# Page:Popular Science Monthly Volume 10.djvu/433

and r the mean radius of the earth; T, the length of the sidereal year, reduced to seconds; and 12 g the distance a body falls in a second at the earth's surface. Now, the distance the earth falls toward the sun in a second, or the curvature of her orbit in a second, is equal to ${\displaystyle \scriptstyle {\tfrac {2\pi ^{2}R}{T^{2}}}}$ (about 0.119 inch). Hence, by the law of gravitation, 12 g : ${\displaystyle \scriptstyle {\tfrac {2\pi ^{2}R}{T^{2}}}={\tfrac {m}{r^{2}}}:{\tfrac {M}{R^{2}}}}$, whence, ${\displaystyle \scriptstyle M=m\left({\tfrac {4\pi ^{2}R^{3}}{T^{2}r^{2}g}}\right)}$ In this formula make it = 3.14159 ; R, 92,250,000 miles ; T = 31,558,149.3 seconds ; r = 3,956.179 miles ; and g = 0.0061035 mile (16.113 feet), and we shall. get the result given in the text, viz., M = 325,600 m.