408 



NOTES. 



NOTE 105, p. 36. Square of time. If the times increase at tlie 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. 37. 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 ellip- 

 tical orbit. For example, in fig. 10, the mean anomaly is PC m, and the 

 true anomaly is P S p. 



NOTE 107, pp. 38, 63. 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, if. must 

 be a prodigious number of ages before it accumulates to many circum- 

 ferences. 



NOTE 108, p. 38. Phases of the moon. The periodical changes in the 

 enlightened part of her disc from a crescent to a circle, depending upon 

 her position with regard to the sun and earlh. 



NOTE 109, p. 39. Lunar eclipse. Let S, fig. 27, be the sun, E the 

 earth, and m the moon. The space a A b is a section of. the shadow, 



Fig. 27. 



- d 



which has 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 centers of the sun and earth, and n m n' is the path of the 

 moon through the shadow. 



NOTE 110 r p. 39. Apparent diameter. The diameter of a celestial body 

 as seen from the earth. 



NOTE 111, p. 39. Penumbra. The shadow, or imperfect darkness, 

 which precedes and follows an eclipse. 



NOTE 112, p. 39.- -Synodic revolution of the moon. The time between 

 two consecutive now or full moons. 



NOTE 113, p. 39. Horizontal refraction. The light, in coming from a 

 celesiial object, is ben. into a curve as soon as it enters our atmosphere, 

 and that bending is greatest when the object is in the horizon. 



NOTE 114, p. 40. Solar eclipse. Let S, fig. 28, be the sun, m the moon, 

 and E the earth. Then a E b is the moon's shadow, which sometimes 



Fig. 28. 



