2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 98 



periodic terms, namely, coefficients of a sine curve drawn through the 

 observations, may be represented by the trigonometrical formulas: 



in which 



L = A + A r cos cfr + Bi sin <f>, (i) 



2/ 



(2) 



(3) 



(4) 



(5) 

 (6) 



(7) 



where = angle of the epoch, namely, the angular distance from zero 

 to the part of the sine curve at the beginning of the period, and a — 

 amplitude, while n = number of terms used. 



The method of computation is shown in table I. In this table the 

 normal monthly temperatures at New York, derived from 50 years 

 of observations, are used, and the coefficients of a sine curve passing 

 through them are computed. From these coefficients, monthly values 

 are then computed and are given at the bottom of the table. It is 

 seen that these differ very little from the observed values, showing 

 that these observed values follow very nearly a sine curve. 



The computed values for each month may, however, be obtained 

 in a different way, as shown in table 2. In this table the normal 

 monthly temperatures at New York are multiplied by the cosine values 

 given in column 3 of table 1. The cosine values are slipped down 

 1 month at a time, and the sum of the products in each case divided 

 by 6 gives the value on a sine curve for the month in which the cosine 

 value is unity. 



For example, in the first column of products the cosine is unity in 

 January and the sum of all the products divided by 6 is —21.7, the 

 same as the computed value in table 1 when A = o. In the second 

 column of products the cosine unity is placed in February, and the 

 sum of the products divided by 6 is —20.7: and so on successively 



