440 Prof. Thomson on the Mechanical Theoiy of Electrolysis, 



the equator and the other touching the surface at one pole. The 

 electrical circumstances would be the same if the earth were at 

 rest, and the conductor were made to revolve once round in 

 23^ 56°* 4*, with one end always touching at the pole, and the 

 other close to the surface at the equator. In such circumstances 

 there would be an electro-motive force equal to f.v . ds on any 

 infinitely small element ds of the moving conductor, if v denote 

 the velocity of its motion, and / the vertical magnetic force at 

 the part of the earth over which it is passing. Now if 6 be the 

 latitude of the element dsj and V the velocity of the surface at 

 the equator, we have 



vsrVcos^; 



if the distribution of magnetic force at the surface be, as in 

 making this rough estimate we may assume it to be, of the sim- 

 plest type, we have 



/=Fsin^, 



where E denotes the vertical magnetic force at the pole ; and if 

 r denote the eai-th's radius, we have 



ds=zrdd. 



The intensity of the total electro-motive force between the equa- 

 torial end of the moving conductor and the earth, being the sum 

 of the electro-motive forces on all its elements, will consequently 

 be equal to 



/^''FVrsin^cos^f^^; 

 and hence, denoting it by i, we have 



Now the eartVs diameter being about 7912 miles, we have 

 r=3956x 5280; and, by dividing the number of feet in the 

 earth's circumference by 86164, the number of seconds in the 

 sidereal day, we find V=1523. If we take r=14, we find, by 

 substituting these values for the factors of the preceding ex- 

 pression, 



1=222,700,000,000. 



This is about 88800 times the intensity of a single cellof DanielPa 

 battery (§ 12), and may therefore be about 50 times that of the 

 battery oi two thousand pairs of copper and zinc plates, charged 

 with nitro-sulphuric acid, by which Sir Humphry Davy only ob- 

 tained sparks half an inch long in the exhausted receiver of an 

 air-pump. Now the electro-motive force we have been considering 

 could in reality only produce galvanic currents by forcing a pas- 

 sage through the whole thickness of the atmosphere, upwards 



