218 POPULAR LECTURES AND ADDRESSES. 



the second order, in the development of a discon- 

 tinuous function equal to the height of the sea at 

 any point above the mean level where there is sea, 

 and equal to zero for all parts of the earth's surface 

 occupied by dry land. This spheroid we shall call 

 for brevity the mean tidal spheroid (lunar or solar 

 as the case may be, or luni-solar when the heights 

 due to moon and sun are added). The fact that the 

 lunar semidiurnal tide is, over nearly the whole sur- 

 face of the sea, greater than the solar, in a greater 

 ratio than that of the generating force, renders it 

 almost certain that the longest axes of the mean 

 luni-tidal and soli-tidal spheroids would each of 

 them lie in the meridian 90 from the disturbing 

 body (moon or sun) if the motion of the water were 

 unopposed by friction ; or, which means the same 

 thing, that there would be on the average of the 

 whole seas, low water when the disturbing body 

 crosses the meridian, were the hypothesis of no fric- 

 tion fulfilled. But, as Airy has shown, the tendency 

 of friction is to advance the times of low and high 

 water when the depth and shape of the ocean are 

 such as to make the time of low water on the 

 hypothesis of no friction be that of the disturbing 

 body's transit. Now, the well-known fact that the 

 spring tides on the Atlantic coast of Europe are 

 about a day or a day and a half after full and 

 change (the times of greatest force), and that 

 through nearly the whole sea they are probably 

 more or less behind these times, which Airy long 



