Haughton and Reynolds — "Brag" of Water upon Water. 287 



where ff denotes the force of gravity, i the slope of Ihe surface, and 

 a; the distance of any particle from the origin measured in the direc- 

 tion of the motion. If v denote the velocity of a particle, equa- 

 tion (10) hecomes at once 



j^+fv=g siui; (11) 



which gives, by integration, 



e^{g sin i - fv) = const. (12) 



This indicates that the velocity will increase from zero up to the 

 value given by 



g sin i — fv = 0, (13) 



after which it will remain constant for ever. 



The final constant velocity given by equation (13) is 



v=^—r-= 32-2 X 307-057 sin t. (14) 



If we express the velocity in feet per second, and call h the slope 

 per mile, we find 



V = 1-8726 X Aft. per second; (15) 

 which is equivalent to 



V - 30-642 h miles per day. (16) 



Dr. Carpenter has proposed to explain the phenomena of ocean 

 circulation by the greater height of the water at the equator as com- 

 pared with that at the poles. 



If we call the distance from the equator to the pole 6000 miles, 

 and suppose the velocity of the surface current towards the pole to be 

 only one mile per day, we find from equation (16), that this would 

 require a head of water at the equator 



h = 195-80 feet 



No such difference of level can be admitted between the equili- 

 brium levels of the equatorial and polar oceans. 



K. I. A. PROC, SEE. II., VOL. III. — SCIENCE. Y 



