86 U. S. COAST AND GEODETIC SURVEY. 



According to the usual summations with the primary stencils, the 

 hourly heights included in a single group may be distributed over an 

 interval from one-half of a component hour before to one-half of a 

 component hour after the hour to be represented. In this case r 



equals one component hour, or — - solar hours. 



Substituting this in (328), the 



augmenting f actor = ^'^^j^ ,^^^. 



24 sin -^ 



which is the formula generally adopted and is the one upon which 

 the augmenting factor of Form 194 is based. 



If the second system of distribution of the hourly heights as 

 described on page 65 is adopted, r equals one solar hour and formula 

 (328) becomes 



augmenting factor = — roon^ 



360 sm ^ 



It will be noted that formula (329) depends upon the value of p and 

 therefore will be the same for all short period components (S excepted) 

 with like subscripts. Formula (330) depends upon the speed a of the 

 component and will therefore be different for each component. 



When the secondar}^ stencils (described in sec. 25) are used, the 

 grouping of the ordinates is less simple than that provided by the 

 primary stencils only. Let it be assumed that the series is of sufficient 

 length so that the distribution of the ordinates is more or less uniform 

 in accordance with the system adopted. 



Suppose the original primary summations have been made for com- 

 ponent A with speed a and that the secondary stencils have been 

 used for component B with speed h. Then let p and p^ represent the 

 subscripts of components A and B, respectively. 



The equation for component B may be written 



y = B cos (bt + ^) (331) 



In the primary summation for component A, the group of ordi- 

 nates included in a single sum covers a period of one component A 



hour or — - solar hours. Expressed in time t, midway of this interval 



and representing the exact integral component A hour to which the 

 group applied, the average value of the B ordinates included in such 

 a group may be written 



= F,B cos (J)t + ^) (332) 



