of the meteor of 1807. 221 
The course from S to M is nearly N 15° W, the distance S M 
4' 29" ; hence the difference of latitude of the points S,M 1s 4’ 20’, 
departure 69’°6, difference of longitude 93”. Hence the latitude of 
the point M is nearly 41° 19’ 20” N, and its longitude 73° 28’ 33" W. 
If it be required to find the change in the above elements arising 
from an error in the altitude at Wenham, it would only be necessary 
to repeat the latter part of the calculation, since the values of SA, 
SWA, AWB, would remain the same in both cases. 
Remark 1. When the distances of the observers from each other 
and from the meteor are small, the correction arising from the spher- 
ical form of the earth may be neglected, supposing the triangle SWM 
to be rectilinear and drawn on a horizontal plane. In this case the 
calculations will be rendered more simple if the heights are estimated 
from a plane drawn through w parallel to the horizon, supposing the 
points w, W, to coincide. Then if the points s, w, are at the same 
height, the points s, S, will also coincide as in Fig. 3. ‘If the points 
s, w, are not at the same level, as in Fig. 4, the lines ms, MS (contin- 
ued if necessary) will meet in S’, in the plane MWS, making SS'=Ssx 
Cotang. alt. meteor at s. In either case there will be given in Prob- 
lem I. the angles SWM, WSM, SMW (=180°—SW M—WSM}) 
and SW to find by plane trigonometry WM, SM. Then the alti- 
tude of the meteor above the level of the point w will be represented 
. WMxTang. elevation of the meteor at w. 
In Problem 2, when the points s, w, are at the same level, as in 
Fig. 3, there will be given the angles Mwm, Msm, WSM, and the 
side SW, to find the angle SWM by the following formula. 
Sine SWM=Tang. alt. meteor at w x Cotang. alt. meteor at ¢ x Sine WSM, 
which being found the rest of the calculation may be made 
28 
