G. I. TAYLOE ON EDDY MOTION IN THE ATMOSPHERE. 11 



and 3'4xl0 3 ; and that for July 17th and July 29th, when the wind force was 

 about 2, the values were very much lower, being 0'57 x 10 3 and 1'3 x 10 3 respectively. 

 The fact that these figures are so consistent, although t varies from 11 hours to 

 7 days and z from 140 metres to 770 metres, seems to indicate that the eddy motion 

 does not diminish to any great extent in the first 770 metres above the surface. 



Vertical Change of Velocity due to Eddy Motion. 



In the first part of this paper the vertical transference of heat by means of eddies 

 has been discussed. For this purpose it was necessary to consider only the vertical 

 component of eddy velocity, but in the questions which are treated in the succeeding 

 pages it is no longer possible to leave the horizontal components out of the calculations. 

 It seems natural to suppose that eddies will transfer not only the heat and water 

 vapour, but also the momentum of the layer in which they originated to the layer 

 with which they mix. In this way there will be an interchange of momentum 

 between the different layers. If U. and V ; represent the average horizontal 

 components of wind velocity at height z parallel to perpendicular co-ordinates x and 

 y, and if?*', t'', w' represent components of eddy velocity so that the three components 

 of velocity are U z + w', V,+ r' and ', then the rate at which a;-momentuiu is trans- 

 mitted across any horizontal area is 



P (U t +u')w'dxdy, (3) 



ff * 



and the rate at which ?/-momeutum is transferred is \\p(V t +v')u/dxdy the integrals 



extending over the area in question. 



If we were to suppose that an eddy conserves the momentum of the layer in which 

 it originated so that IL+ H' = U, and V ; + v' = V,,,, where z is the height of the layer 

 in question, we could obtain the values of the integrals in the same way that we did 

 in the case of heat transference. In the case of heat transference, owing to the small 

 value of the ordinary coefficient of " molecular " conductivity, the only way in which 

 an eddy can lose its temperature is by mixture ; but in the case of transference of 

 momentum the eddy can lose or gain velocity owing to 'the existence of local variations 

 in pressure over a horizontal plane. Such variations are known to exist ; they are in 

 fact a necessary factor in the production of disturbed motion, and they enter into all 

 calculations respecting wave motion. We cannot, therefore, leave them out of our 

 calculations without further consideration, though it will be seen that they probably 

 do not affect the value of the integral (3) when it is taken over a large area. 



Consider a particular case of disturbed motion. Suppose that the fluid is incom- 

 pressible and that the motion takes place in two dimensions x and z. Suppose that 

 originally the fluid is flowing parallel to the axis of x with velocity U, and that the 



c 2 



