264 TJie Philosophical Society of Glasgow. 



way of establishing a complete agreement between theory and observa- 

 tion. This agreement, said Bessel, thirty years ago, is always affirmed, 

 yet has never been hitherto verified in a sufficiently serious manner. 



" The study of the difficulties offered by the Sun has been long and 

 comphcated. It has been necessary, in the first place, to revise the cata- 

 logue of the fundamental stars, so as to leave no systematic error there. 

 I have next taken up the whole theory of the inequaUties in the Earth's 

 motion ; in connection with which I have been led to discuss as many 

 as 9,000 observations of the Sun, made in different observatories. This 

 work has shown that the meridian observations may not always have 

 had the precision which has been attributed to them, and that thus the 

 discrepancies at first indicated as belonging to the theory must be 

 rejected, because of iincertainty as to the observations. 



" The theory of the Sun's appai-ent motion once put beyond question, 

 it became possible to resume, with advantage, the study of the motion 

 of Mercury. It is this work on which I wish now to engage your 

 attention. 



" "^Tiile for the Sun we possess only meridian observations Hable 

 to great objections, we have, for the planet Mercury, a certain number 

 of observations of an extremely accurate character, made in the course 

 of a centmy and a-half. I mean the internal contacts of the disc 

 of Mercury with the disc of the Sun, at the end of a transit of that 

 planet. Provided that the place of observation is well known, and 

 provided that the observer has had a passable telescope, and a clock 

 showuig time within a few seconds of perfect accuracy, his observation 

 of the instant of the internal contact ought to affijrd an estimate of 

 the distance between the centres of the two bodies, with no error 

 exceeding a second of ai'c. From 1697 to 1848, we have twenty-one 

 observations of this kind, which ought to be perfectly satisfied if the 

 perturbations in the motions of the Earth and Mercury have been well 

 calculated, and if correct values have been attributed to the disturbing 

 masses. 



" The results of my first studies on Mercmy, pubhshed in 1842, did 

 not represent with great accuracy the transit observations. Among 

 other discrepancies was to be remarked a progressive error in the 

 transits of the month of May, reaching as much as nine seconds of arc 

 in the year 1753. Deviations such as this could not be attributed to 

 errors of observation ; but not having revised the theory of the Sun, 

 I believe that I ought to abstain from drawing any conclusion from 

 them. 



" The use of the corrected tables of the Sun has not, however, in my 

 new work, made these discrepancies disappear ; — systematic discrepancies 



