32 RESULTS OF METEOROLOGICAL OBSERVATIONS 



a direction corresponding to that of the rotation of the winds in the northern hemi- 

 sphere, and v^ v^ v-i the respective velocities which may be supposed 



expressed in (st.) miles per hour. The observations are supposed to be made at 

 equal intervals. Adding up all velocity numbers referring to the same wind 

 during a given period (say one month) and representing these quantities by s^ s^ s^ 



, the number of miles of air transferred bodily over the place of observation 



by winds from the southward is expressed by the formula 



B^ = Si cos Oi. + S2 cos 62 + S3 cos 03 -f . . . 

 and for Avinds from the westward 



jBjo = Sj sin $1 + S2 sin 6^ + S3 sin 63 -\- . . . 

 the resulting quantity E and the angle 4- it forms with the meridian, are found by 



R = ^Ef + BJ tan 4. = ^ 



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

 lowing convenient form: — 



B^ = (S—N) + {SW—NE) v/i — (NW—SE) V^ 

 i?^= ( W—E) + {SW—NE) n/J + {NW—SE)s/\ 

 where the letters S, SW, TF, etc., represent the sum of aU the velocity numbers, 

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

 in the directions S, SW, W, etc. respectively. B^ represents the total quantity of 

 air transported to the northivard, and Bj„ the quantity transported to the eastward. 

 These formulae for practical application may be used under the following form : — 

 Put.S'— iV=a SW—NE=zc 



W—E=h NW—SE=d 



Then 



B, = Bcos^ = a + 0.707 {c—d) 



B^^ B sin ^=b + 0.707 (c + d) 



Since Bg B^ B represent the quantity of air passed over during the given period 



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



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



during that period ; we have consequently : — 



r, = ^ K, = =^ and 7 = - 



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° + i^? 



B 



and at a distance of B miles, equal to a movement with an average velocity of — ; 



n 



this supposes an equal and parallel motion of all particles passing over. The length 



of path described by each can be found by summation of all the v's during the 



period. 



In the present case the above formulae become simplified since we have no record 



of velocities ; they may, therefore, all be put equal unity, and in consequence the 



summations give at once the relative frequency with which each wind occurred 



during the given period. 



