110 ON THE MAGNITUDE OF THE SOLAR SYSTEM. 



in measuring with them, but their limit can not be far oft', because they 

 already show the disturbing ettects of slight inequalities of temperature 

 and other uncontrollable causes. So far as these effects are accidental 

 they eliminate themselves from every long series of observations, but 

 there always remains a residuum of constant error, perhaps quite 

 unsuspected, which gives us no end of trouble. Encke's value of the 

 solar parallax aftbrds a fine illustration .of this. From the transits of 

 Venus in 1701 and 1769 he found 8.58" in 1821, which he subsequently 

 corrected to 8.57", and for thirty years that value was universally 

 accepted. The first objection to it came from Hansen in 1854, a second 

 followed from Leverrier in 1858, both based ui)on facts connected with 

 the lunar theory, and eventually it became evident that Encke's parallax 

 was about one-fourth of a second too small. 



Now please observe that Encke's value was obtained trigonometric- 

 ally, and its inaccuracy was never suspected until it was revealed by 

 gravitational methods, which were themselves in error about one-tenth 

 of a second and required subsequent correction in other ways. Here, 

 then, was a lesson to astronomers, who are all more or less specialists, 

 but it merely enforced the perfectly well-known principle. that the con- 

 stant errors of any one method are accidental errors w^ith respect to all 

 other methods, and therefore the readiest way of eliminating them is 

 by combining the results from as many different methods as possible. 

 However, the abler the specialist the more certain he is to be blind to 

 all methods but his own, and astronomers have profited so little by the 

 Encke-Hansen-Leverrier incident of thirty-five years ago that to-day 

 they are mostly divided into two great parties, one of whom holds that 

 the parallax can be best determined from a combination of the constant 

 of aberration with the velocity of light and the other believes only in 

 the results of heliometer measurements upon asteroids. By all means 

 continue the heliometer measurements and do everything possible to 

 clear up the mystery which now surrounds the constant of aberration, 

 but why ignore the work of predecessors who were quite as able as 

 ourselves? If it were desired to determine some one angle of a triangu- 

 lation net with special exactness, what would be thought of a man who 

 attempted to do so by repeated measurements of the angle in question 

 while he persistently neglected to adjust the net? And yet until 

 very recently astronomers have been doing precisely that kind of 

 thing with the solar parallax. I do not think there is any exaggeration 

 in saying that the trustworthy observations now on record for the 

 determination of the numerous quantities which are functions of the 

 parallax could not be duplicated by the most industrious astronomer 

 working continuously for a thousand years. How, then, can we suppose 

 that the result properly deducible from them can be materially affected 

 by anything that any of us can do in a lifetime unless we are fortunate 

 enough to invent methods of measurement vastly superior to any 



