480 Intelligence and Miscellaneous Articles. 



already cited) diminished by the constant 0"4957, B is the barometer 

 reading in English inches, and T is the thermometer reading in de- 

 grees of Fahrenheit (Bessel's log a" takes account approximately of 

 the variation depending on zenith distance of the factor A in the 

 expression, A tan zen. dist. for the total refraction). To select the 

 proper value of log k, the argument zenith distance (z) is first ob- 

 tained by the formula, sec z = sec QZ sec (A — PQ). The calcula- 

 tions are much facilitated by the formation of two tables ; one con- 

 taining the values of PQ, log sec QZ, and log -, for every ten 



15 

 minutes of hour angle from h to 6 h , whence, by interpolation, and 

 by proper attention to changes of sign, the values may be obtained 

 for any given hour-angle ; the other, a table of values of log k, in 

 which the argument is z, or, which is preferable, log sec z, the dif- 

 ference between the consecutive logarithms being 0*01. 



In an instance in which the apparent difference of north polar di- 

 stance was 32'-l, the hour-angle 3 h 49 m, 7, and the zenith distance 

 82°"3, the corrections calculated by the above approximate formulae 

 were 18" - 12 and O s, 769. By exact calculation they were found to 

 be 18"' 2 7 and s - 7 62. 



When differences of right ascension and north polar distance are 

 measured while the equatoreal is carried by clock-movement (which 

 is sometimes done with the Northumberland equatoreal), it is ne- 

 cessary to compute exactly the total refractions in right ascension 

 and north polar distance of each object, no other method appearing 

 to possess sufficient accuracy. 



Extract of a Letter from Mr. Alfred Weld, Director of the Obser- 

 vatory at Stonyhurst College. 



" On September 20, I observed a large spot on the sun with our 

 equatoreal, and found that it consisted of several dark nuclei enve- 

 loped in one large penumbra. On the 21st, I made several obser- 

 vations, from which I deduced the following values of the angles 

 subtended by the spot and nucleus : — , 



Greatest diameter of spot 2 41*1 



nucleus 1 7*2 



Equatoreal diameter of spot 2 141 



nucleus ... 49*2 

 Meridian diameter of spot 2 14*1 



" The spot was distinctly visible to the naked eye before sunset." 



By comparisons with 5 Ophiuchi, Spica and Antares, Mr. Weld 



found the declination of Mr. Hind's changing star to be— 12° 37' 15". 



LXXI. Intelligence and Miscellaneous Articles. 



ON A SIMPLE AND READY WAY OF PRODUCING TOOLS FOR 

 GRINDING LENSES. BY N. S. HEINEKEN. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, Sidmouth, Nov. 15, 1848. 



IF you think the following simple and ready way of producing 

 tools for grinding lenses likely to be of service to any of the 



