1838.J Numerical l?egi.s!er of ihe Direclien of the Wind. 103 



corresponding to any series of directions, as the mean direction of the 



series for example, = 15/ 5, corresponding 



4 



to N. N. W., as the mean direction of W., N. W., N., N. E. 



But since, in the above division of the horizon, the position of zero 

 is altogether arbitrary, any change in its position ought not to alfect 

 the mean result deducible from a given set of observations. It how- 

 ever admits of proof that if zero of the scale be supposed to move, from 

 south towards west, round the whole horizon, as soon as it reaches the 

 point corresponding to the first of a series of observations, the mean 

 result begins to vary, and continues to do so until, afier a complete re- 

 volution, the scale again commences at the south. Consequently, 

 Lambert's mode of deducing the mean direction of the wind is inde- 

 terminate, and furnishes only one of many possible results. 



It may also be observed that the horizon being divided into 360°, the 

 arithmetical mean of the numbers denoting any two opposite points of 

 the compass is never less than 90^ nor greater than 2/0° ; and 

 hence that the method in question not only assigns a mean to two ex- 

 actly opposite directions of the wind, which is absurd, but likewise in- 

 variably refers it to the northern half of the compass. 



The object of the remainder of this short paper is to propose a mode 

 of avoiding these defects, by dct(?rmining the mean direction of the 

 wind in a ditFerent manner. 



The accompanying circular figure (-yee p/a^e), may be supposed to re- 

 present the dial of an Anemoscope. The circumference of the innermost 

 circleis divided into thirty-two points, adivision which appearssuOiciently 

 minute for meteorological purposes,v/ithout beingextended to quarters of 

 points. The different points of the circumference are referred to two rec- 

 tangular axes having their origin at the centre : of these the line joining 

 the north and south points is the axis of ordinates, and that joining the 

 east and west points is the axis of abscissas.. The arithmetical values, 

 of the co-ordinates of each pointy aliecied with their proper signs, aiie 

 laid down opposite to it, tlie abscissa occupying the first space from 

 the centre, .'ind the ordinate the second. Tlie third space contains the 

 letters by which the point is distinguished; and the fourtli its tangent, 

 or rather that of the arc intercepted between it and the east point. 

 The arithmetical values of these lines are assigne^l '>:'v^^\ reference to- 

 radius ■-= 1. 



If now a series of directions of the vvind be dcnoled by their corres- 

 ponding points on the circumference, and the arithiiKdical mean, first ' 



