By Logarithms.-Add 0,7981799 to the logarithm of the planet's mean distance from the Sun, and from the sum substract the logarithm of the planet's revolution expressed in hours.

EXAMPLE. Required the Earth's hourly motion in its orbit.
Log. of Earth's distance = 7 9789738+0.7981799 —
Substract log. of Earth's revolution

Gives Earth's horary motion, 68,288 miles,

PROBLEM XVI.

8.7771537

3.9428090

4.8343447

TO FIND THE HOURLY MOTION OF A PLANET ON ITS AXIS.

RULE.-Multiply the diameter of the given planet by 3.14159, and divide the product by the period of its diurnal rotation.

By Logarithms.-Add 4.0534524 to the logarithm of the planet's diameter, and from the sum substract the logarithm of its diurnal rotation, expressed in seconds.

TO FIND THE RELATIVE MAGNITUDE OF THE PLANETS.

RULE.-Divide the cube of the diameter of the larger planet, by the cube of the diameter of the less.

By Logarithms.-From three times the logarithm of the larger, substract three times the logarithm of the less.. EXAMPLE.-How much does the size of the Earth exceed that of the

Moon?

Earth's diameter, 7912 log. 3.8982863X3
Moon's diameter, 2160 log. 3.3343376X3

The Earth exceeds the Moon, 49.1865 times. Ans.

11.6948589

10.0030128

1.6918461

In this example. 7912 miles is assumed as the mean between the Earth's equatorial and polar diameter: the former being 7924, and the latter 7898 miles

PROBLEM XVIII.

TO FIND THE PROPORTION OF SOLAR LIGHT AND HEAT AT EACH OF THE PLANETS.

RULE.-Divide the square of the planet's greater distance from the Sun, by the square of the less.-Or, substract twice the logarithm of the greater distance, from twice the logarithm of the less.

EXAMPLE.-How much greater is the Sun's lignt and

eat at Mercury, than at the Earth?

Log. of Earth's distance of Mercury's

Ans. 6.6736 times greater

7.9789738X2
7.5667959X2

.5.9599476
15 1335918
0.8243558

PROBLEM XIX.

TO FIND THE CIRCUMFERENCE OF THE PLANETS.

RULE.-Multiply the diameter of the planet by 3.14159 ›r, add the logarithm of the planet's diameter to 0.4971 139

PROBLEM XX.

TO FIND THE CIRCUMFERENCE OF THE PLANETARY ORBITS.

RULE.-Multiply the planet's mean distance from the Sun, by 6.2831853: or, to the logarithm of the planet's mean distance, add 0.7981799, and the sum will be the logarithm of the answer.

PROBLEM XXL

TO FIND IN WHAT TIME ANY OF THE PLANETS WOULD FALL T4 THE SUN IF LEFT TO THE FORCE OF GRAVITATION ALONE.

RULE.-Multiply the time of the planet's sidereal revolu tion, by 0.176776; the result will be the answer.

By Logarithms.-From the logarithm of the planet's si dereal revolution, substract 0.7525750, and the remainder will be the logarithm of the answer, in the same denomination as the sidereal revolution.

Required the times, respectively, in which the several planets would fall to the Sun by the force of gravity.

0.387099031323|1.587622,083445
0.723332175563|1.859337,782897

36,880,422.34907587 7.566795,885867 0.387099031323 1.587622,083445
68,914,654.84245489 7.838311,585319
95,273,868.86774855 7.978973,802422 1.000000000000 0.090000,000000
686.9796458 2.836943,867587 145,168,094.89281471 8.161871,177396 1.523692662196 0.182897.374974
1325.7431000 8.122459,408208 225,016,762.14714600 8.352214,871143 2.361788860064 0.373241.068721
1592.6608000 3.202123,345262 254,287,002.55155636 8.405324,162513 2.669010984581 0.426350,36009 |
1681.3931000|3 225669,267668 263,646,156.30912176 7.421021,444117 2.767245199994|0.442047,641635.
1686.5388000 3 226996 342519 264,183,786.59075400 8.421906,160684 2.772888198314j0 442932,3582621
4332.58482123.636747,074052 495 533,836.87042950 8.695073,315039 5.201151614387 0.716099,512617
10759.2198174 4 031780,779676 908,717,975.06526816 8.958429,118755 9.5379560614530 979455,316333
30686.8208296 4.486951,895561|1827,580,558 25499525 9.261876,529379 19.182390512469/1.282902,726957
Hourly Motion, Comparative
in miles. Light and Heat.

Diameters at the Relative Diame- Trae Diame-
Earth's M. Dist.

ters in miles.

TABLE 1.

Containing the names of the Constellations, the number and magnitude of the Stars in each, and the days on which they come to the meridian at 9 o'clock in the evening.