DISTANCE AND DIMENSIONS OF THE SUN. 403 



Now, the slightest error in the data, though hardly affecting the 

 result for epochs near the present, leads to uncertainty which accumu- 

 lates with extreme rapidity in the lapse of time ; so that even the 

 present uncertainty of the sun's distance, small as it is, renders pre- 

 carious all conclusions from such computations when the period is ex- 

 tended more than a few hundred thousand years from the present 

 time. If, for instance, we should find as the result of calculation 

 with the received data that two millions of years ago the eccen- 

 tricity of the earth's orbit was at a maximum, and the perihelion so 

 placed that the sun was nearest during the northern winter (a condi- 

 tion of affairs which it is thought would produce a glacial epoch in 

 the southern hemisphere), it might easily happen that our results 

 would be exactly contrary to the truth, and that the state of affairs 

 indicated did not occur within half a million years of the specified 

 date and all because in our calculation the sun's distance, or solar 

 parallax by which it is measured, was assumed half of one per cent, 

 too great or too small. In fact, this solar parallax enters into almost 

 every kind of astronomical computations, from those which deal with 

 stellar systems and the constitution of the universe to those which 

 have for their object nothing higher than the prediction of the moon's 

 place as a means of finding the longitude at sea. 



Of course, it hardly need be said that its determination is the first 

 step to any knowledge of the dimensions and constitution of the sun 

 itself. 



This parallax of the sun is simply the angular semi-diameter of 

 the earth as seen from the sun ; or, it may be defined in another way 

 as the angle between the direction of the sun ideally observed from 

 the centre of the earth, and its actual direction as seen from a station 

 where it is just rising above the horizon. 



We know with great accuracy the dimensions of the earth. Its 

 mean equatorial radius, according to the latest and most reliable de- 

 termination (agreeing, however, very closely with previous ones), is 

 3962.720 English miles [6377.323 kilometres], and the error can hardly 

 amount to more than T o 0V0T f tne whole perhaps, 200 feet one way 

 or the other. Accordingly, if we know how large the earth looks 

 from any point, or, to speak technically, if we know the parallax of 

 the point, its distance can at once be found by a very easy calcula- 

 tion : it equals simply [206,265 * X the radius of the earth] -*- [the 

 parallax in seconds of arc]. 



Now, in the case of the sun it is very difficult to find the parallax 

 with sufficient precision on account of its smallness it is less than 

 9", almost certainly between 8.8" and 8.9". But this tenth of a second 



1 This number 206,265 is the length of the radius of a circle expressed in seconds of 

 its circumference. A ball one foot in actual diameter would have an apparent diameter 

 of one second at a distance of 206,265 feet, or a little more than 39 miles. If its appar- 

 ent diameter were 10", its distance would, of course, be only fe as great. 



