DISTANCE AND DIMENSIONS OF THE SUN 405 



we shall at once have the ratio of Q E and E S. Aristarchus thought 

 he had ascertained that the first quarter of the month (from N to Q) 

 was about 12 hours shorter than the second, from which he computed 

 the sun to be about 19 times as distant as the moon. The difficulty 



Fig. 1. 



lies in the impossibility of determining the precise moment when the 

 disk of the moon is an exact semicircle. The real difference between 

 the first and second quarters is really not quite 36 minutes, and the 

 sun's distance is about 400 times the moon's. 



The different methods upon which our present knowledge of the 

 sun's distance depends may be classified as follows : 



1. Observations upon the planet Mars near opposition, in two distinct ways : 



(a) Observations of the planet's declination made from stations widely sep- 



arated in latitude. 



(b) Observations from a single station of the planet's right ascension when 



near the eastern and western horizons known as Flamsteed's 

 method. 



2. Observations of Venus at or near inferior conjunctions : 



(a) Observations of her distance from small stars measured at stations wide- 



ly different in latitude. 



(b) Observations of the transits of the planet: 1. By noting the duration 



of the transit at widely-separated stations ; 2. By noting the true 

 Greenwich time of contact of the planet with the sun's limb ; 3. By 

 measuring the distance of the planet from the sun's limb with suit- 

 able micrometric apparatus ; 4. By photographing the transit, and 

 subsequently measuring the pictures. 



3. By observing the oppositions of the nearer asteroids in the same manner as 



those of Mars. 



4. By means of the so-called parallactic inequality of the moon. 



5. By means of the monthly equation of the sun's motion. 



6. By means of the perturbations of the planets, which furnish us the means of 



computing the ratios between the masses of the planets and the sun, and 

 consequently their distances known as Leverrier's method. 



7. By measuring the velocity of light, and combining the result (a) with equa- 



tion of light between the earth and sun, and (b) with the constant of ab- 

 erration. 



Our scope and limits do not, of course, require or allow any ex- 

 haustive discussion of these different methods and their results, but 

 some of them will repay a few moments' consideration : 



The first three methods are all based upon the same general idea, 

 that of finding the actual distance of one of the nearer planets by ob- 



