286 SUN'S DISTANCE. 



The question naturally rises, cannot the same method be applied 

 to the Sun? Practically it cannot, for the following reasons: First, 

 if errors of equal amount were committed in determining the inclina- 

 tion of the two lines AM, BM, for the Sun and for the Moon, their 

 effects on the results would be enormously unequal. Thus, if the 

 error were 2", it would produce an error of one hundred miles in the 

 Moon's distance; but it would produce an error of sixteen millions of 

 miles in the Sun's distance. Secondly, no stars can be seen for obser- 

 vation in apparent contact with the Sun's limb. Thirdly, if for want 

 of observable stars we rely upon the instrumental measure of the 

 angular elevation of the Sun's limb, we introduce the risk of instru- 

 mental errors, and (far worse) of errors in the computation of atmo- 

 spheric refraction at the most unfavorable of all times of observation; 

 and these are sufficient completely to vitiate the method. 



In consequence of these difficulties, astronomers have always 

 sought to determine the distance of the Sun indirectly by determining 

 the distance of a planet, either by referring the planet's apparent 

 place to stars or by referring it to the Sun. In order to make this 

 indirect process available, it is necessary to rely upon the antecedent 

 determination of the proportion of the distances of the different plan- 

 ets from the Sun. 



It is a historical fact that, in the time of Copernicus and Keppler, 

 when astronomers did not know whether the Sun's distance from 

 the Earth was nearer to ten millions or to a hundred millions of miles, 

 Fig. 2. the proportion of the distances of the different 



Proportions of Orbits planets was known almost as exactly as at present. 

 of Planets The first and rudest means of obtaining these pro- 



portions may be understood from figure 2. Com- 

 mence with the assumption that the planets move 

 in circular orbits. At the Earth E the apparent 

 angle S E V, between the Sun and Venus, reaches, 

 but does not overpass, a certain value. At this 

 time, then, the angle E V S is a right angle. 

 Therefore, in the triangle E V S, two angles 

 are known, (namely, at E and at V, ) and therefore 

 the proportions of the three sides can be found, 

 and two of these sides are the distances of 

 the Earth and Venus from the Sun. Again, conceive that from the 

 Earth E' the planet Mars is seen in the direction E' M'. By an ac- 

 quaintance with the movements of 3Iars, derived from the observa- 

 tions of many preceding years, it is known that his position, as seen 

 from the Sun, is in the direction S M'. The angular difference between 

 these two directions is the angle S M' E'. Also we know the angle 

 S E' M', the apparent angular distance of Mars from the Sun. Hence 

 (as in the instance of Venus) we know two angles of the triangle 

 S E' M', and therefore we know the proportion of its three sides, two 

 of which are the distances of the Earth and Mars from the Sun. 

 These, at first, are very rude determinations; but they aid materially 



