NOTES. 



397 



one urging it in the direction of the tangent mT, and another pulling it 

 toward the sun in the direction mS. Its velocity, which is greatest at 

 P. decreases throughout the arc to P D A to A, where it is least, and 

 increases continually as it moves along the arc A Q,P till it comes to P 

 again. The whole force producing the elliptical motion varies inversely 

 as the square of the distance. See Note 23. 



NOTE 40, p. 8. Radii vectores. Imaginary lines joining the center of 

 the sun and the center of a planet or comet, or the centers of a planet and 

 its satellite. In the circle, the radii are all equal ; but in an ellipse, fig. 6, 

 the radius vector SA is greater, and SP less than ail the others. The 

 r;idii vectores, S Q, S D, are equal to C A or C P, half the major axis P A, 

 and consequently equal to the mean distance. A planet is at its mean 

 distance from the sun when in the points Q, and D. 



NOTE 41, p. 8. Equal areas in equal times. See Kepler's 1st law in 

 Note -26. p. 5. 



NOTE 42, p. 8. Major Axis.. The line P A, fig. 6 or 10. 



NOTE 43, p. 9. If the planet de- J*^ Fig. 10. 



scribed a circle, S,-c. The motion of 

 a planet about the eun, in a cirele 

 A B P. fig. 10, whose radius C A is 

 equal to the planet's mean distance 

 from him, would be equable, that 

 is, its velocity, or speed, would al- 

 ways be the same. Whereas, if it 

 moved in the ellipse A Q. P. its 

 speed would be continually vary- 

 ing, by Note 39 ; but its motion is 

 such, that the time elapsing be- 

 tween its departure from P, and its 



return to that point agaiq, would be 

 the same, whether it moved in the 

 circle or in the ellipse ; for these 

 curves coincide in the points P & A. 



NOTE 44, p. 9. True motion. The motion of a body in its real orbit 

 PDA a, fig. 10. 



NOTE 45, p. 9. -Vean motion. Equable motion in a circle P E A B, 

 fig. 10, at the mean distance C P or C m, in the time that the body would 

 accomplish a revolution in its elliptical orbit P D A Q,. 



NOTE 46, p. 9. The equi- 

 nox. Fig. 11 represents the 

 celestial sphere, and G its 

 center, where the earth is sup- 

 posed to be. q T Q ^= is the 

 equinoctial or great circle, 

 traced in the starry heavens 

 by an imaginary extension of 

 the plane of the terrestrial 

 equator, and E T e == is the 

 ecliptic, or apparent path of " 

 the sun round the earth. T :=, 

 the intersection of these two 

 planes, is the line of the equi- 

 noxes ; T is the vernal equi- 

 nox, and == the autumnal. 

 When the sun i.s in these 

 points, the days and nights 

 are equal. They are distant 

 from one another by a aetni- 



Fig. 11. 



