4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 66 



There is no great geometrical difficulty in so solving the general 

 problem that the three co-ordinates in space of the end-point, together 

 with the spherical co-ordinates of the radiants, are obtained by the 

 method of least squares from one system of equations. But such a 

 solution, independently of the fact that it would be extremely tedious 

 and have little importance, would only seldom lead to any useful 

 result. It will therefore not be further considered here, but the 

 determination of the end-point will be separately treated as a neces- 

 sary preliminary work. 



A. DETERMINATION OF THE GEOGRAPHIC CO-ORDINATES AND THE 

 ALTITUDE OF THE END-POINT 



There are good reasons why it will generally be useful to divide 

 this problem into two parts, determining first the geographical loca- 

 tions and afterwards the linear altitudes. In certain cases the general 

 treatment of the problem is necessary or at least appropriate. In 

 order to determine all three unknown quantities the observations of 

 three appropriate elements, including one apparent altitude angle, 

 must be furnished by at least two places. The other two elements 

 may be directions or azimuths and it is generally best that this should 

 be the case. Evidently three azimuths are not sufficient if we wish 

 to find the linear altitude, but on the other hand, the problem can 

 generally be solved with three apparent altitudes. The determination 

 of the geographical location merely by means of parallax in altitude 

 will indeed be the only possibility if the parallax in azimuth is not 

 given, for example, if the locations of the places of observation fall 

 in the same vertical plane as the terminal point of the meteor's path. 



Sometimes the observed altitudes are so uncertain that the accuracy 

 of the result is diminished by combining them with the observed 

 directions. If we have reliable azimuths with a sufficiently accurate 

 parallax, then it is preferable to determine the location of the terminal 

 point from these alone, whereby we assume that the spheroidal earth 

 can be replaced with sufficient accuracy by a sphere of corresponding 

 radius. We can with advantage make use of the following approxi- 

 mate method. 



At the locations 0^, Oo. . . . on the earth's surface specified by the 

 geographic co-ordinates L and ^, let observations be made of the 

 azimuth A*ie of the terminal point E (Le, (f>e) of the meteor's path. 



First of all let approximate values Lo, <^o of L, ^ be found by some 

 short, perhaps graphical, method, also let an approximate value Ho 

 for the linear altitude He be sought out. Ordinarily these come, so 

 to speak, of their own accord before the commencement of the real 



