Theory of Fractional Precipitation. 121 



these affinities or attractions constitute a very complex system 

 of forces. There is a set of forces tending to change the 

 system from the state represented by the left-hand member of 

 the equation to the state represented by the right-hand one, 

 and another set of forces tending to bring the system back to 

 its initial state. If, instead of one, two or more precipitable 

 salts be present, then the system of forces at work becomes 

 much more complex ; and to attempt to introduce all these 

 attractions or affinities into formulae relating to fractional 

 precipitation would lead to complicated results ; the equations 

 would be as complex as those proposed by Guldberg and 

 Waage in their theory of limited chemical actions. It is here 

 assumed, however, that one of the products of the change of 

 each particular constituent is practically insoluble ; and that 

 the inverse action does not take place, at least to any extent 

 compared with that producing the precipitate. 



If a number of solutions, each containing an equal mass of 

 a single sulphate, as M80 4 ,CoS0 4 , MnS0 4 , &c, be considered, 

 to which a common precipitant is added, the experimental 

 conditions being the same in each case, the changes occurring 

 in the several solutions will be brought about by forces ana- 

 logous in kind, but the intensity of the action of the precipi- 

 tant may differ in degree with the nature of the sulphate : this 

 may be expressed by saying that each system exhibits a re- 

 sistance to undergoing change, differing in degree according to 

 the sulphate employed. This resistance is here looked upon 

 as being exhibited by the sulphate, nitrate, or other salt that 

 is submitted to the action of the precipitant, and the relative 

 values of which may be determined by the simultaneous action 

 of the precipitant on mixtures of two or more such salts. 

 Representing the resistance of a particular salt to the action 

 of a precipitant by the symbol e, it becomes a measure of the 

 stability of the salt, or of the intensity of the affinities holding 

 the structure together, and is probably of a complex character, 

 a function of the conditions to which the chemical system may 

 be subjected. If a hydrate, such as NaHO, be the precipi- 

 tant, e measures the intensity of the attraction of the metallic 

 base for the acid with which it may be united : the greater the 

 value of e, the greater the attraction between the base and acid. 



The symbol e might be defined as the coefficient of resist- 

 ance to change for a particular chemical system, or as the 

 basic power of a particular base with relation to a particular 

 acid ; but the phrase "coefficient of affinity," however appro- 

 priate it may seem, is objectionable, as there has been already 

 sufficient confusion introduced into science by the use of this 

 term ; besides, as this value e is interpreted above, it has the 



