214 Mr. Bowditch’s estimate of the height Se. 
of Salem, by Mrs. Gardner, a very intelligent lady, who had an opper- 
tunity of observing it with great attention; those at Weston by Judge 
Wheeler and Mr. Staples ; and those at Rutland in Vermont by Wil- 
liam Page Esq. In collecting and combining these observations I 
have received great assistance from my friend, John Pickering jun. 
Esq. A.A. s. particularly in the observations at Wenham. These 
observations are given after the problems, and the results from com- 
bining them in various manners are stated at the end of this memoir. 
PROBLEM I. Fre. 1. 
Suppose that in two places in given latitudes and longitudes the 
azimuths ofa meteor were observed at the same moment of time, and 
its angular elevation above the horizon of one of those places. _ It is 
———— 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. w, s, the places of observation, m the place of the meteor. 
Draw Cw, Cs, Cm, cutting the spherical surface in the points W, S, 
M. Then Ww, Ss, will represent the vertical heights of the places 
of observation, and Mm the vertical height of the meteor above the 
level of the sea; PWM the azimuth of the meteor observed at w, and 
PSM its azimuth observed ats, Then in the spherical triangle PWS 
are given PW, PS, the co-latitudes 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 difference of PWS, PWM, will give the angle SWM; and 
the sum or difference of PSM, PSW, will give the angle WSM- 
