582 Dr. Harold Jeffreys on 



and maximum velocity of the water 5^- ft./sec. Then the 

 product of the height and the velocity of the particles is 

 <S0 ft. 2 /sec. or 72000 cm. 2 /sec. This is of the order of 500 

 times the turbulence found, so that very little irregularity 

 in the wave-motion is required to give the turbulence 

 indicated by the current theory. 



II. Vertical Transference of Heat. 



Turbulence facilitates the downward transfer of heat in 

 much the same way as it does that of momentum ; this 

 satisfies the equation 



3v a/,dv 



a* ~a 



KC> 



where V is the temperature, t the time, and h the thermo- 

 metric coefficient of eddy-conductivity, which is numerically 

 equal to the fiddy-viscosity. The only indication I have 

 found of the character of this transfer is given by Murray 

 and Hjort *, in the following table showing the temperature 

 variations in the Atlantic outside the Sognefiord in 1903. 

 Temperatures are expressed in degrees centigrade. 



Depth 

 (metres). 



February. 



May. 



August. 



November 







4-8 



7-3 



13-8 



8-7 



100 



6-8 



64 



6-9 



9-3 



200 



7-9 



7-0 



6 7 



7-9 



300 



63 



65 



6-4 



? 



It will be noticed that at the surface the highest temper- 

 ature for the year occurs in September ; at 100 metres it is 

 in November ; at 200 metres in December ; and at 300 

 metres in the spring. Thus the maximum occurs later and 

 later as the depth increases, owing to the time needed for 

 heat to penetrate downwards. It takes over six months to 

 reach a depth of 300 metres, so that the phase of the annual 

 variation is there reversed. To determine the vertical 

 distribution of turbulence from the few data available is a 

 matter of some difficulty, and I finally adopted the following 

 method. The annual parts of the temperature variation 

 depending on the sine and cosine of /, the increase in the 

 sun's longitude since February 15th, were found for the four 

 depths given. The coefficients of these were plotted against 

 the depth on squared paper. If the annual part of the 



* ' Depths of the Ocean,' p. 228 (1913). 



