DIRECTION AND FORCE OF WIND. 235 



Method of Reduction. 



The same method of discussion will be employed here as that used for Dr. Kane's 

 and Sir F. L. McClintock's observations. 



Let O-i do O3 .... be the angles which the direction of the wind makes 

 with the meridian (true), reckoned round the horizon according to astronomical 

 usage, from the south, Avestward to 360°, a direction corresponding to that of the 

 rotation of the winds in the northern hemisphere ; and ■^i V2 v^ . . . its 

 respective velocities, which may be supposed expressed in miles per hour, and let 

 the observations be made at equal intervals (for instance hourly). Adding up all 

 velocity-numbers referring to the same wind during a given period (say one month), 

 and representing these quantities by Si S3 Sg . . . . the number of miles 

 of air transferred bodily over the place of observation by winds fw7n the southward 

 is expressed by the formula. 



H^ = Sj cos 61 + So cos 60 + S3 cos 63 + 



and for winds /;-o??j the westward 



R^ = Si sin di + §2 sin 6^ + S3 sin 63+ 



The resulting quantity R, and the angle 4/ it forms with the meridian, are found 

 by the expressions 



R,n 



R = v/ig/ + RJ and tan ^ = ^ 



The general formulae, in the case of eight principal directions 0, assume the fol- 

 lowing convenient form : — _ 



R^ =(S—N) + {SW—NE) s/T_(^NW—SE) v/| 

 R^={W—E) + {SW—NE) ^1 + {NW—SE) ^/l 

 where the letters S, SW, W, etc., represent the sum of all velocities expressed in 

 miles per hour, during the given period, or the quantity of air moved in the direc- 

 tions S, SW, W, etc., respectively. R, represents the total quantity of air trans- 

 ported to the northioard, and R^ the same transferred to the easitvard. These 

 formulfe, for practical application, may be put in the following convenient form : — 

 Let S—N=a SW—NE^c 



W—E=b NW—SE=d 



Then 



R,=^Rcosi=a + 0.707 (c—d) 



R^ = R sin ^+h ■{- 0.707 {c+d) 



Since R, R„ R represents the quantity of air passed over during the given 



period, in the direction 0° 90° ^P respectively, we must, in order to find the average 



velocity for any resulting direction, divide by n or by the number of observations 



during that period ; we then have 



V,^^ V^ = '^ andF=-^ 



n n n 



A particle of air which has left the place of observation at the commencement 



of the period — of a day, for instance — will be found at its close in a direction 



180° + ■»]/ and at a distance of R miles, equal to a movement Avith an average 



velocity of — . This supposes an equal and parallel motion of all particles passing 



