TRANSACTIONS OF THE SECTIONS. 39 



are as marked on the map. The variable star is compared with these selected 

 standards on each occasion. Thus, on 1855, December 18, my record made with 

 the equatorial of the Radcliffe Observatory was — R, 0"8 of a magnitude less than 

 comparison star d ; 0'3 less than e. ; equal to/; 0*6 brighter than g ; which differ- 

 ences, applied to the adopted magnitudes of the references employed, yield the four 

 values 10-6, 107, 10"4, 10"6. The mean of these, 10'6, is then the relative magni- 

 tude of R Ursse Majoris on that night, eliminating all the liabilities to error which 

 could attend direct estimation. The eye is wonderfully acute, after a little practice, 

 in detecting differences of brilliancy, second only to the ear in distinguishing small 

 intervals of musical sound; and an inequality between two stars of only ^th of their 

 light, considerably less than a tenth of a magnitude, is fairly appreciable. 



Three maxima, forming a portion of the light-curve of S Ursse Majoris, another of 

 the four circumpolar variables found at the Radcliffe Observatory, are projected in a 

 precisely similar manner, and on the same scale as in the preceding example. The 

 period and range of variation of this star are each considerably less than in the 

 case of R Ursse Majoris. Its changes are completed in 222£ days or about 7£ 

 months. The brilliancy at different maxima fluctuates between the 7'5 and 8"5 

 magnitudes. The minima also lie between the 1T8 and 12'8 magnitudes. The 

 times of increase and decrease are performed in 95 and 127 days respectively. The 

 most singular feature exhibited by this star, is the different duration of greatest bright- 

 ness at certain maxima. For instance, at the very flat-looking maximum which 

 occurred on 1855, June 17, S Ursse Majoris preserved the same intensity, viz. the 

 8'4 magnitude, for nearly two months. At the next maximum, 1856, February 

 11, the star acquired the 8'2 magnitude, but changed more in twenty days than pre- 

 viously in nearly three times that interval. At the next return, 1856, September 14, 

 it increased to the 7'7 magnitude, but scarcely remained a fortnight at greatest bril- 

 liancy. The minimum also, on 1855, October 24, when of the 12"3 magnitude, 

 compared with the next on 185C, January 14, is much sharper and shorter, as well 

 as fainter in its actual light. Since May 1853, when its variability was first detected, 

 the star has been examined on 270 nights, comprising eleven minima and ten maxima 

 in unbroken succession. 



On looking at such a long flat vertex to a curve, as the first on the diagram of 

 S Ursse Majoris, it may be asked how the exact day of maximum is deduced, when 

 the star remained so little changed for two months ? The small circular marks and 

 the short line traced through them are the reply to this inquiry. Reading from the 

 light curve the days on which the star was of equal brightness during increase and 

 decrease, a mark is placed half-way, or at the mean of the two days. This is done 

 for different stages of brightness, — in this instance when the star was of the 10' 2, 

 9"8, 9 - 4, 9"0, and 8'6 magnitudes. A curve is then smoothly passed through these 

 points, and the point defined by the intersection of the light-curve with this line is 

 regarded as the day of maximum intensity. Any more refined process would be but 

 labour lost. Projection has two great advantages over calculation, when applied 

 to these observations ; it economizes time, and by the flagrant outstanding of any 

 particular dot, immediately detects errors which might easily escape notice when 

 intermingled in a column of figures, but which would not fail to vitiate our results if 

 overlooked, in the deduction of the elements of variation. 



R Cygni, a star of 417 days period — discovered in August 1852, and since then 

 continuously examined on 243 nights — is a third circumpolar variable, extremely 

 steady in its changes. It descends from the 8th to below the 14th magnitude in 

 245 days, but returns to its next maximum in 168 days. It is quite invisible with a 

 7-inch object-glass for above three months. 



The fourth circumpolar variable, R Cassiopeia?, likewise increases rapidly, fading 

 away very gradually ; the whole period extending over 435 days or more than 14 

 months, and ranging generally from the 6th to the 13th magnitude. At maximum 

 this star emits a vivid red or almost a scarlet light. R Cygni and S Ursse Majoris 

 also show a fine deep red tinge. R Ursse Majoris, on the contrary, never appears 

 red, nor indeed deviates from its ordinary yellowish-white colour at any part of its 

 period. 



In striking contrast to these, and indeed to most other variables, stands U Gemi- 

 norum — a truly wonderful star, discovered by Mr. Hind in December 1855. Its 



