30 REPOHT 1861. 



single experiment, showing exactly how much of the substance measured remains 

 after the lapse of any interval. The numbers, 1, 2, 3, &c., here represent the num- 

 ber of minutes during which the con-esponding experiment was allowed to procee 1. 

 The mode of conducting an experiment was briefly as follows : — The solution con- 

 taining all the substances except the permanganate was brought to the requu'ed 

 temperature, and the permanganate added from a pipette exactly at the beat of a 

 seconds' pendulum. When the time had expired, the temperatm-e of the solution 

 having been kept rigidly constant throughout, a solution of iodide of potassium 

 was added again at the beat of the clock. During and after both additions the 

 liquid was strongly agitated to secure rapid and perfect mixture. The addition of 

 iodide of potassium stops the action. The remaining permanganate is at once re- 

 duced, and liberates thereby an equivalent of iodine which can be detennined at 

 leisure in the usual way. Of such series of experiments the author has made a great 

 number. In the first instance he took the exact quantities of the different substances 

 which react one with another, according to these equations : — 



(I.) K,Mn,0, + 3MnSo,+2H,0 = 2H,SO,+K,SO,+ 5Mn02; 

 (2.) 5Mn02+5H, 80^4- lOH, C^ 0^=15H, O + SMnSO^+SOCOa ; 

 t. e., K, Mn, 0, ; 3MnS0, ; 3H, SO, ; lOH, C, 0„ 2H' 0. 



But he was led to abandon atomic quantities principally by two considerations : 

 first, any error in the proportion of the substances becomes magnified as the expe- 

 riment proceeds ; secondly, the solution changes, not in one particular only, but in 

 several. The quantities of sulphuric acid, oxalic acid, and permanganate diminish, 

 the quantitv of sulphate of manganese increases, while that of the water alone re- 

 mains sensilily constant. In later experiments he had taken all the other substances 

 in such excess, as compared with the permanganate, as to be practically, like the 

 water, infinite in relation to it. Of all, he has taken 100 times the atomic propor- 

 tion, so that the total change taking place in the solution from end to end of the 

 reaction would be a diminution in the amoimt of oxalic acid and sulphuric acid 

 from 100 to 90 pai-ts, and an increase of 1 per cent, in the amoimt of sulphate of 

 manganese. He found by an experiment in which the quantities at starting were 

 varied 1 per cent., that such an alteration did not perceptibly affect the residt. 

 Under these conditions, then, one chemical substance gradually disappears, all aroimd 

 it remaining unchanged. A known quantity is introduced into the solution, which 

 has from the first, where the oxalic acid and sulphate of manganese are in large 

 excess, not a red, but a deep brown colour ; the siibstance thus formed, and whose 

 gradual disappearance we desire to trace, is in all probability binoxide of manga- 

 nese. Having made a number of determiuations after the lapse of various times, we 

 can follow exactly the com'se of its diminution. At first the colour changes rapidly, 

 but as it becomes paler it fades more and more slowly. The axis of x is, no doubt, 

 an asymptote of the curve ; theoretically the whole would never disappear. The 

 problem, then, to be determined was to find the relation between these two series 

 of numbers — or, in other words, given this curve to find its equation. Both in it and 

 in many of the experiments already described, the author enjoyed the cooperation of 

 Mr. Esson, Fellow of Mertou College, Oxford. The result at which the author and 

 Mr. Esson believe themselves to have arrived is, that the mmibers representing the 

 quantities remaining after equal intervals of time are in geometrical progression, and 

 the curve consequently a logarithmic curve. This result admits of a simple and in- 

 teresting interpretation. It is precisely that which would follow fi-om the hypothesis 

 that the dissolved binoxide exists in the fluid in the form of minute spheres upon 

 whose unit of surface is performed a constant action. The total action thus at any 

 moment varies with the surface exposed, and diminishes continually as the spheres, 

 shell after shell, melt away. But the result may ])e explained without the introduc- 

 tion of an hypothesis, if we suppose the binoxide of manganese to be replaced as it 

 disappears, so that the quantity present is always the same, chemical change wUl 

 proceed, since no condition alters, at a imifomi rate, a certain fraction of the whole 

 amount disappearing in a unit of time. But since the relation between the binoxide 

 and the solution in which it is, is not affected by a change in the quantity of the 

 former, one of these magnitudes being infinite relatively to the other, this fraction 

 will remain always constant when the binoxide is not replaced, but is allowed to 



