GEOLOGY.
The variation of the density, acceleration and pressure are shown graphically in the following diagram, Fig. 5, in which these quantities are all measured horizontally from the line AO, repre senting the earth's radius, to the right. The curves have different horizontal scales and are designated, respectively, D.C. (density curve), A.C. (acceleration curve), and P.C. (pressure curve). The pressure curve intersects the axis OQ at right angles at Q.
Another interesting question in this connec tion is what total radial compressibility is com patible with this Laplacian distribution of den sity, acceleration and pressure. The answer may be stated in convenient form thus: If the pressure of the atmosphere were to be doubled the radius of the earth would be shortened everywhere by about 2 metres, or 6.5 feet. This explains how mere inequalities in surface load ing of the earth may account for some of the great observed movements of the earth's crust.
The Rigidity of the It cannot be doubted (as shown below) that the temperature of the nucleus of the earth is very high, probably sufficiently high, under normal condi tions, to melt and even render vaporous the materials of which it is composed. But if the figures of the last column of the above table are examined, it will appear reasonable to sup pose that the behavior of the central mass under such great pressures may be very dif ferent from that ordinarily associated with fluids. The first attempt directly to measure the rigidity of the ball of the earth was made by G. H. and Horace Darwin in 1880. They employed for this purpose a horizontal pendu lum, but the results were not conclusive. Their method has since been successfully employed, however, by several observers (Ehlert, Hecker, Kortazzi, Schweydar and Orloff), who arrived at definite and consistent results. All of these observations, as well as the classic investigation of G. H. Darwin based upon the phenomena of the tides, concur in showing that the nucleus of the earth is solid throughout and that it is somewhat more rigid than if composed of steel.
A most promising investigation of the re sistance which the earth offers to change of shape was recently begun by A. A. Michelson. (Consult The Astrophysical Journal, Vol. XXXIX). The method is based essentially on a very accurate measurement of the tides pro duced in the water level in two buried pipes, each 500 feet long, one running in an east and west and the other in a north and south direc tion. It is the intention to measure the varia tion with the interferometer, the observations being carried on continuously for a long time. Though this has not yet been done, the meas ures thus far having been secured with a microscope merely, it is evident that even the preliminary results are of a very high order of accuracy. They indicate that the rigidity of the earth, or its resistance to change of shape, is about one-third greater than the rigidity of steel.
Acceleration at Surface of What is commonly called the acceleration of gravity at the surface of the earth is the resultant of the accelerations due to the attraction and to the rotation of the earth. This quantity has been measured with considerable precision at many points of the earth's surface by means of the pendulum, and the results have been combined in the following formula, g being the accelera tion at any point of the sea-level whose latitude is #: sin' # centimeters / (seconds)' =32.087-F0.171 sin' # feet / (second)'.
Mean Density and Mass of the Earth.— Since the volume of the earth is known accu rately, the mass can be computed if its density can be ascertained. The author has recently shown (The Astronomical Journal, No. 424), that the product of this mean density and the gravitation constant may be derived with a pre cision comparable to that of the value of the acceleration just given above. The gravitation constant is the quantity essential to convert the proportionality of Newton's law of gravity into an equality. That is, if m and m' are two masses, D their distance asunder, F the force of attraction they exert on one another, and k the gravitation constant, then tnns' F=k—.