38 



REPORT 1859. 



observation of every night is represented by a black spot. Thus, on 1855, September 

 19, the magnitude of the star was recorded 6"6 ; on November 8, it had diminished 

 to 8 - 8 ; and on 1856, March 7, when only just discernible, it was noted 13"5. It 

 appears therefore, that if R Ursse Majoris never becomes visible to the naked eye, 

 on the other hand it never quite vanishes with an object-glass of 7 inches in aperture. 

 A waved line, smoothly traced among these dots, so as to pass as nearly as possible 

 through the mean of each three successive observations, is adopted as the curve 

 which represents the variations of the star with the most probable exactitude. The 

 general regularity and similarity of the different periods is strikingly evident, also 

 the gradual descent of the curve corresponding to diminution of light, and its rapid 

 ascent or brightening up before each maximum. The whole period being 302 days 

 or ten months, the interval from maximum to minimum is 191 days, that from 

 minimum to maximum only 111 days. 



Closer inspection will bring to view some more interesting details. At the first 

 observed maximum the star acquired only the 8th magnitude. At the next it became 

 0"6 of a magnitude brighter, or shone with half as much light again as on the first 

 occasion. On the photometric scale adopted, which is an average of those employed 

 by all the chief catalogue constructors who paid attention to the relative magnitudes 

 of the fixed stars, and is in exact accordance with the notation of Professor Arge- 

 lander, the highest authority on that point, one star is said to be a magnitude brighter 

 than another, when it contains 2^ times the actual light of the fainter star. Thus 

 a 7th magnitude is 1\ times as bright as an 8th. At the next three maxima, viz. 

 1854, November 22 ; 1855, September 15 ; and 1856, July 10, R Ursa? Majoris was 

 within 0*1 of the 7th magnitude. But at the next maximum on 1857, May 15, it 

 reached the 6 - 7 magnitude — the brightest on record; a veritable maximum maximo- 

 rum ! On the last two occasions, viz. 1858, March 16, and 1859, January 5, it did 

 not exceed the 7'G magnitude. Owing to the extreme faintness of this star at its 

 minima, less weight can be assigned to their determination, but similar fluctuations 

 are manifested, especially by the first four. After reducing the fifteen equations 

 afforded by this curve, by the method of least squares, the resulting elements of 

 variation are: — period, 30T91 days; epoch of minimum, 1858, September, 15 - 9; 

 and that of maximum, 1859, January, 6 - 6 ; which represent the original observations 

 with surprising accordance. The mean difference between an observed maximum 

 and one computed from the elements is 2| days ; the extreme difference 5 J days. 

 For the minima, these differences are — mean, 4| ; extreme, 8 days. Strong evidence 

 this, in favour of the regular periodicity of the star, and the sufficiency, both of the 

 observations and their treatment by this simple but effectual method of projection, 

 when for two of the oldest known variables, o Ceti and x Cygni, the most refined 

 formulae of calculation often disagree with observation to the extent of twenty-five 

 and forty days respectively ! 



It must not be supposed that the observations here projected are mere estimations 

 of the magnitude of the variable ; nei- r 

 ther are they photometric measures of lo 

 the actual light emitted by the star. In +g 9 

 either case, the changes in the atmosphere 

 or in the sensibility of the observer's eye 

 would materially affect the estimation, 

 and the dots would stand out very un- 

 satisfactorily from the interpolating light- 

 curve. The method employed is as fol- 

 lows : — A map of the neighbourhood of 

 each variable is constructed, and a cer-i | 1( 

 tain number of stars selected, if possible 

 in the same telescopic field of view, as ^ 

 standards of reference. One of these 

 maps, viz. that of the variable just de- + 70 " 

 scribed, is here given for the purpose of s 

 illustration. j° 



The comparison stars, nine in number, are lettered in order of brilliancy, and their 

 adopted magnitudes, the means of careful estimations on twenty favourable nights. 



t Mimdes of Right Ascension 



2» M 31 32 33 3& 35 3C 37 33 39 40 n 



10' 



13 



i 



115 



20 .2 



10 fc; 



50' 



20 30 31 33 33 31 35 36 37 33 39 40 41 

 Minnies of Right Ascension 



+70° 



lo* 



