74 RECORD AND DISCUSSION OF FORCE OF WIND. 



The immediate bearing of the wind on the temperature, the weight and moisture 

 of the atmosphere, and upon the climate in general, as well as its practical relation 

 to navigation, renders this meteorological element of equal importance with any of 

 the others, though it has, perhaps, received comparatively less attention. 



Method of Reduction. In the following discussion, we have to consider the 

 average direction and force, as well as the quantity of air blown over the place of 

 observation. 



In regard to the mean direction and velocity of the wind for any given period 

 a day, month, or year the customary formula of Lambert has been so far modified 

 as to include the velocity, and not to depend on the relative frequency of the 

 winds alone. 



Let O l 6 2 0., ..... be the angles which the directions of the wind make with the 

 meridian, reckoned round the compass, according to astronomical usage, from the 

 south, westwards to 360, or in a direction indicated by the law of rotation; and 

 v l v v 3 ..... its respective velocities, which may be supposed expressed in miles 

 per hour; and let the observations be made at equal intervals of time, say hourly. 

 By adding up all velocity-numbers referring to the same wind during a given 

 period, and representing these quantities, or the number of miles of air transferred 

 bodily over the place in each direction, by Sj s 3 s s ..... , then the quantity of air 

 passed over the place of observation by winds from the southward is expressed by 



R a = Sj COS 61 + S 2 COS 2 + S 3 COS 6 3 + ..... 



And for winds from the westward 



R w = s, sin 6 l + s z sin 0. 2 + s 3 sin 3 + ..... 



The resulting quantity R, and the angle q&amp;gt; it forms with the meridian, is found by 

 the expressions 



R = &amp;lt;/R? +Rj, and tan $ = HL. 



&quot; 



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

 convenient form 



E s = (SN) + (SWNE)Sb (NWSE] v/1 

 R W = (WE) + (S WNE] v/T + (N WSE] x/I 



Where the letters S, SW, W, etc., stand for the sum of all velocities during the 

 given period, or for the quantity of air moved in the directions S, S W, W, etc., 

 respectively ; R s stands for the total quantity of air transported to the northward, 

 and R w for the same transferred to the eastward. These formula?, for practical 

 working, may be put in the following shape : 



Put SN= a SWNE=c 



WE = b N WSE = d 



Then 



R s = R cos q = a+ 0.707 (c d) 

 R w = R sin $ = I + 0.707 (c+d). 



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

 period in the direction 0, 90, &amp;lt;&amp;gt;, respectively, we must, in order to find the mean 



