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8. TO FIND THE DIAMETER OE 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 diet, of paper disk : dlst. of sun's disk :: diam. of paper d. : diam. son'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.

143 19.7 132.716
38710 87.969 183421
72333 224.701 133413
365.256
1.52369 686.979 133410
5,2027 4,332.585 183294
9.53878 10,759.220 133401
19.18239 30,686.821 183422
60,126.710 133405

*

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.”

MEASUREMENTS OF THE EARTH's DIAMETER.

Airy. Bessel.
Polar diameter.................. "899.17 7899.11
Equatorial diameter 7925.64 "925.60
Compression................... 26.47 26.49

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