OCEAN TEMPEEATUEES 337 



INTRODUCTION 



THE PLACE OP MATHEMATICAL METHODS IN RESEARCHES ON 

 OCEANOGBAPHIC PROBLEMS 



The present paper deals with the formulation and solution of 

 several quantitative problems suggested by data on ocean winds, 

 temperatures, and circulation. Before formulating these problems 

 a brief general discussion of the place of mathematical methods in 

 oceanographic researches is given. 



The process of testing physical laws in the laboratory is greatly 

 facilitated by devising appropriate experiments in which the variables 

 are largely under the control of the investigator. Even under these 

 favorable conditions the actual phenomena are too complex for de- 

 tailed representation in a mathematical formula, and an appropriate 

 simplification by abstraction is required to formulate problems that 

 are amenable to mathematical treatment. This is true in a much 

 greater degree of the more complex phenomena occurring in nature; 

 yet a rigorous mathematical treatment of natural problems capable of 

 yielding results in agreement with observations, while in general more 

 difficult, is necessary and fully justifies the increasing attention being 

 given to terrestrial and cosmic physics. 



The actual phenomena of heating and cooling of the water in the 

 ocean are far too complex to be considered in detail. Therefore, in 

 order to apply rigorous mathematical reasoning to these phenomena, it 

 is necessary to devise a comparatively simple ideal system which would 

 behave in essentially the same way as the actual one with reference to 

 the observations in question. Certain problems can then be formulated 

 definitely in such a way as to permit of the precise calculation of 

 results, the comparison of which with observations tests the practical 

 value of the abstract system. 



It is fortunate for the problems considered in this paper that the 

 proper choice of the simple assumptions needed in devising the ideal 

 system is facilitated by certain general results of numerous and extended 

 ocean as well as laboratory observations. An abstract system founded 

 on such assumptions would in general agree much better with the 

 conditions in nature than one in which the assumptions were hypo- 

 thetical or carried over from some other field. Evidently deductions 

 from any group of simple assumptions cannot have the same degree 



