40 J. F. TWISDEN OK" POSSIBLE DISPLACEMENTS 



of the axis of figure oannot be so great as the value of 6 given "by 

 the equation 



tan20=7-; — r 



and, further, if we suppose the whole amount of matter in the equa- 

 torial bulge to be denoted by M, this equation, combined with 

 equation (1), will give 



5/*= M tan 20. 



If, now, 6 is an angle of 20°, /x must be rather more than a sixth 

 part of the equatorial bulge — a quantity of matter which would 

 cover the whole of the torrid zone on both sides of the equator — 

 and have a thickness of more than 3 J miles. In whatever way this 

 enormous amount of matter were transferred from one part of the 

 earth to another, it could not shift the axis of figure through an angle 

 of 20°. It is to be particularly observed that the transfer of matter 

 might take place in such a way as to produce no effect of the kind 

 contemplated ; or, again, it might be made in such a way as to pro- 

 duce but little effect, or, indeed, any effect, up to a point short of 

 20°. Within that limit the effect would depend on whence the 

 matter was taken, and where it was placed. If, for instance, the 

 elevations and depressions in the zones considered in art. 6 had been 

 on such a scale that the quantity of matter transferred had been a 

 sixth part of the equatorial bulge, the axis of figure would be dis- 

 placed through no more than an angle of about 1° 30'. 



13. If we suppose the axis of figure by any means to be brought 

 to an inclination of several degrees (say 20°) with the axis of revo- 

 lution, results would follow which it may be just worth while to 

 mention. Referring to the figure, suppose that CD is the meridian 

 of Greenwich ; then D will be a point in latitude 50° !N . If we 

 suppose the earth on a given day to be revolving, in these altered 

 circumstances, round OC, about a hundred and fifty days after 

 OD will come into a position very near to O2, and will then be the 

 axis of rotation. Supposing the earth rigid, its form would undergo 

 no change ; but in the one case the minor axis of the ocean-surface 

 would coincide with OC, and about 150 days after it would coincide 

 with OD. The effect which this would tend to produce can be 

 readily ascertained by supposing two ellipsoids of revolution, shaped 

 like the earth, and of the same size, to have coincident centres, and 

 their axes of revolution to be inclined at an angle of 40°. It would be 

 found that at certain points one of the ellipsoids would have its surface 

 8 miles above, and at other points 8 miles below the surface of the 

 other ellipsoid. In other words, the effect would be to cause in the 

 ocean a huge tidal motion with a period of about 300 days. The 

 various effects which such a tide would produce would be highly com- 

 plicated ; but it may be pretty confidently asserted that one of the 

 effects produced would be that the ocean would sweep over the earth 

 and render it quite uninhabitable. 



