276 Notice of the Periodical Cotnet of 1819. 



The second part of the memoir of which we have been 

 speaking contains also the calculation of the perturbations of 

 the comet from its appearance in 1805 to its return in 1819. 

 Thus the entire interval of twenty-four years, which the au- 

 thor has embraced in his calculations, comprehends three ob- 

 served passages through the perihelion, and the two nearest 

 returns to that point. The comparison of the three observed 

 passages furnishes, for the epoch of each one of them, three 

 values of mean daily motion, which differ but little from each 

 other. The author has concluded for the last appearance upon 

 the mean of these three values, by uniting with this the other 

 elliptic elements calculated according to the observations at 

 Paramatta. He has formed a table which may be regarded as 

 containing the definitive results of all his labours, and in which 

 he has collected the elliptic elements answering to five pas- 

 sages through the perihelion, comprehended in the twenty- 

 four years which he had been considering. If we compare 

 these elements, relative to the years 1805 and 1819, with 

 those which are derived from actual observation made at those 

 epochs, it will be seen that they agree in such a manner, that 

 the greatest deviations are but one minute in the longitude of 

 the perihelion, five in that of the node, and two in the incli- 

 nation of the orbit ; but this comparison is not the best means 

 of ascertaining the degree of exactness in the results obtained 

 by M. Damoiseau. To judge of it properly, it will be neces- 

 sary that the author should calculate according to the ele- 

 ments, the places of the comet in these two epochs, in order to 

 compare them with the places which have been directly observed. 

 M. Damoiseau has followed, in the calculation of the per- 

 turbations, the known method which consists in dividing the en- 

 tire curve described by the comet, into portions, for each one 

 of which we determine the effect produced by the disturbing 

 forces of the planets. In the first part of his memoir these 

 portions answer to angles of 10® of eccentric anomaly. In the 

 second part he has preferred to take intervals of time nearly 

 equal to each other, and each about thirty days ; but in both 

 cases he is confident that he can, without any sensible error, 

 observe in each portion of the orbit the variations of the mean 

 motion as proportional to the square of the time, and those of 



