Application of Harmonic Analysis to Tidal Theory. 209 



I do not think it worth while to enter into further detail regarding 

 the experiments in question. 



The following summary gives the densities of the various gases 

 relatively to air, all obtained by the same apparatus.* The last 



figure is of little significance. 



Air free from H 2 and C0 2 1-00000 



Oxygen 1*10535 



Nitrogen and argon (atmospheric) .... 0*97209 



Nitrogen 0'96737 



Argon 1-37752 



Carbonic oxide 0*96716 



Carbonic anhydride 1*52909 



Nitrons oxide , 1*52951 



The value obtained for hydrogen upon the same scale was 0*06960 ; 

 but the researches of M. Leduc and of Professor Morley appear to 

 show that this number is a little too high, 



" On the Application of Harmonic Analysis to the Dynamical 

 Theory of the Tides. Part II. On the general Integration 

 of Laplace's Dynamical Equations." By S. S. HouGH ; 

 M.A., Fellow of St. John's College, and Isaac Newton 

 Student in the University of Cambridge. Communicated 

 by Professor G. H. Darwin, F.R.S. Received October 27, 

 —Read December 9, 1897. 



(Abstract.) 



The former part of this paper deals with solutions of Laplace's 

 differential equations for the tides symmetrical with respect to the 

 axis of rotation. In the present part the restriction of symmetry is 

 no longer imposed, and a general solution is sought, the law of depth 

 of the ocean, however, being limited to the case which will admit 

 of both the interior and exterior surfaces being regarded as spheroids 

 of revolution. It is found that, subject to this limitation, if the 

 solution sought represent a simple harmonic motion of any period 

 whatsoever, and the height of the surface-waves be expressible as an 

 infinite series of tesseral harmonics of the same rank but different 

 orders, a linear relation connecting three successive coefficients of 

 the series can be deduced similar to that obtained in. Part I.f 



From this relation a period-equation for the free vibrations is 

 deduced, and a method of determining approximate values of the 



* 1 Roy. Soc. Proc.,' vol. 53, p. 148, 1893 ; vol. 55, p. 340, 1894 ; ' Phil. Trans.,' 

 vol. 186, p. 189, 1895 ; < Roy. Soc. Proc.,' vol. 59, p. 201, 1896. 

 f 1 Roy. Soc. Proc.,' vol. 61, p. 236. 



