464 



NOTES. 



and that of the ship, yet each takes place independently of the other. We 

 walk about as if the earth were at rest, though it has the double motion of 

 rotation on its axis and revolution round the sun. 



NOTE 38, p. 10. Tangent. A straight line which touches a curved line in 

 one point without cutting it. In fig. 4, m T is tangent to the curve in the point 

 m. In a circle the tangent is at right angles to the radius, C m. 



NOTE 39, p. 10. Motion in an elliptical orbit. A planet m, fig. 6, moves 

 round the sun at S in an ellipse P D A Q, in consequence of two forces, one 

 urging it in the direction of the tangent m T, and another pulling it towards 

 the sun in the direction m S. 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 pro- 

 ducing the elliptical motion varies inversely as the square of the distance. See 

 note 23. 



NOTE 40, p. 10. Radii vectores. Imaginary lines adjoining the centre of the 

 sun and the centre of a planet or comet, or the centres of a planet and its satel- 

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

 vector S A is greater, and S P less than all the others. The radii 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. 10. Equal areas in equal times. See Kepler's 1st law, in note 26, 

 p. 7- 



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



NOTE 43, p. 10. If the planet de- 

 scribed a circle, fyc. The motion of 

 a planet about the sun, in a circle 

 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 always 

 bethesame. Whereas, if it moved in 

 the ellipse AQP, its speed would 

 be continually varying, by note 39; 

 but its motion is such, that the time 

 elapsing between its departure from 

 P, and its return to that point again, 

 would be the same, whether it moved 

 in the circle or in the ellipse ; for 

 these curves coincide in the points 

 P and A. 



NOTE 44, p. 11. True motion. The motion of a body in its real orbit PDA Q, 

 fig. 10. 



NOTE 45, p. 11. Mean 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. 



