 aq 



22 M0O3 • P2O5 . 3 H^O 44 M0O3 . 2 P^Og . 5 Kf) . Hp + 21 aq 



24 M0O3 . PA • 3 HP 48 M0O3 . 2 P^O^ . 5(NH J,0 . Hp+l 6 aq 



All these salts appear to have an acid reaction. They may all be 

 regarded as acid six-basic salts, and it is easy to see that the two series 

 may be reduced to one by doubling the formulas of all the terms on the 

 left, so that we shall have a single series, of which the successive terms 

 are 



This view in no wise excludes acids or salts of a higher degree of 

 basicity. It has the advantage of bringing all the compounds to- 

 gether, and of being more completely in accordance with what we 

 know of the constitution of salts belonging to simpler types. The 

 structural formulas which I have given — provisionally, of course — 



