234- Royal Astronomical Society. 



neous in magnitude, and one omitted. I corrected these, and then 

 proceeded in the construction of my tables." 



" In the first instance, however, to which I applied the calculations, 

 I found, to my great astonishment, that, at the time when I had ob- 

 served the satellite at extreme elongation, the tables represented it 

 as between the earth and Jupiter. I satisfied myself that this was 

 owing to no error in my own calculations, and I then compared La- 

 place's numbers with those of Halley and Delambre. From the tables 

 of the former I could only infer that there was some very strange 

 error in Laplace's epoch for 1750; from the mean conjunctions of 

 the latter I could calculate its quantity. It will scarcely be believed, 

 that the epoch of mean longitude in page 139 of the fourth volume 

 of the Me'caniqne Celeste is erroneous to the amount of nearly one third 

 of the circumference, and that this is not a typographical error, as 

 several numbers are combined with it by addition and subtraction in 

 the pages following it, and all correctly. 1 confess that my faith in 

 the numerical results of the Me'caniquc Celeste has been very much 

 weakened by these discoveries." 



"At the same time, I am far from imputing any negligence to the 

 author of that great work ; for I know too well the difficulty of in- 

 suring correction in long calculations from complex formulae : and 

 in some of the fundamental numbers of the present computations 

 I was saved from error only by Mr. Lubbock's re-calculations." 



A list of the errata in the Mecanique Celeste is appended to the 

 memoir. 



Returning to Professor Airy 's own researches, it is stated, — 



" After applying two small corrections, one for the clock rate during 

 the observations, and the other for obtaining the whole mass of the 

 Jovial system, Professor Airy concludes, that we have for the log. 



mass of the Jovial system 6*9793486, and for the mass 1048 . 70 * " 



U In conclusion I may remark, that 1 do not think this value liable 

 to any serious error, except from a possible error in the inclination of 

 the orbit of the fourth satellite. The effect of the greatest error of 

 the instrument in azimuth (0'*5) that any observations have shown, 

 acting at the greatest disadvantage, would not alter the denomination 

 of the fraction by 2. But the observations used here have been 

 made when Jupiter was in the most unfavourable of all positions, 

 both from the effect of such errors, and from the smallness of the dif- 

 ference of right ascension, which is the immediate subject of the 

 measures. The oppositions of 1834-5 and 1836 will be very mucK 

 more favourable." 



" I am far from regarding the question as definitively settled by these 

 measures ; and I offer these results to the Society as only the first fruits 

 of my investigations. Should the regular business of the Observatory, 

 and my other employments, leave me sufficient leisure, I hope to add 

 considerably to their number. The necessary tables and forms of 

 calculations are prepared ; some theoretical and numerical difficulties 

 have been surmounted; and the labour of calculating future observa- 

 tions will therefore be very much less than that of calculating the first." 



