X PREFACE. 



which the direction of A B makes with the meridian at B, or (<;> + 180°) the angle 

 which it makes at A ; then we have 



Ssine 6-\-Si sine 01+ ^2 sine 02+ ^3 sine 03 etc _ a 



tang. <p = ^^^()s~0+^i cos 01-1-^2 cos 0^ -\-~S^ cos 63 etc. ~ b 



putting for the sake of brevity the sum of the terms in the numerator equal to a 

 and of those in the denominator equal to b. 



" The value of <^, expressed in the ordinary method of reading bearings with refer- 

 ence to the four cardinal points, is given in the tables in the fifth column from the 

 right, and as the numerical value of the tangent of <p is the same for angles in each 

 of the four quadrants, recourse must be had to the algebraic signs of the numerator 

 and denominator. If both are -|-, the direction is in the northeast quadrant; if 

 the numerator is -\- and the denominator — , it is in the southeast quadrant ; if 

 both are — , it is in the southwest quadrant; and if the numerator is — and the 

 denominator -(-, it is in the northwest quadrant; thus: — 



a b 



Northeast quadrant ..... -|- -|- 



Southeast " .....-[- — 



Southwest " ..... — — 



Northwest " . ... — + 

 Also we have 



sine <p cos ^ 



r> 

 the last two forms being the most convenient for computation, the values of — 



are given in the tables in the fourth column from the right. 



"Where the places of observation are isolated, resultants are computed for each 

 separately ; but where there are several in the same vicinity, they are often grouped 

 together, and the resultants for the group only computed. The observations made 

 at the different stations in a group are ordinarily combined by simply adding them 

 together, in the same manner as if they had all been made at one station ; but it 

 did not seem best to adhere uniformly to this method. Suppose, for illustration, 

 that the group consists of but two places, and that the number of observations made 

 at them is very unequal, at each of which the number of observations is sufficient 

 to determine the character of its winds ; but that, owing to local influences, the 

 results at the two differ widely. Now if the number of observations at the two 

 places was nearly equal, their sum would afford a tolerable mean between the two ; 

 but if very unequal, the place which had the greater would have more weight than 

 properly belonged to it, and a more reliable resultant could be obtained, either by 

 equalizing the numbers representing the observations, or by computing a oew 

 resultant from the separate ones of the two places. On the same principle, when 

 in any group, or at any place, the number of observations in the different seasons 

 of the year differ materially, the resultant for the year is computed, not from the 

 sum of all the observations, but from the resultants for the separate seasons. 



"The method of computing monsoon influenres, or the forces which deflect the 

 wind from its mean annual direction in the different months or seasons of the year, 



