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



It will be seen that after six minutes the residues still unreduced are inversely propor- 

 tional to the time during which the action has continued. In the earlier stages of the 

 reaction its rate follows a less simple law, probably for the reason already stated — the 

 gradual though relatively rapid action of permanganic acid on the excess of manganous 

 salt. The actual modification thus introduced will be considered subsequently, and it 

 will be shown that, from an equation in which account is taken of this action, the earlier 

 numbers may be calculated as well as the later. A curve representing this series will 

 be found in Plate XVII. fig. 6. The duration of the reaction is measured along the axis 

 of X, and the remaining chemical energy along the axis of y. The former is an asymptote 

 of the curve: the absolute disappearance of the oxidizing and reducing substances 

 requires theoretically an infinite time. The other asymptote falls just beyond the axis 

 of y : no amount of binoxide can be taken so great, as that with it this reaction should 

 proceed for six minutes and six seconds, and still leave a residue of 25' 7 parts. The 

 best equation for the lower part of this curve is (a;-|-0-l)y=157. 



In the foregoing series of experiments the principal reagents have been employed in 

 the proportions in which they act one upon another, that so their ratio might remain con- 

 stant throughout. The same result may be approximately attained by taking very large 

 quantities of all the I'eagents except one, or at least such quantities that the alteration 

 which they undergo in the course of the experiment can produce no appreciable effect 

 upon the rate at which the chemical change is proceeding. It is most convenient to 

 select the substance of which the residue can be determined as that of which a relatively 

 small quantity is to be employed. The conditions of the reaction under these circum- 

 stances are indeed simpler than in the former case ; for then each of the substances 

 acting on one another is diminished, and thus two or more variations are made simul- 

 taneously, while in this case a single substance gradually disappears, all around it 

 remaining unchanged. 



Accordingly solutions were prepared of the different reagents, of such a strength as 

 that one measure of each should contain a large excess, as compared with the amount 

 contained in one measure of the standard solution of potassic permanganate. 



The actual quantities used in each experiment were the following : — 



By proportional parts are meant those quantities which react according to the equa- 

 tions before written. 



The method of performing these experiments underwent various modifications during 



