58 Royal Astronomical Society. 



of the discovery of 13 comets, and that the number of communica- 

 tions received by the Society respecting them amounted to 140. 

 The greater number of these comets* were telescopic ; but there 

 were three (viz. the Great Comet of 1843, that of 1844-45, and the 

 second Great Comet of 1845) which were visible to the naked eye, 

 and therefore capable of being observed with instruments of the 

 smallest optical power. A considerable number of sextant observa- 

 tions of each of these comets had been communicated, but especially 

 of the comet of 1843, made chiefly by naval officers well-accustomed 

 to the use of that instrument. The number of these observations 

 was so great, that it was deemed proper by the Council, in the be- 

 ginning of the year 1844, to appoint a committee to provide for 

 their discussion and reduction ; and the author, in conjunction with 

 Mr. Galloway and Mr. Stratford, undertook this responsibility. The 

 task of performing the computations was given to Mr. Harris, the 

 late Assistant Secretary ; and the author took upon himself the pre- 

 paration of the necessary formulae and the arrangement of the steps 

 of the calculations. The author took occasion, in this part of the 

 paper, to point out to the meeting how satisfactorily Mr. Harris had 

 performed the work entrusted to him, the errors detected in a mi- 

 nute examination of it being far fewer than might reasonably be ex- 

 pected in a mass of work of so laborious and troublesome a character. 

 Mr. Main then proceeded to give an account of the observations 

 which had been reduced, and an explanation of the different steps 

 of the processes employed. With very few exceptions, the observa- 

 tions are contained in the fifth and sixth volumes of the Monthly 

 Notices, and the total number of results deduced from them was 

 199 ; and in a table is given the page of the volume at which the 

 observations under discussion are to be found, together with the 

 place and circumstances of observation, &c. Mr. Main then pro- 

 ceeded to mention in detail the principal processes of the calcula- 

 tion. The principal step that needs mention here is the formula 

 which has been employed for correcting the observed distance from 

 the effects of refraction and parallax. It was shown by a mathema- 

 tical investigation, that if Z and z be the zenith distances of the 

 comet and one of the stars of comparison, and the vertical refrac- 

 tions be a c tan Z and a 8 tan z ; if, also, II be the horizontal parallax 

 of the comet, and d the distance of the comet from the star, then 

 the whole correction of the distance will be, 



(a c — II cos Z) . ( - — cos d ) -f a. ( — cos d ) . 



v J \cos Z / \cos z J 



After the computation of the approximate zenith distances of the 

 comet and stars, this formula was found to be of very easy applica- 

 tion. It was also explained how the values of the barometer and 

 thermometer readings used in the work had been conjecturally sup- 

 plied in cases (the greater number were such) where they had not 

 been given by the author. 



With respect to the deduction of the R. A. and N. P. D. of the 

 comet from the corrected distances, the author first gave the follow- 



