Royal Astronomical Society. 59 



ing theoretical solution, which, though of no direct practical utility, 

 may be interesting to the mathematician. 



Let A, A', and <r be the N. P. D.'s and distance of the* stars of 

 comparison ; if the N. P. D. of the comet ; d and d' the observed 

 corrected distances ; then, 



sin 2 A sin 2 d' 1 f cos A cos * ^ cos d ~ cos d ' cos ^ 1 



■ „., . „, , n J + cos A' cos* (cose?' — cos d cos <r) I ~ 

 -f sin 2 A' sin 2 d > + 2 < , ,,/ A A ,<> = 2. 



. . . ~ ( 1 + cos d cos d' (cos <r— -cos A cos A') f 



+ sin 2 <r sin 2 ?r A A , ' 



J (__ + cos A cos A' cos <r J 



Again, if the difference of R. A. of the star whose N. P. D. = A 

 and the comet be x, and the angle at the comet subtended by that 

 star and the pole be x' ; a the difference of the R. A.'s of the stars, 

 and /3 the angle subtended by them at the comet ; then, 



cot x' — cot /3 _ sin A' sin ex. 

 cot x — cot a sine? sin |3 

 j 1 + cot 2 x _ sin 2 A 



1 + cot 2 x' sin * d ' 



from which two equations cot x' may be eliminated, and a quadratic 

 equation will result for the determination of x. 



The author then proceeded to explain the practical rules which 

 had been given for the solution of the spherical triangles requisite to 

 determine the R. A. and N. P. D. of the comet. 



In conclusion he animadverted upon several imperfections in the 

 observations which had been discussed, and particularly on the want 

 of sufficient explanation of several circumstances materially affecting 

 their accuracy. 



Extract of a Letter from C. Piazzi Smyth, Esq., to the Presi- 

 dent, Dec. 1845, accompanying some drawings of the Great Comet 

 of 1843. 



The drawings in question are in Indian ink, and comprise five 

 naked-eye views of the Great Comet on the nights of March 3rd, 

 4th, 9th, 18th, and 25th ; and six telescopic views of its head on the 

 nights of March 3rd, 4th, 6th, 9th, 22nd, and 31st. 



The former are 6*4 by 5 inches, containing 57° of altitude and 

 45° of azimuth ; the latter are in circular spaces, o, 5 in diameter, 

 on a scale of 2*7 inches to 1 Q . • 



The writer remarks on the extensive and regularly progressive 

 character of the changes of the comet's appearance in both series of 

 drawings, and especially (as being directly contrary to the general 

 opinion) on the concavity of the tail to the direction in which the 

 body was proceeding ; its angular advance on the line passing 

 through the sun and the nucleus ; and its continual increase in length : 

 all the observations being subsequent to the perihelion passage. 



He remarks also on the manner in which the principal pheno- 

 mena seem to be accounted for by Sir John Herschel's mathematical 

 theory (published in the sixth volume of the Memoirs) ; the very 

 simple nature, or rather the reasonableness of that theory ; the im- 

 possibility of refusing the little that is assumed in it ; and the ira- 



