1877.] The Rev. S. Haughton on Physical Geology. 53 



or, neglecting small quantities, 



—tan 20=935-6 p sin 2X (7) 



This equation shows that the pole moves away from the mass fx, and 

 that this mass is most effective at the latitude of 45°. 



3. In order to apply the preceding to the case of our actual conti- 

 nents and oceans, we integrate (7) along the meridian as follows, 



a rHdl , 



p M TT- cosX ^' 



where 



r = radius of earth, 

 I = longitude, 

 X= latitude, 



t = height of continent or depth of sea above or below the 

 zero plane. 



Hence we have 



tan 20=20=-935-6 t=\ cos K sin 2\d\, 



and finally 



0= -935-6 !^(l_cos~3\) (8) 



The zero plane, from which t is measured, is the surface of the ellip- 

 soid similar to the sea-surface, and containing the same volume as the 

 total solid matter of the globe. It is thus found : assuming the mean 

 height of the continents above the sea-level at about 1000 feet, and the 

 mean depth of the ocean at about two miles, we have, in miles, 



x ~w+l- • • • • w 



where oc is the height of the zero plane above the present mean sea- 

 bottom, and L, W are the areas of land and water : 



L= 52 millions of square miles. 

 W = 145 „ 



Substituting in (9) we find 



a?=0-58 mile. 



The zero plane, therefore, or original surface of the solid earth before 

 it became wrinkled by geological forces, lies at a depth of 1-42 foot 

 below the sea-level. In using equation (8) we must therefore write 



t— -f 1*62 mile (continent). 

 t=— 0-58 „ (ocean). 



