Anniversary Address of the President, 1840. 155 



on which their tables are to be constructed ; that is to say, the 

 computed values of the coefficients of terms having the same argu- 

 ment, when assembled from all the points whence they arise in 

 the algebraic processes and amalgamated together. M. Plana ap- 

 pears to have proposed to himself the gigantic task of revising and 

 correcting not only those algebraic developments, but the actual 

 numerical calculations of the whole ' Mecanique Celeste ; ' and this 

 paper contains many examples sufficiently proving the necessity of 

 such revision, and leading the way to those further and more elevated 

 researches on the theory of Jupiter and Saturn, to which the latter 

 part of this memoir must be considered as having given occasion ; 

 and which are further developed in several other memoirs published 

 in various academical and other collections. 



Neither the time nor the nature of this occasion would allow of 

 my entering into any history of the controversy to which the revi- 

 sion thus set on foot, and the discordant results arrived at in this 

 memoir, gave occasion. Suffice it to say, that errors — venial, no 

 doubt, and such as it would be miraculous did they not exist — 

 were discovered on all sides, and the absolute necessity established 

 not merely of a thorough revision of every part of these immense 

 computations, but of printing and publishing the steps in that regu- 

 lar and methodical form, which alone can put it in the power of 

 subsequent calculators to lay their finger on the precise point where 

 error shall have crept in ; and to resume the calculations from that 

 point without sacrificing the whole of what precedes. 



It is this methodical clearness — this letting in of the light on 

 every dark comer of every intricate combination and heart-breaking 

 numerical calculation, which may be regarded as marking from this 

 time a new era almost in the planetary theory itself. In the ' Meca- 

 nique Celeste,' we admire the elegance displayed in the alternate 

 interlinking and development of the formulae, and exult in the 

 power of the analytical methods used ; but when we come to the 

 statement of numerical results, we quail before the vast task of 

 filling-in those distant steps, and while cloud rolls on after cloud in 

 majesty and darkness, we feel our dependence on the conclusions 

 attained rather to partake of superstitious trust, or of amicable con- 

 fidence, than of clear and demonstrative conviction. Let me not be 

 misunderstood as by these expressions casting any reflection on the 

 conduct of that immortal work. The surest proof of its titles to 

 such immortality which can be given, is that microscopic examina- 

 tion subsequently lavished on every point embraced in its immense 

 outline. It is no disparagement to the agriculturist, whose energies 

 have extirpated the wilderness, and established in its place cultiva- 

 tion and wealth, that a period shall arrive when his furrows shall, 

 in their turn, be replaced by the garden, and his system of culture, 

 by a measured and calculated succession. Neither would I be un- 

 derstood to lay the sole stress of our applause of M. PI ana's re- 

 searches on the luminousness of their statement. His analysis is 

 always graceful, his combinations well considered, and his con- 

 ceptions of the ultimate results to be expected from them perfectly 

 just, and justified by the results when obtained. 



