312 Mr. J. Stevenson on the Chemical and 



Proceeding to consider the larger values of mh, to which 



Oil 



this expansion for ^ becomes inapplicable ; Scott Russell's 



observations led him to the conclusion that the height of the 

 solitary wave might be increased until it became about equal 

 to the depth of the undisturbed fluid; and he gives c 2 = 2gh 

 as the empirical formula for the velocity in this case. Making 

 a comparison of the formulas again with this value for c 2 , the 

 exact formula gives tan 2mh = 4^mh, and 



mA=*583, approximately. 



The approximate formula in this case gives 



mh = ' 57 '7, approximately; 



so that, even in this extreme case, the formulse are in very 

 close agreement, the difference in the values of mh being just 

 over 1 per cent. 



This comparison seems fully to justify the use of the method 

 I have employed to obtain the approximations. 



As the first approximation is that most likely to be em- 

 ployed, it is perhaps worth while to record that the exact and 

 approximate expressions for the relation between m and the 

 parameters are identical for small values of mh if two terms 

 are taken in the expansion for gh/e*, and that the difference 

 in the terms of the next order is 2m i c 8 /5g i . Taking the 

 extreme case when c 2 = 2gh, the approximate value of mh falls 

 short of the exact value by about 7 per cent. 



XXX. The Chemical and Geological History of the 

 Atmosphere. By John Stevenson, M.A., F.I. C* 



I. — The History of Free Oxygen. 



THE question as to whether any notable change has taken 

 place in the chemical composition of the atmosphere 

 in the course of geological history is one that has received a 

 considerable amount of attention from chemists and geologists, 

 though probably not so much as the importance and interest 

 of the subject deserve. It has been sufficiently clear to 

 geologists for many years that the carbon of our coal supplies 

 has been derived from carbonic acid formerly diffused through 

 the atmosphere or dissolved in the ocean ; and that if all this 

 carbonic acid existed at one time in the atmosphere, the 

 atmosphere must have been very much richer in carbonic 



* Commimicatecl by Prof. G. F. FitzGerald, F.K.S. 



