108 PROCEEDINGS OF THE AMERICAN ACADEMY 



practically unlimited extent, as even an elementary application of the 

 algebraiciil theory of permutations and combinations will show. 



Pyrophospho-tungstates are formed when tungstic hydrate or tung- 

 stic oxide which has not been ignited is boiled with an alkaline pyi'o- 

 phosphate. The oxide readily dissolves, usually forming a yellow 

 liquid. It is best to emplo}' sodic pyrophosphate, as this gives a much 

 more soluble salt, but the pyropho-phate must be specially prepared 

 in the laboratory, and the tungstic oxide should be in excess. Neutral 

 salts of the heavy metals usually give precipitates in solutions of the 

 alkaline pyrophospho-tungstates ; those precipitates are not neces- 

 sarily salts of the same group, but are very often at least either pyro- 

 phosphates of the metallic bases or double pyrophosphates of the metal 

 and of sodium or potassium. 



Analytical Methods. — These are the same as those which I have 

 emploj'ed in the case of the orthophospho-tungstates, only in the de- 

 termination of the phosphoric oxide it is necessary to evaporate the 

 salt two or three times in succession to diyness with an excess of 

 chlorhydric acid, so as to convert the phosphoric acid present com- 

 pletely into the ortho or tribasic form. In the absence of any stan- 

 dard of comparison, it is necessary to speak with much hesitation, but 

 it has always appeared to me that in these salts — in other words, in 

 the presence of tungstic oxide — the conversion of pyrophosphoric 

 acid into orthophosphoric acid is more difficult, or at least takes place 

 more slowly, than in the case of the ordinary pyrophosphates. Tung- 

 stic and phosphoric oxides may in these compounds also be precipitated 

 together by mercurous nitrate and mercuric oxide. 



22 : 3 : G Ammonio-sodic PyrophospJio-tungstate. — A boiling solution 

 of sodic pyrophosphate readily dissolves tungstic oxide as prepared 

 by the action of chlorhydric or nitric acid upon calcic tungstate, but 

 not ignited. The filtrate has a dull yellow color, and gives with a 

 strong solution of amnionic chloride an abundant white crystalline 

 precipitate, which cannot be purified by recrystallization, but which 

 may be well washed upon the filter-pump with cold water, in which 

 it is soluble to a very small extent. Hot water in large excess dis- 

 solves it, but even cold ammonia water dissolves it with much difficulty. 

 When boiled for a long time with a solution of mercurous nitrate, the 

 salt gives at first a white and finally a yellow mercurous salt. Argentic 

 nitrate in solution gives at first with the salt extremely minute talcose 

 scales, but on boiling for some time the whole dissolves to a clear 

 liquid. When the salt is boiled with a solution of baric chloride, a 

 fiocky-crystalline white baric salt is formed. Cupric sulphate on boil- 



