184 Trench Report on the Lunar Tables. 



the national obfervatory of Parts, from the laft publications 

 of the aftronomer royal in England, and from the correspond- 

 ence of the director of the obfervatory of Gotha. It is fuf- 

 ficient to fay, that it was impofiible to find any deferving of 

 more confidence, either on account of the excellence of the 

 inftuments with which they were made, or the known merit 

 of the obfervers. 



We (hall defcribe in a few words the difficulties which the 

 author of the tables had to furmount, and the precifion to 

 which he has attained. 



By thoufands of comparifons he has proved, in the fir ft 

 place, that the periodical inequalities before determined were 

 fufeeptible only of very frnall amelioration. He introduced 

 fome equations imperfectly indicated, and afterwards neg- 

 lected, by 'Mayer and Mafon ; and fome others much more 

 important, indicated in the laft volumes of the Cotino'iffance 

 des Terns by C. Laplace: they rendered the tables much 

 better, but did not correct the inequality of the mean motion. 



It remained to try equations of a long period. As theory 

 had not furniftied any, the author endeavoured to determine 

 empirically the law of the anomalies obferved : he loft him- 

 felf in an inextricable labyrinth ; but, at the time when, fa- 

 tigued with fo many vain efforts, he had renounced all hope, 

 he learned that Laplace had difcovercd the form and argu- 

 ments of two new equations, the dcterminatiori'bf which he 

 deferred till he could obtain a more precife observation. With 

 this aid, almoft unhoped for, our author undertook a new 

 labour, and was able to fix the value of the two equations, 

 which explained the whole in the happieft manner. The 

 refult was, a more exact knowledge of the mean motion ; a 

 more perfect agreement between calculation and observation; 

 and a well-founded hope that this agreement will he main- 

 tained, and that we thall no more fee, as of late years, errors 

 increafe ill a rapid and alarming manner. 



This is not the place for entering into numerical details; 

 they will be found in a paper and taWe£ Submitted to the 

 board. To giVe an idea of the preciiion of the new tables, it 

 will be fufficient to lay that the errors which can be afcribed 

 to them very feldom amount to 12': whence it follows, that 

 the aftronomer who obferves the moon will rarely find be- 

 tween the real and the calculated place a greater difference 

 than the thicknefs of the very delicate thread which is in 

 the focus of the telefeope ; and, to (how of what importance 

 this exactnefs is to navigation, we mall fay, that as thefe 11" 

 of motion do not require above a minute of time, the navi- 

 gator will never err eight minutes in his longitude, at leaft 

 4 for 



