338 MISCELLANEOUS STUDIES 



of certainty as direct observations, since the ideal system cannot con- 

 form accurately to all the details of the phenomena of the actual one. 

 However, if in this way a logical and reasonably accurate description 

 of a wide range of physical quantities is obtained there is good reason 

 to believe that deductions or predictions relative to quantities not yet 

 observed will be in agreement with the facts. This is especially true 

 if two or more lines of reasoning converge to the same conclusion. 



When it is impossible or impracticable to make the appropriate 

 direct observations the theoretical results must be regarded as the 

 best estimates, even though it is not impossible that future observations 

 may show important deviations from theory. Finally, while the exist- 

 ing observations may be logically described by means of the ideal 

 system, and deductions based on it, extended results reached by apply- 

 ing purely deductive methods to the ideal system are not substitutes 

 for a correspondingly extended series of new observations. The neces- 

 sity for making observations will always exist. 



SOLAR RADIATION AND SURFACE TEMPERATURE, ASSUMING THE 



AVERAGE RATE OF FLOW OF THE WATER TO BE ZERO 

 Preliminary discussion, and statement of certain generally accepted 



conclusions as to the way in ichich the water gains and loses heat. 



In order to have a basis for estimating the effect of circulation on 

 ocean temperatures it is necessary to work out quantitatively the rate 

 at which the heat of the water is gained and lost under the more 

 simple condition of no flow. This will be done by devising an ideal 

 ocean, based on assumptions agreeing as nearly as possible with the 

 following conclusions which are founded on numerous and widely 

 extended ocean observations. 



1. The primary source of heat is the radiant energy of the sun. 

 both direct and diffuse, that penetrates the water (Murray, 1912, p. 

 225, Gehrke, 1910, p. 67, Helland-Hansen, 1911-12, pp. 64-66). 



2. Absorption of this radiation directly heats the water in the 

 upper layers (Nansen, 1913, pp. 21-22), and only a small fraction of 

 this radiant energy penetrates below 25 meters (Kriimmel, 1907. pp. 

 253-270, Helland-Hansen, 1911-12, pp. 65-68, and Knott. 1903-05). 



3. There is always a complex vertical circulation (Helland-Hansen, 

 1911-12, p. 68, Gehrke, 1910, p. 68, Nansen, 1913, p. 21, Murray. 

 1912, p. 226) due to a lack of balance of the many forces acting on 

 the water particles. The resultant vertical flow through a finite sec- 

 tion due to this motion may be very small and may be either upward 



