92 PRINCIPLES OF GENERAL PHYSIOLOGY 



methods, formulated a law according to which, if we call the precipitating power 

 of a univalent ion, x, that of a bivalent ion will be a; 2 , and that of a trivalent 

 one,, a; 3 . Whetham (1899) showed that this result could be deduced from the 

 theory of probability. Suppose that the charge of a trivalent ion is required to 

 precipitate a certain number of colloidal particles ; to obtain the same charge 

 from bivalent ions, these particles will have to meet two instead of one ; and 

 if from univalent ions, three will be necessary. Now the chances of meeting 

 two or three separate ions, instead of one only, are proportional to the square 

 and cube of their concentration. 



Hardy proceeded further to show (1900, 1, p. 242) that the active ion is that 

 one whose charge is of the opposite sign to that of the colloid precipitated. He 

 gives the following general statement: "The coagulative power of a salt is 

 determined by the valency of one of its ions. This prepotent ion is either the 

 negative or the positive ion according to whether the colloidal particles move 

 down or up the potential gradient. The coagulating ion is always of the opposite 

 electrical sign to the particle." This is known as "Hardy's rule." 



It may be asked, how do we know which is the active ion, since we cannot add 

 one without the other ? This is possible by taking a series of salts with the same 

 anion or the same cation respectively. We find, for example, that potassium 

 chloride, sulphate, and phosphate, of the same concentration in K' ion, have the 

 same effect on a negative colloid, say arsenious sulphide, although the valency of 

 the anions is respectively one, two, and three. On the other hand, the chlorides 

 of potassium, calcium, and lanthanum differ widely in their action. On a positive 

 colloid the members of the latter series are equal, whereas the chloride, sulphate, 

 and phosphate of the same metal are of greatly increasing potency in the order 

 mentioned. 



The following may be given as instances of electro-negative colloids : gold, 

 platinum, arsenious sulphide, silicic acid, " insoluble " organic acids, such as 

 caseinogen, mastic, or the free acid of Congo-red ; suspensions of most powders, 

 charcoal, kaolin, etc., are electro-negative. The hydroxides of aluminium, thorium, 

 iron, are electro-positive. 



The student is recommended to perform the following experiments on arsenious sulphide, 

 made by passing hydrogen sulphide through a saturated solution of arsenious acid. The 

 resulting hydrosol should be dialysed. On standing, the coarse particles will subside. Add 

 to samples of this solution an equal volume of O'OOOOS molar lanthanum sulphate, 0'027o molar 

 calcium chloride and 0*74 molar potassium chloride. The concentrations of the mixtures will 

 then be as a; to a? 2 to ar* in La - ", Ca" and K' ions respectively. The precipitating powers will 

 be found to be about equal. Experiments may also be made with varying amounts ; it will be 

 found that a concentration of Ca" or K" equal to that of La"' used is quite inactive, while if 

 the concentration of K' be taken equal to the active one of Ca", it also will be inactive. 

 Corresponding experiments may be made with a hydrosol of ferric hydroxide, prepared by 

 dialysis of a strong solution of ferric chloride, which is hydrolysed, so that the free acid is 

 gradually removed by diffusion. Potassium chloride, sulphate, and phosphate may be used. 

 The phosphate should be neutral and may be made by mixing ten parts of molar phosphoric 

 acid with 17 '7 parts of molar sodium hydroxide and diluting to a concentration in PO/" ion 

 of about 0'00057 molar (Prideaux, 1911). The corresponding solutions of sulphate and 

 chloride may be O0067 and T35 molar in S0 4 " and Cl' ions respectively. It will be found, 

 however, that different preparations of colloids require different concentrations for precipita- 

 tion, owing to their varying degrees of dispersion, as will be shown later. It may be added 

 that lanthanum is used as a trivalent ion on account of the fact of the minimal hydrolytic 

 dissociation of its salts. 



Before proceeding further, it is necessary to remark that the two great classes 

 of colloids, the suspensoid or lyophobe and the emulsoid or lyophile, differ widely 

 in their sensibility to the precipitating action of electrolytes, the former class 

 being very sensitive, the latter comparatively insensitive. The difference, however, 

 is merely one of degree and not fundamental, as the following facts will show. 

 Wiegner (1910, p. 235) showed that even potassium chloride in a concentration of 

 2*5 millimols to 1,000 of emulsoid (olive oil and water) caused obvious aggregation 

 when observed by the ultra-microscope. Mines (1912, p. 211) finds that egg-white 

 is at once precipitated by a simple trivalent ion, such as La - ", even in a 

 concentration of only 0*0016 molar, although comparatively insensitive to 

 univalent ions. Hopkins and Savory (1911, p. 213), in their investigation of the 



