272 On Chemical Equivalence. [Jan. 23, 



Equations. 



A y = 9-6785+ -56035*3- -036214*. 



B 2/=9-6500+ -63271a;- ■04690aj». 



C y=9 -6827 + 1 -04941*3- 11635a! 2 . 



D y=9 '7283 + 1 '00775a;- 11090aj 2 . 



E 2/=9'6889+ -98951*3- 1093133 2 . 



In each equation y is the rotation in degrees, x is the time in half- 

 hours. By placing -^=0 in each equation, we find the value of x when 



dx 



y has its highest value. The corresponding value of y is thence 

 calculated by substitution in the equation considered. We thus find 

 data for the comparison of the two acids. 



HC1 



H 3 S0 4 



A 33=7-74, ^=11-846 



C . . , *-4 -51, y-12 -048 



B,. 33-6-74, y-11'780 

 D 33-4-54, y-12 -017 



2HC1 



H 2 S0 4 



E 93=4-53, y — 11 -928 



B 33-6-74, 2,-11-780 



These results show that though 2HC1 may be the "equivalent" of 

 H 2 S0 4 in weight for saturation (i.e., in the ordinary sense), it certainly 

 is not the equivalent in the dynamical sense. They also render it 

 highly probably that HC1 is equal dynamically to H 2 S0 4 . Ostwald,* 

 by a method based on the alteration of the specific volume of solutions, 



2HC1 



has shown that the ratio — o7T = ^ a resu ^ which our numbers, 



H0SO4 



though not as perfect as we could wish, nevertheless strongly con- 

 firm. I 



* " Journ. Prakt. Chem.," N.F. xvi, p. 419. 



f If the curve equations be examined, it is found that the highest value of y \% 

 practically the same in each. By taking the average value = 11 0, 924, and calculat- 

 ing to specific rotation (assuming that the action involves no change of weight), the 

 number 73*78 is obtained. This falls short of the specific rotation of galactose 

 (83°), and seems to point to the dual nature of lactin mentioned in the researches 

 on lactin ; probably at this point the sugar in solution is Fudakowski's lacto-glucose. 

 ("Deut. Chem. G-es. Ber.," ix, 42-44.) 



