Royal Astronomical Society. 479 



an exquisitely delicate double-star, Tethys was still south of Mimas, 

 although, as Tethys was receding from the planet and Mimas ap- 

 proaching it, the reverse ought to have been the case if the former 

 really revolves in the plane of the ring. 



" At 10 h 5 m this evening (September 16) Mimas was, as nearly as 

 could be estimated, at his greatest elongation eastward ; and on the 

 16th of October 1847, at b h 35 m , I observed him at or very near his 

 greatest elongation westward. The interval elapsing amounts to 

 336*045 days ; and supposing him to have made in that time 356*5 

 revolutions, 22 h 37 m 22 s * 6 will be the period of one revolution." 



Extract of a Letter from Mr. Lassell. 



" I am happy to tell you that I have at length brought my polish- 

 ing machine to do all that I ever hoped or purposed it should do. I 

 had previously obtained very good surfaces with it, but they were 

 obtained with some anxiety and uncertainty. I wished to be able to 

 repolish a known good surface without hurting it, as well as to turn 

 a bad one into a good one with certainty and expedition. This, I 

 am happy to say, I can now do ; and by certain rules, varying with 

 the proportion of the focal length to the aperture, I can produce a 

 parabolic surface which shall have the same focus in every part of its 

 surface to the hundredth of an inch. The improvement in regula- 

 rity of curve is not less than in the truth of its general form. I am 

 about to make some experiments on the further shortening of focus, 

 viz. a 12-inch metal of 7-feet focus, more, however, as a curiosity 

 than for utility*." 



Professor Challis's method of correcting Equatoreal Observations 

 for refraction. 



The corrections for refraction in differential equatoreal observa- 

 tions made at the Cambridge Observatory, when the hour-angles for 

 the star of comparison and object compared are the same, are calcu- 

 lated by the formulae given in p. 188, vol. i. of Bessel's Astronomische 

 Untersuchungen. Tn the triangle of which the angular points are at 

 P the pole of the heavens, Z the zenith of the observer, and S the 

 place of the star, draw from Z a perpendicular ZQ on PS. Let d'—d 

 be the apparent excess of the north polar distance of the object com- 

 pared, above that of the star of comparison, and A the true north 

 polar distance of the latter, or, more correctly, the mean of the north 

 polar distance of the two objects; and let jtV — u. be the excess of 

 right ascension given by the difference of times of transit. Then 

 Correction applied to d' — d=*.(jd' — «?)sec 2 (A — PQ) 



Correction applied to fc'-f*=*(.d'-d)secKA-PQ) . tan QZ c^s(gA-PQ) 



15 sin^A 



For calculating x, which depends both on the zenith distance and 

 on the barometer and thermometer readings, the following empirical 

 formula is sufficiently accurate and of ready computation : — 



log k = log k + 0015 B + C-001 (100°-T), 



where log k is log a" (in Bessel's table, pp. 198 and 199 of the work 



* Mr. Lassell is preparing an account of his polishing-machine and me- 

 thods of grinding specula, &c. to be laid before the Society. 



