448 PHYSICAL SCIENCES. 



latter, however, it has no permanent effect, because it affects them in 

 opposite directions in very moderate intervals of time, whereas a very 

 small error in the amount ot' the acceleration goes on increasing as long as 

 the eccentricity of the earth's orbit diminishes, so that it would ultimately 

 vitiate calculations of the moon's place for distant periods of time. This 

 shows how complicated the moon's motions are, and what rigorous accu- 

 racy is required in their determination. 



To give an idea of the labour requisite merely to perfect or correct the 

 lunar tables, the moon's place was determined by observation at the Green- 

 wich Observatory in 6000 different points of her orbit, each of which was 

 compared with the same points calculated from Baron Plana's formulas, 

 and to do that sixteen computers were constantly employed for eight years. 

 Since the longitude is determined by the motions of the moon, the lunar 

 tables are of the greatest importance. 



NOTE 107, 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 elliptical 

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

 anomaly is P Sp. 



NOTE 108, pp. 38, 68. 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 109, p. 39. 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 earth. 



NOTE 110, p. 39. 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 



Fig. 27. 



has the form of a cone or sugar-loaf, and the spaces A a c, Abd, 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 111, p. 39. Apparent diameter. The diameter of a celestial 

 body as seen from the earth. 



NOTE 112, p. 40. Penumbra. The shadow or imperfect darkness which 

 precedes and follows an eclipse. 



