00 ACCOJJKT OF THE MlitEOJl SEEN, IJiCU^'Nt^TICUT. 



lu collectini^ and combining these observations I have re- 

 ceived great assistance from my friend, John Pickering, 

 jun. Esq* A.A.S., particularly in the observations at Wen- 

 ham. These observations are ^iven after the problems, 

 and the results from combining; tbem in various manners are 

 stated at the end of this memoir. 



Prohfem \, Plate III. Fig, \, 



M(?t>imlsof (If- Suppose that in two places in given latitudes and longi- 



lervminni: the tudes the azimuths of a meteor were observed at the sam«» 

 \ Uce of a me»' ^ . , • , , . , , t • 



teoT* moment of tmie, and its angular elevation above the horizon 



of one of those places. It is required to determine the situa^ 



tion of the meteor. 



Solution* 



* Let C be the centre of the Earth, PWSM a portion of 

 its surface reduced to the level of the sea supposed to be 

 spherical, P the pole of the Earth, it', 5, the places of ob- 

 servation, m the place of the meteor. Draw Ctr, C^, Cm, 

 cattin<5 the spevical surface in the points W, S, M. Then 

 Wtr, S*, vvillrepresent the vertical heights of the places of 

 observation, and Mw the vertical height of the meteor above 

 ttie level of the sea; PWM the azimuth of the meteor ob» 

 ,3 '^ '* . , eervcd at ?r, and PSM its azimuth observed at s. Then in 

 i . the spherical triangle PWS are given PW, PS, the colati- 

 tudes of the places of observation, and the angle WPS 

 equal to their difference of longitude, to find by spherics 

 the angles PWS, PSW, and the side SW. The sum or dif- 

 ference of PWS, PWM, will give the angle SWM ; and 

 the sum or difterence of PbM, PSW, will give tlie angle 

 WSM» Then in the spheric triangle WSM will be given 

 the angles SWM, WSM, and the side SW, to find the sides 

 WM, SM, which are respectively equal to the angles mC^c, 

 ^Ctw^ The altitude of the meteor observed at «?, added to 

 90% and -f*^-th part of the arch WM subtracted from the sum 

 iw terrestrial refraction, wi'fi leave the correct value of the 

 Jingle Cwm'. this added to 7»C?«?, and the sum subtracted 

 from 180% will leave the angle Cmu?. Then in th« plane 

 triangle Cm?»>, will be given the angles and the side Cuv 

 (vuhicb may in general ^ when Ww i* small, he taken equal 



