of the meteor of 1807. 215 
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 re- 
spectively equal to the angles mCw, sCm. The altitude of the mete- 
or observed at w, added to 90°, and #;th. part of the arch WM sub- 
tracted from the sum for terrestrial refraction, will leave the correct 
value of the angle Cwm: this added to mCw and the sum subtracted 
from 180° will leave the angle Cmw. Then in the plane triangle Cwm, 
will be given the angles and the side Cw (which may in general, when 
Ww is small, be taken equal to the semidiameter of the earth, 3982 
‘miles*) to find wm the distance of the meteor from the observer at 
w, and Cm its distance from the centre of the earth, from which sub- 
tracting CM equal to 3982 miles, there will remain the vertical altitude 
of the meteor above the level of theséa. In the plane triangle sCm are 
given Cs, Cm, and the included angle sCm (= arch SM) to find sm 
the distance of the meteor from the observer ats, and the angle Csm 
equal to the supplement of the zenith distance of the meteor at s. The 
co-latitude of the meteor is equal to the arch PM, and the angle SPM 
is equal to the difference of meridians between the meteor and the ob- 
server at s. These quantities may ‘be easily found, by means of the 
spheric triangle PSM, in which PS, SM and the angle PSM are giv- 
en. They may also be found in a more simple manner, and to a suf- 
ficient degree of accuracy, by the usual rules of navigation, supposing 
the angle PSM to be the course and SM the distance, whence may 
be found the difference of latitude, departure, and difference of a ae 
tude between the points S, M. 
* The mile made use of i in this memoir is the statute mile of 5280 feet, In 
the following calculations on the Weston meteor, it will be supposed that Com 
Cs=3982 miles; the part Ww or Se being but a small fraction of a mile. 
