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Mr. G. H. Darwin on Problems connected [Dec. 19, 



effective forces give bodily forces in the interior, the sum of whose 

 moments about the axis of rotation is equal and opposite to the tidal 

 fractional couple. The problem is thus reduced to finding the dis- 

 tortion of a sphere subject to bodily force equilibrated by surface 

 action, and it is solved by Sir W. Thomson's method of finding the 

 internal strain of an elastic sphere under like conditions, although 

 here the bodily force has no corresponding potential function. 



The solution shows that the distortion consists in a simple cylin- 

 drical motion round the axis of rotation, each point moving from east 

 to west with a linear velocity proportional to the cube of its distance 

 from that axis. 



The distortion of the surface of the globe consists of a motion in 

 longitude from west to east, relatively to a point in the equator, the 

 rate of change of longitude being proportional to the square of the 

 sine of the latitude. 



Numerical calculation shows, however, that in the later stages of 

 the earth's history (the development being supposed to follow the 

 laws found in the paper on " Precession"), the distortion must have 

 been very small. With a certain assumed viscosity, it is found that, 

 looking back 45,000,000 years, a point in latitude 60° would lie 14' 

 further east than at present. From this it follows, that this cause 

 can have had little or nothing to do with the crumpling of geological 

 strata. 



As, however, the distorting force varies inversely as the sixth power 

 of the moon's distance, it seems possible that in the very earliest 

 stages this cause may have had sensible effects. It is, therefore, note- 

 worthy that the wrinkles raised on the surface would run north and 

 south in the equatorial regions, with a tendency towards north-east 

 and south-west in the northern hemisphere, and north-west and south- 

 east in the southern one. The intensity of the distorting force at the 

 surface varies as the square of the cosine of the latitude. 



An inspection of a map of the earth shows that the continents (or 

 large wrinkles) conform more or less to this law. But Professor 

 Schiapparelli's map of Mars* is more striking than that of the earth, 

 when viewed by the light of this theory ; but there are some 

 objections to its application to the case of Mars. If, however, there 

 is any truth in this, then it must be postulated, that after the wrinkles 

 were formed the crust attained sufficient local rigidity to resist the 

 obliteration of the wrinkles, whilst the mean figure of the earth 

 adjusted itself to the ellipticity appropriate to the slackening diurnal 

 rotation ; also, it must be supposed that the general direction of the 

 existing continents has lasted through geological history. 



The second question, considered in the first part, deals with the 



* "Memorie della Societa degli Spettroscopisti Italiani," 1878, toL rii. 



