NOTES. 477 



radial force in the direction S p, fig. 14, which sometimes increases and some- 

 times diminishes the earth's attraction to the moon. It produces a correspond- 

 ing temporary change in the excentricity, which varies with the position of 

 the major axis of the lunar orbit in respect of the line S d, joining the centres 

 of the earth and sun. 



NOTE 104, p. 41. Variation. The lunar perturbation called the variation is 

 the alternate acceleration and retardation of the moon in longitude, from the 

 action of the tangential force. She is accelerated in going from quadratures 

 in Q and D, fig. 14, to the points C and O, called syzygies, and is retarded in 

 going from the syzygies C and O to Q and D again. 



NOTE 105, p. 42. Square of time. If the times increase at the rate of 1 , 2, 3, 

 4, &c., years or hundreds of years, the squares of the times will be 1, 4, 9, 16, 

 &c., years or hundreds of years. 



NOTE 106, p. 43. Mean anomaly. The mean anomaly of a planet is its 

 angular distance from the perihelion, supposing it to move in a circle. The 

 true anomaly is its angular distance from the perihelion in its elliptical orbit. 

 For example, in fig. 10, the mean anomaly is P C m, and the true anomaly is 

 PSp. 



NOTE 107, pp. 44, 77- Many circumferences. There are 360 degrees, or 

 1,296,000 seconds in a circumference ; and, as the acceleration of the moon 

 only increases at the rate of eleven seconds in a century, it must be a prodigious 

 number of ages before it accumulates to many circumferences. 



NOTE 108, p. 45. Phases of the moon. The periodical changes in the en- 

 lightened part of her disc from a crescent to a circle, depending upon her posi- 

 tion with regard to the sun and earth. 



NOTE 109, p. 45. Lunar eclipse. Let S, fig. 27, be the sun, E the earth, 

 and m the moon. The space a A 6 is a section of the shadow, which has 



Fig. 27. 



the form of a cone or sugar-loaf, and the spaces A a c, A b d, are the penumbra. 

 The axis of the cone passes through A, and through E and S, the centres of 

 the sun and earth, and n m n' is the path of the moon through the shadow. 



NOTE 110, p. 45. Apparent diameter. The diameter of a celestial body as 

 seen from the earth. 



