Page:Newton's Principia (1846).djvu/414

 diameter of the earth, according to Picart's mensuration, is 19615800 Paris feet, or 3923,16 miles (reckoning 5000 feet to a mile), the earth will be higher at the equator than at the poles by 85472 feet, or 17⅒ miles. And its height at the equator will be about 19658600 feet, and at the poles 19573000 feet.

If, the density and periodic time of the diurnal revolution remaining the same, the planet was greater or less than the earth, the proportion of the centrifugal force to that of gravity, and therefore also of the diameter betwixt the poles to the diameter at the equator, would likewise remain the same. But if the diurnal motion was accelerated or retarded in any proportion, the centrifugal force would be augmented or diminished nearly in the same duplicate proportion; and therefore the difference of the diameters will be increased or diminished in the same duplicate ratio very nearly. And if the density of the planet was augmented or diminished in any proportion, the force of gravity tending towards it would also be augmented or diminished in the same proportion: and the difference of the diameters contrariwise would be diminished in proportion as the force of gravity is augmented, and augmented in proportion as the force of gravity is diminished. Wherefore, since the earth, in respect of the fixed stars, revolves in 23h.56′, but Jupiter in 9h.56′, and the squares of their periodic times are as 29 to 5, and their densities as 400 to 94½, the difference of the diameters of Jupiter will be to its lesser diameter as $$\scriptstyle\frac{29}{5}\times\frac{400}{94\frac12}\times\frac1{229}$$ to 1, or as 1 to 9⅓, nearly. Therefore the diameter of Jupiter from east to west is to its diameter from pole to pole nearly as 10⅓ to 9⅓. Therefore since its greatest diameter is 37″, its lesser diameter lying between the poles will be 33″ 25‴. Add thereto about 3″ for the irregular refraction of light, and the apparent diameters of this planet will become 40″ and 36″ 25‴; which are to each other as 11⅙ to 10⅙, very nearly. These things are so upon the supposition that the body of Jupiter is uniformly dense. But now if its body be denser towards the plane of the equator than towards the poles, its diameters may be to each other as 12 to 11, or 13 to 12, or perhaps as 14 to 13.

And Cassini observed in the year 1691, that the diameter of Jupiter reaching from east to west is greater by about a fifteenth part than the other diameter. Mr. Pound with his 123 feet telescope, and an excellent micrometer, measured the diameters of Jupiter in the year 1719, and found them as follow.