186 Proceedings of Royal Society of Edinburgh. [sess. 1 
the paper already cited, I was led to fix the position of mean-sphere 
level at about 1400 fathoms below sea-level; that is to say, nearly 
midway on the very steep descent which everywhere separates the 
comparatively flat-topped world-ridges from the still flatter-bottomed 
world-hollows. My friend Mr J. G. Bartholomew has drawm my 
attention to the fact that recent hydrographic exploration in the 
Pacific and Indian Oceans has revealed the existence of a far greater 
area more than 3000 fathoms deep than was supposed to exist when 
the maps for Dr Murray’s paper were constructed. Hence in that 
paper the area with depths between 2000 and 3000 fathoms must 
be restricted, and the area with depths greater than 3000 fathoms 
enlarged to the same extent. The other contour-lines are practically 
unaltered, but the volume of the hydrosphere is greater than was 
assumed, and the contour-line of mean-sphere level must lie at a 
somewhat greater depth than 1400 fathoms. 
It is obvious that the two areas into which the mean-sphere level 
line divides the surface of the globe bear no necessary relation of 
size to one another. If, for example, the elevated area were a vast 
pillar 1 square mile in section, the mean-sphere level line would be 
traced round it very near the base ; if, on the other hand, the elevated 
area were a mass 166,000,000 square miles in section, mean-sphere 
level would be close to the mouth of the narrow pit which formed 
the depressed area. 
When a map of the sphere on an equal surface projection is cut 
out along the contour-line of 1400 fathoms of ocean depth (assumed 
mean-sphere level), the area above that level is, as estimated by 
weighing the two portions, 20 per cent, smaller than the area beneath 
that level. In this experiment, the red line marking mean-sphere 
level on the map was visible on the portion representing the de- 
pressed area. This line was 80 inches long, and assuming that of 
an inch were left on the one side, this would account for one quarter 
of the difference, leaving the depressed area 15 per cent, larger than 
the elevated area ; i.e, the two areas would be equalised by trans- 
ferring 7J per cent, of the larger to the smaller. In so rough an 
experiment it is not a great assumption to take the two areas as 
equal, but if instead of doing so we inquire into one or two other 
ratios, the equality in area of the elevated and depressed region is 
practically proved. 
