i6x] Parallax 207 



vvhic.i the distance in terms of the radius of the earth, and 

 hence in miles, can readily bj deJucad when desired. 



The parallax of a heavenly boJy such as the moon, the 

 sun, or a planet, being in the first instance defined generally 

 (chapter IL, 43) as the angb (o M P) between the lines 

 joining the heavenly body to the observer and to the 

 centre of the earth, varies in general with the position of 

 the observer. It is evidently greatest when the observer 

 is in such a position, as at Q, that the line M Q touches the 

 earth ; in this position M is on the observer's horizon. 

 Moreover the angle o Q M being a right angle, the shape 

 of the triangle and the ratio of its sides are completely 

 known when the angle o M Q is known. Since this angle 

 is the parallax of M, when on the observer's horizon, it is 

 called the horizontal parallax of M, but the word horizontal 

 is frequently omitted. It is easily seen by a figure that 

 the more distant a body is the smaller is its horizontal 

 parallax ; and with the small parallaxes with which we are 

 concerned in astronomy, the distance and the horizontal 

 parallax 'can be treated as inversely proportional to one 

 another ; so that if, for example, one body is twice as 

 distant as another, its parallax is half as great, and so on. 



It may be convenient to point out here that the word 

 "parallax" is used in a different though analogous sense when 

 a fixed star is in question. The apparent displacement 

 of a fixed star due to the earth's motion (chapter iv., 92), 

 which was not actually detected till long afterwards 

 (chapter xin., 278), is called annual or stellar parallax 

 (the adjective being frequently omitted) ; and the name 

 is applied in particular to the greatest angle between the 

 direction of the star as seen from the sun and as seen from 

 the earth in the course of the year. If in fig. 69 we regard 

 M as representing a star, o the sun, and the circle as being 

 the earth's path round the sun, then the angle o M Q is the 

 annual parallax of M. 



In this particular case Cassini deduced from Richer's 

 observations, by some rather doubtful processes, that the 

 sun's parallax was about 9"'5, -corresponding to a distance 

 from the earth of about 87,000,000 miles, or about 360 

 times the distance of the moon, the most probable value, 

 according to modern estimates (chapter xin., 284), being 



