168 



Mr. G. H. Darwin. 



[June 19 y 



Thalen and that given by Boisbaudran for the bright line to which we 

 assume it to correspond, it was determined in the way above described, 

 and must not be taken to have more importance. By our method of 

 working, the very high dispersive power required for the specific 

 identification of any substance by the determination of an individual 

 wave-length is avoided ; as we depend on the greatly diminished 

 likelihood of error when several groups of lines of the same substance 

 are seen to be continually present at the time of one or more reversals. 

 It was the necessity of being able to rapidly sweep the entire spectrum 

 for the above purpose that caused us to limit the dispersion. 

 A large majority of the wave-lengths given by Thalen were obtained 

 by means of the moderate dispersion of one bisulphide of carbon prism, 

 a less dispersion than we have used ; and it would be incorrect to 

 suppose that no enduring work in this field of spectroscopy can be 

 effected except with the enormous dispersive power which Mr. Lockyer 

 recommends. 



VIII. "The Determination of the Secular Effects of Tidal Friction 

 by a Graphical Method." By G. H. Darwin, M.A., formerly- 

 Fellow of Trinity College, Cambridge. Communicated Jby 

 J. W. L. Glaisher, M.A., F.K.S. Received May 31, 1879. 



Suppose an attractive particle or satellite of mass m to be moving 

 in a circular orbit, with an angular velocity O, round a planet of mass 

 M, and suppose the planet to be rotating about an axis perpendicular 

 to the plane of the orbit, with an angular velocity n ; suppose, also, 

 the mass of the planet to be partially or wholly imperfectly elastic or 

 viscous, or that there are oceans on the surface of the planet ; then 

 the attraction of the satellite must produce a relative motion in the 

 parts of the planet, and that motion must be subject to friction, or, in 

 other words, there must be frictional tides of some sort or other. 

 The system must accordingly be losing energy by friction, and its 

 configuration must change in such a way that its whole energy 

 diminishes. 



Such a system does not differ much from those of actual planets 

 and satellites, and, therefore, the results deduced in this hypothetical 

 case must agree pretty closely with the actual course of evolution, 

 provided that time enough has been and will be given for such 

 changes. 



Let C be the moment of inertia of the planet about its axis of 

 rotation ; 



r the distance of the satellite from the centre of the planet ; 

 h the resultant moment of momentum of the whole system ; 

 e the whole energy, both kinetic and potential of the system. 



