78. Wijkander (1879) gives the following values for

79. Schöttner found for glycerine the values 42 at 3°, and 8 at 20°.

Obermayer (1877) found for pitch the values 2.1 × 109 between 6° and 7°, 5·3 × 108 at 10°·1, 2·6 × 108 at 12°·2; and for storax the value 13 x 1010 between 15° and 16°.

Carl Barus (1890) has found for marine glue at about 25° the value 2 × 108; and for paraffin at about 25° a value exceeding 2 × 1011.

Viscosity of Gases.

80. Schumann (1884) found for air (omitting superfluous decimals), by vibration experiments :

Tomlinson (Phil. Trans. 1886) found 000177 as the

value at 12° from a great variety of vibration experiments.

Obermayer (1876) gives as the result of his transpiration experiments the approximate formula

·0001683 (1+00274 0),

or the nearly equivalent one

001683 (1+a0)76,

Ø denoting temperature, and a the coefficient of expansion of air.

81. Carl Barus (1889) from experiments ranging from 418° to 1216° infers, for air and for hydrogen, that the viscosity varies as (1 + a0)3.

Obermayer (1876) gives the following values at 0°

O. E. Meyer (1873) deduces the following values at

20° from Graham's transpiration experiments.

70

CHAPTER VI.

ASTRONOMY.

Size and Figure of the Earth.

82. ACCORDING to the latest determination (Geodesy, by Col. A. R. Clarke, 1880), the semiaxes of the ellipsoid which most nearly agrees with the actual earth are, in feet,

a = 20926629, b = 20925105, c = 20854477, which, reduced to centimetres, are

a = 6·37836 × 108, b = 6·37790 × 108, c =

6.35639 × 108,

giving a mean radius of 6.37090 × 108, and a volume of 1.0832 × 1027 cubic centims.

The ellipticities of the two principal meridians (defined as difference divided by half-sum of axes) are

The longitude of the greatest axis is 8° 15′ W.

The ellipsoid of revolution which most nearly represents the actual earth has for its major and minor semiaxes, in feet,

a = 20926202, c = 20854895,

or, in centimetres,

a = 6·37825 × 108, c = 6·35651 × 108; the ratio of c to a being 292-465: 293-465.

The average length of one ten-millionth of a quadrant of a meridian is 39.377786 inches, whereas a legal metre is 39-370432 inches. The difference is 1 part in 5354. Hence the mean length of a quadrant of the meridian is 1-00019 × 109 centims.

The lengths of a degree of latitude and longitude, in centims., in latitude 4, are respectively

and

(1111-317-5.688 cos ) 104,

(1114-164 cos - 950 cos 3 ) 104.

83. The mass of the earth, assuming Baily's value 5.67 for the mean density, is 6·14 × 1027 grammes. With the value 5.56 obtained by Baille and Cornu (Com. Ren., 1878) for the mean density, the mass is 6·02 × 1027.

84. The mass of the moon is about of the earth's

mass.

The mean distance of the centres of gravity of the earth and moon is 60.2734 equatorial radii of the earth -that is, 3.8444 x 1010 centims.

The mean horizontal parallax of the sun is about 8"-8;

hence his mean distance is about 1·493 × 1013 centims., or 92.8 million miles.

The intensity of centrifugal force due to the earth's

motion in its orbit (regarded as circular) is (2)3r, r de

T

noting the mean distance, and T the length of the sidereal year expressed in seconds. This is equal to the acceleration due to the sun's attraction at this distance. Putting for r and T their values, 1·493 × 1013 and 3·1558 × 107, we have

r = 5918.

T

( )

1

This is about

of the value of g at the earth's

1660

surface.

The intensity of the earth's attraction at the mean distance of the moon is about

This is less than the intensity of the sun's attraction upon the earth and moon, which is 5918 as just found. Hence the moon's path is always concave towards the sun.

85. The mutual attractive force F between two masses m and m', at distance 7, is

where C is a constant. To determine its value, consider the case of a gramme at the earth's surface, attracted by the earth. Then we have