Royal Astronomical Society. 145 



The principle of this method consists in expressing the square of 

 the ratio of the distance between the two planets to the radius vector 

 of the more distant planet, under the form of P— Q, in which P is the 

 product of any convenient number of factors of the form 1 + A cos a, 



and all the terms in Q have small coefficients. Then (P— Q)""'' 

 may be developed by the binomial theorem in a series of ascending 

 powers of Q, which consequently converges rapidly, and the values of 



the quantities P"*^, P""*, &c., which enter into the successive terms 

 of this series, may be found by multiplying together the developments 



1 3 



of the several factors (1 + A cos a) ^, (1 + A cos a) ^, &c. If then 

 tables were prepared, giving for different values of A the coefficients 

 of the development of these quantities in cosines of multiples of a, 

 all the operations requisite for the development of the disturbing 

 function might be performed with great facility. 



The author remarks, in conclusion, that instead of developing, as 



is usually done, in powers of the ratio of the mean distances ( — )' 



it would be preferable to develope according to powers oi ,-^ 



which is much less than the former when a and a' do not 

 widely from each other. 



Observations of Hind's Second Comet in full Sunshine*. By Mr. 

 Hind. 



I take the liberty to send you two positions of the comet discovered 

 here Feb. 6, obtained yesterday in full daylight, and about five hours 

 before the perihelion passage. The visibility of a comet in the day- 

 time, and within 2° distance from the sun, is a phBenomenon of so 

 rare occurrence, that it may in some measure interest you if I give 

 very briefly the particulars of our observations. 



I had determined, by theory, that the intensity of light on March 

 30 ought to be 100 times stronger than that of a star of fourth mag- 

 nitude, and was induced to make preparations for a daylight obser- 

 vation. I first saw the comet about 11 a.m. When the sky was 

 perfectly cloudless about the sun, it had a whitish appearance, which 

 rendered it a matter of no little difficulty to see the comet ; but 

 during the passage of some cumuli clouds over the sun, and between 

 the breaks, I obtained some excellent views of the comet, and several 

 observations, which will no doubt be of great assistance in the accu- 

 rate determination of the elements. The nucleus was nearly, if not 

 perfectly, round, beautifully defined and planetary, the diameter 8" 

 or 1 0". Two faint branches of light formed a divided tail, extend- 

 ing about 40" from the head, like two longish erect ears or horns 

 rising from each side of the disc. At times I felt certain that the 

 nucleus twinkled. The tail resembled a thin smoke. 



With respect to the observations for position, I can only add that 

 they were as good as could possibly be made, under the circum- 



* The comet was seen at noon near the sun by two other observers, at 

 Truro and in the Isle of Anglesey. 



Phil. Mag, S. 3. Vol. 31. No. 206. Aug. 1847. L 



