NOTES. 447 



coming from the sun, or a planet, to the earth moving in its orbit in the 

 direction A B. If a telescope be held in the direction AS, the ray SA, 

 instead of going down the tube, will impinge on its side, and be lost in 

 consequence of the telescope being carried with the earth in the direction 

 A B. But, if the tube be held in the position A E, so that A B is to A S 

 as the velocity of the earth to the velocity of light, the ray will pass 

 through S' E A. The star appears to be in the direction A S', when it 

 really is in the direction A S ; hence the angle S A S' is the angle of 

 aberration. 



NOTE 99, p. 32. Density proportional to elasticity. The more a 

 fluid, such as atmospheric air, is reduced in dimensions by pressure, the 

 more it resists the pressure. 



NOTE 100, p. 32. Oscillations of pendulum retarded. If a clock be 

 carried from the pole to the equator, its rate will be gradually diminished, 

 that is, it will go slower and slower : because the centrifugal force, which 

 increases from the pole to the equator, diminishes the force of gravity. 



NOTE 101, p. 34. Disturbing action. The disturbing force acts here 

 in the very same manner as in note 63 ; only that the disturbing body d, 

 fig. 14, is the sun, S the earth, and p the moon. 



NOTE 102, pp. 35, 36, 86. Perigee. A Greek word, signifying round 

 the earth. The perigee of the lunar orbit is the point P, fig. 6, where 

 the moon is nearest to the earth. It corresponds to the perihelion of a 

 planet. Sometimes the word is used to denote the point where the sun is 

 nearest to the earth. 



NOTE 103, p. 35. Ejection. The evection is produced by the action 

 of the radial force in the direction Sp, fig. 14, which sometimes increases 

 and sometimes diminishes the earth's attraction to the moon. It pro- 

 duces a corresponding 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. 35. Variation. The lunar perturbation called the 

 variation is the alternate acceleration and retardation of the moon in longi- 

 tude, 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 0, called 

 syzygies, and is retarded in going from the syzygies C and to Q and 



NOTE 105, p. 36. 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. 37. In all investigations hitherto made with regard to 

 the acceleration, it was tacitly assumed that the areas described by the 

 radius vector of the moon were not permanently altered ; that is to say, 

 that the tangential disturbing force produced no permanent effect. But 

 Mr. Adams has discovered that, in consequence of the constant decrease in 

 the excentricity of the earth's orbit, there is a gradual change in the 

 central disturbing force which affects the areal velocity, and consequently 

 it alters the amount of the acceleration by a very small quantity, as well 

 as the variation and other periodical inequalities of the moon. On thfc 



