DYNAMICAL THEORY OF TIDES 85 



There are many cases in which the phenomena 

 to be investigated are complicated by so many 

 details of local or other circumstances that they 

 do not lend themselves to immediate treatment 

 by pure theory without the admixture of a large 

 amount of purely empirical data. In such cases 

 results of great value have often been obtained by 

 a mixed method, partly dynamical, and partly 

 empirical ; this is frequently the case when a purely 

 mathematical analysis of the phenomena con- 

 cerned is beyond the present powers of mathe- 

 maticians. A striking instance of such mixed 

 method is afforded by the case of the calculation 

 of tables predicting the tides at a particular port. 

 In accordance with the dynamical theory of the 

 tides regarded as due to the disturbing effect of 

 the attraction of the moon and sun on the water 

 the actual height of the tide at a given time has 

 been shown to be due to the superimposition of 

 a number of simple tides each of which has a 

 definite period. One of these simple tides, the 

 chief one in most parts of the world, has a period 

 of half a day, another has a period of a whole day, 

 and there are others of various periods dependent 

 on the month and the year. A considerable 

 number of these simple tides, the period of each 

 of which has been obtained by the mathematical 

 theory, must be taken account of; but though 

 the period of each of these is thus given by theory 

 the maximum height of each is not so ascertainable 



