222 Mr. Bowditch’s estimate of the height, &c. 
as above. When the points s, w, are not on the same level, as 
in Fig 4, the line SS’ being found as above, and the angle WSS" equal 
to WSM or its supplement, SW being also given, the side S’W and 
the angles WS'S, S’WS, may be found by plane trigonometry. Then - 
as before we shall have | 
Sine S’'(WM = Tang. alt. meteor at w x Cotang. alt. meteor at s x Sine WS'M, 
which gives the bearing of the meteor from W, whence the distance 
WM, and the height of the meteor as in Problem IL 
Remark 2. When either of the azimuths or altitudes is not accu- 
rately known, but the limits between which the real value is contain- 
ed are given; the situation of the meteor may be calculated for each 
of these limits, and by this means the limiting values of the required 
elements of the motion of the body may in general be obtained. This 
method is frequently made use of in this memoir. 
Remark 3. In order to judge of theaccuracy of the results obtained by 
the preceding problems, it will be useful to repeat the operation, mak- 
ing successively a small change in each of the given quantities. For if 
any one of the required quantities be not materially affected by these 
changes, the calculated value will in general be nearly correct. 2 
the other hand if a small error in the observed angles produces a great 
error in the result, it will be proper to reject it, Thus, in Problem 1. 
if the given angles WSM, SWM, are both very small, the least 
change in either of those angles will in general produce a great change 
in the situation of the point M, as is well known; and if the two 
places of observation s, m, are thus situated with respect to the mete- 
or, the observations made at those places must not be combined t0- 
gether. This is the case with the observations of the Weston me 
teor made at Rutland and Weston, and for that reason the observa- 
tions made at those places are not combined together, in the calcula 
tions made for determining the place of the meteor. : 
