GRAVITATIONAL STABILITY OF THE EARTIL 227 



adopting a systematic process for the discovery of appropriate coefficients. He very 

 kindly made, and placed at my disposal, a rough preliminary calculation, and the 

 results were sufficiently encouraging to warrant the undertaking of a considerable 

 piece of computation. A professional computer was employed for a time, but 

 eventually I relied upon my own calculations, taking many precautions to ensure 

 accuracy. The systematic process consists in devising a function to represent the 

 " value of land " at any point, and determining, by the method of approximate 

 quadrature, the coefficients of an expansion of the function in spherical harmonics. 

 The results of such a computation clearly depend upon the chosen " value of land," 

 and judgment must l>e exercised in selecting appropriate values. Little importance 

 can be attached to the heights of mountains, l>ecause the highest mountain ranges 

 are, geologically speaking, modern, the ancient mountains being worn down by 

 denudation and erosion. Too much importance is not to be attributed to the actual 

 coast-line, localise this line is subject to many causes of change. The coast-line is 

 but one of the contour-lines of the continental block (the geoid being the level of 

 reckoning), and the shaj>e of the block at considerable depths differs a good deal from 

 that at the surface. At mean-sphere-level (8400 feet below sea-level) the continents, 

 with the exception of the Antarctic continent, form a continuous block.* The Arctic 

 Ocean is reduced, so far as is known, to a trough running nearly along the meridian 

 of Greenwich, from about latitude 05 N. to about latitude 80 N. It may extend to 

 the North Pole and surround it. The polar block spreads southwards in two great 

 masses America and Eurasia. These are joined through the British Isles, Iceland 

 and Greenland on the one side, and across Behring's Strait on the other ; the contour- 

 line at mean-sphere-level runs practically along the 60th parallel between America 

 and Europe and along the 50th parallel between America and Asia. The Eurasian 

 division of the block forks near the Persian Gulf, and tapers southwards in two 

 branches, one containing Africa and the other the Malay Peninsula, adjacent islands, 

 Australia and New Zealand. The Red Sea does not go down to mean-sphere-level, and 

 the Mediterranean does so only in two small patches. The American division of the 

 block is continuous across the Gulf of Mexico, the West Indies and the Caribl>ean 

 Sea, which, at this depth, equally with Mexico, Central America, and the Isthmus of 

 Panama, form part of the ridge joining North and South America. The ridge has 

 some local depressions. The block tapers towards Cape Horn, in the neighbourhood 

 of which, however, it has a great eastward extension, and this extension turns 

 westward and nearly joins the northern continental block to the Antarctic continental 

 block through the South Shetland Islands.! The Antarctic block also shows a 



* The information here detailed in regard to the distribution of the continental blocks and oceanic 

 regions at mean-sphere-level is taken from a map drawn by H. R. MILL in ' The Scottish Geographical 

 Magazine ' (Edinburgh), vol. 6 (1890), p. 184. Reference may be made to the rough map on p. 237 below. 



t It is now known that the depth of the channel is not so great as it was for a long time supposed to be. 

 See a paper by W. S. BRUCE in 'The Scottish Geographical Magazine ' (Edinburgh), vol. 21 (1905), p. 402. 



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