42 Rev. B. Bronwin 07i Jacobi's General Transformation 



2'4> 

 period only amounted to — — . The temperature had reached 



its greatest of heat on the 24th at 4^ p.m., viz. + 70°*1, at which 

 time the hygrometer was +59°'2; the wind nearly calm and 

 veering to E., and in the evening to S. The barometer had 

 been gradually falling from the morning of the 21st, and at 

 6^ p.m. a heavy thunder-storm passed over High Field House 

 from the S. moving to the N. ; the lightning was most vivid 

 at 6^ \B^ p.m. In the morning a faint solar halo was formed, 

 and in the evening an arc of a solar iris, very sensibly pris- 

 matic, was visible. At 9^ SS"" (mean time), the night, which 

 was very dark, suddenly became light as day, and the objects 

 near and distant were visible as plainly as in broad daylight: 

 immediately a magnificent meteor, of a blue colour, was seen 

 traversing the interval from the zenith, through the stars 21, 

 30, 40 and 41 of the constellation of Leo Minor, and the stars 

 95, 9Qi X, 59, T and 75 of the constellation of Leo Major (a 

 distance of 30°), which it accomplished in little less than three 

 seconds of time: it exploded very near the star ^, Leonis 

 Majoris, and, after falling in small fragments of light for the 

 space of 1°, became suddenly extinguished. Its apparent size 

 was very nearly equal to the disc of the moon, and perfectly 

 round in form ; but its brilliancy very far surpassed that lumi- 

 nary, and its intensity could not possibly have been less than 

 three times as light as our satellite. No train of light was left 

 behind the meteor, as is seen with the caudate meteors. It 

 appeared of no considerable height above the surface of our 

 earth. There were no clouds visible at the time ; but a few 

 cumuli appeared soon after, and the moon rose of a red 

 colour. 



Should any one have noticed this phaenomenon in the azi- 

 muth of the meteor, a comparison of remarks would prove 

 both interesting and important, for the height of the meteor 

 above the surface of our earth might be ascertained. 



XII. Reduction of the Four Forms of w in Jacobi's General 

 Transformation of an Elliptic Function to one form only. 

 By the Rev. Brice Bronwin*. 



T^HE constants in Jacobi's transformation of an elliptic 

 -■■ function are all expressed by the two series of quanti- 

 ties — 



sin^am (4«)), s\n^am{%w) sin^am (2?z — 2) w, 



sin^ CO am (4aj), sin^ co am (8 m) ...... sin^ co am (2 w — 2) co. 



* Communicated by the Author. 



