6. TO FIND THE CIRCUMFERENCE OF THE EARTH.—If the earth were a perfect sphere, it is obvious that degrees of latitude would be of the same length wherever measured on its surface. Each would be of the entire circumference. If, however, a person sets out from the equator, and travels along a meridian toward either pole, and when the polar star has risen in the heavens one degree above the horizon, he marks the spot, and then continues his journey, marking each degree in succession, he will find that the degrees are not of equal length, but increase gradually from the equator to the pole. If now the length of a degree be measured at different places, the rate of variation can be found, and then the average length be estimated. Measurements for this purpose have been made in Peru (almost exactly at the earth's equator), Lapland, England, France, India, Russia, etc. So great accuracy has been attained, that Airy and Bessel, who have solved the problem independently, differ in their estimate of the equatorial diameter but 77 yards, or only 880 · of a mile. 7. TO FIND THE RELATIVE SIZE OF THE PLANETS.The volumes of two globes are proportional to the cubes of their like dimensions. The diameter of Mercury is 2,962 miles, and that of the earth 7,925; then, The volume of Mercury: the volume of the earth: 2962: 79259. The same principle applied to the volume or bulk of the sun gives The bulk of the sun bulk of earth :: 852584: 79253. 8. TO FIND THE DIAMETER OF THE SUN.—(1.) A very simple method is to hold up a circular piece of paper before the eye at such a distance as to exactly hide the entire disk of the sun. Then we have the proportion, As dist. of paper disk: dist. of sun's disk :: diam. of paper d. : diam. sun's d. (2.) The apparent diameter of the sun, as seen from the earth, is about 32': the apparent diameter of the earth, as seen from the sun, is twice the solar parallax, or 17.88". Thence, the Ap. diam. of earth: ap. diam. of sun :: real diam. of earth: real diam. of sun, (3.) Knowing the apparent diameter of the sun, and its distance from the earth, the real diameter is found by Trigonometry. In figure 95, let S represent the earth, AB the radius of the sun, and ASB half the apparent diameter of the sun. We shall then have the proportion, AS AB :: radius: sin. 16' (half mean diam. of sun). By a similar method the diameters of the planets are obtained. APPENDIX. TABLE ILLUSTRATING KEPLER'S THIRD LAW. (CHAMBERS.) IN the first column are the relative distances of the planets from the sun; in the second, the periodic times of the planets; and in the third, the squares of the periodic times divided by the cubes of the mean distances. The decimal points are omitted in the third column for convenience of comparison. The want of exact uniformity is doubtless due to errors in the observations. 66 Arago, speaking of Kepler's Laws, says: These interesting laws, tested for every planet, have been found so perfectly exact, that we do not hesitate to infer the distances of the planets from the sun from the duration of their sidereal periods; and it is obvious that this method possesses considerable advantages in point of exactness." |