374 CARNEGIE INSTITUTION OF WASHINGTON. 



between, as in tidal deformations. In all these cases of deformation, 

 the stresses permeate the whole body and are greatest in the central 

 parts. Sir George Darwin^ found that for a homogeneous, incom- 

 pressible earth the stress ratios would be 8 at the center, 3 at the 

 equator, and 1 at the poles. For a compressible earth they would be 

 relatively lower at the surface and higher at the center. For a certain 

 compressibility the surficial stress-differences disappear and those at 

 the center increase one-sixth in value. The actual stress-differences 

 generated by changes of rotation, tidal attractions, and other in- 

 fluences of this type may be taken as ranging from vanishing quantities 

 at the surface to 9 or 10 at the center. These stress-differences are 

 superposed on hydrostatic stresses of much higher orders. While the 

 tidal stresses are small, they are not only frequent and rhythmical, but 

 follow persistently in a given direction. In certain respects their 

 effects are thus cumulative. Tidal influences of some sort must have 

 arisen as soon as the segregation of the planetary nuclei began. Changes 

 in rotation were probably frequent in the formative stages and probably 

 then had high deformative value. The combination of these agencies 

 is regarded as highly potential, because they brought to bear higher 

 stresses on the central parts than on the outer parts, thus giving rise 

 to a graded squeeze with least resistance outwards. Obviously this 

 graded squeeze would tend to force surfaceward the less-resisting 

 matter. The stresses worked in rhythmic kneading fashion. They 

 doubtless had special effectiveness in the formative stages when the 

 masses were youngest, and when self-compression, selective removal, 

 readjustment, and reorganization were most easily accomplished. 

 The combination was admirably fitted to give that increasing distri- 

 bution of density and rigidity centerward, towards which the united 

 testimony of astronomical evidence, body tides, polar nutation, and 

 seismic data are now so strongly converging. The normal results of this 

 combination of forces are equally in harmony with the results reached 

 in the present inquiry by a comparison of the earth, Venus, Mars, and 

 the moon. 



THE BEARINGS OF THE SIZE AND RATE OF INFALL OF THE PLANETESI- 

 MALS ON THE LIQUIDITY OR SOLIDITY OF THE EARTH. 



Under the planetesimal view the concentration of each nucleus was 

 followed by growth from the infall of planetesimals. The chief sources 

 of planetesimals were (1) dispersion by solar propulsion and (2) mole- 

 cular escape. The latter was important only where self-control was 

 limited, but, as already pointed out, all the solid bodies must have 

 lost much of their original substance, and this was probably due in the 

 main to molecular activity. The matter so lost would be subject to 

 recapture, though it could not usually be held permanently unless cool- 



'Scientific Papers, vol. 2, 475-4S1, 1908. 



