84 EXPERIMENTAL OBSERVATIONS ON 



pared to k v k 2 x 2 is small compared to A^ (a x) and may be neglected, 

 when the formula becomes 



This may be written 



dx 



dt 



which is Henri's formula that is to say, during this period when 

 k^x 2 is small compared to 7^ (a-x), or in other words, when reversion 

 may still be neglected, Henri's formula holds. The curve of velocity 

 shows a greater value than is given by the simple logarithmic law, 

 and the constant calculated on the simple logarithmic basis will 

 increase in this stage of the reaction, while a constant calculated on 

 the above formula will remain approximately constant. 



As x goes on increasing, however, the value of A: 2 x 2 will cease to 

 be negligible as compared with k-^ (a - x), and in the end k^ (a - x) 

 will become less than k 2 x 2 , when the expression within the square 

 brackets will become negative in value. Just around the point where 

 k 2 x 2 = jfej (a - x), the simple logarithmic law will approximately hold, 

 for then the expression in square brackets will be almost zero and 

 negligible in comparison to 7^ (a - x), so that the equation becomes 



=&! (a-x), which yields the simple logarithmic formula. But 

 ct r 



as x goes on increasing, and a x diminishing, it is obvious that the 

 negative value of the expression in square brackets will rapidly 

 increase, and that the reaction will proceed much more slowly with 

 ever-increasing deviation from the logarithmic law. 



Finally, the reaction will come into equilibrium, and beyond this 

 point will be reversed. 



For the reversed reaction near the end-point, since a x is small 



compared to x and hence - = 1, the equation becomes = k a 2 , or the 



velocity of reaction is constant and the curve expressing it a straight 

 line as at the beginning of the reaction. Since, however, the whole 

 of the reversed stage is short, and an appreciable amount of a - x 



relatively to x is soon formed since the reaction runs -^- = k 2 x 2 , and x 



ctt 



is here large, the straight line portion on this side is infinitely short 

 and cannot be demonstrated experimentally. 



The equation given above hence serves to demonstrate that the 

 law governing the reaction is the same throughout, and that the 



