No. 11. From the observed shape of Jupiter or any planet the length of its day could be estimated.
Jupiter is much more oblate than the earth. Its two diameters are to one another as 17 is to 16; the ellipticity of its disk is manifest to simple inspection. Hence we perceive that its whirling action must be more violent—it must rotate quicker. As a matter of fact its day is ten
Fig. 72.—Jupiter.
hours long—five hours daylight and five hours night. The times of rotation of other bodies in the solar system are recorded in a table above.
No. 12. The so-calculated shape of the earth, in combination with centrifugal force, causes the weight of bodies to vary with latitude; and Newton calculated the amount of this variation. 194 lbs. at pole balance 195 lbs. at equator.
But following from the calculated shape of the earth follow several interesting consequences. First of all, the intensity of gravity will not be the same everywhere; for at the equator a stone is further from the average bulk of the earth (say the centre) than it is at the poles, and owing to this fact a mass of 590 pounds at the pole; would suffice to balance 591 pounds at the equator, if the two could be placed in the pans of a gigantic balance whose beam straddled along an earth's quadrant. This is a true variation of gravity due to the shape of the earth. But besides this there is a still larger apparent variation due to centrifugal force, which affects all bodies at the equator but not those at the poles. From this cause, even if the earth were a true sphere, yet if it were spinning at its actual pace, 288 pounds at the pole could balance 289 pounds at the equator; because at the equator the true weight of the mass would not be fully appreciated, centrifugal force would virtually diminish it by 1⁄289th of its amount.
In actual fact both causes co-exist, and accordingly the total variation of gravity observed is compounded of the real and the apparent effects; the result is that 194 pounds at a pole weighs as much as 195 pounds at the equator.
No. 13. A homogeneous sphere attracts as if its mass were concentrated at its centre. For any other figure, such as an oblate spheroid, this is not exactly true. A hollow concentric spherical shell exerts no force on small bodies inside it.