202 MESSES. A. V. HAECOUET AND W. ESSON ON THE LAWS OF CONNEXION 



The reaction under consideration has already been shown to occur in two stages, in 

 the first of which manganic binoxide is produced by the reaction of permanganic acid 

 on manganous sulphate, and in the second of which it is reduced by oxalic acid, after 

 previous combination, when that acid is present in excess. 



(1) K2Mn2 08+3MnS04+2H2 0=K2S04+2H2S04+5Mn02. 



(2) Mn02+H2S04+H2C2 04=MnS04+2H2 0+2C02. 



Unfortunately both these reactions belong to the class, comparatively rare in inorganic 

 chemistry, of slow actions. If either of them occurred very rapidly as compared with 

 the other, the curve representing the reaction of proportional quantities would doubtless 

 be a hyperbola from its starting-point. As it is, the first action takes place more rapidly 

 than the second, their relative rates varying, however, according to the conditions of each 

 experiment. In the present case the first action has nearly attained its limit at the end 

 of four minutes, and thenceforward the only change taking place is that which the 

 second equation expresses. After this time the simple law already enunciated holds 

 good, and the residues become inversely proportional to the duration of the action. 

 In this case the actual moment of starting the experiment happens, through the com- 

 plication of the double action, to be the true epoch from which to reckon its duration. 

 But in other cases it is not so : the zero of the series of numbers representing the time 

 should correspond to an infinite amount of the active substances, and not to 100 

 parts. The full discussion of the significance of this relation, and of the course of the 

 reaction when the two changes are occun'ing simultaneously, is reserved until the entire 

 series of experiments has been brought forward ; but it may be shown that the inverse 

 proportionality of the residue to the time depends upon a law the generality of which 

 we hope hereafter to establish, namely, that the total amount of chemical change varies 

 directly with that of each of the substances partaking in it. 



Let x= the duration of the action dated from a point such that when x=0, ym oo; 

 and let y=. the number of molecules of the oxidizing and reducing substances present 



in the solution at the time x. Then 4- is the amoimt of change in a unit of time, 



and this is proportional to "ip-, since both substances are changing, and the amount of 

 change varies directly vrith the quantity of each of them. Hence we have the equation 



%<.-f=-\.y. 



2 



which gives 



ocy=.k, oryac -, 



The following Table contains the results of thri&e similar series of experiments, 

 differing from the last and from one another only in respect of the quantity of sulphuric 

 acid used in each. 



