86 MATHEMATICS 



because it depends on a vast variety of special 

 circumstances, such as the conformation of the 

 land and the shape of the basin of the sea. Ac- 

 cordingly the problem of determining the height 

 of the tide at a given future time is resolved by 

 making a very considerable number of observations 

 of the tide at the particular port, and utilizing the 

 results of such observations to determine the 

 maxima of the simple tides of known periods of 

 which the actual tide is made up. This process 

 is actually carried out by a machine devised for 

 the purpose, and thus a table available for future 

 times can be calculated on the basis of this 

 combination of theory with observation. Other 

 examples of this mixed method are being applied 

 in the processes adopted for the calculation of the 

 trajectories of projectiles, and in problems con- 

 nected with air-craft, especially in relation to the 

 very important questions as to the stability of 

 machines of various types. In recent years mathe- 

 matical methods have been applied with increasing 

 frequency to the statistical analysis of large masses 

 of measurable observations of some prescribed 

 type, in cases in which no dynamical or other 

 theory as to the cause of the phenomena in question 

 is assumed a -priori. The statistical method has 

 been largely applied in biological science by a 

 school of investigators to obtain information as 

 to the correlation of different determining factors. 

 Although there is at present much difference of 



