72 U. S. COAST AND GEODETIC SURVEY. 



The 24 integral component A hours of the middle component day 

 of the page will therefore be the integral component A hours which 

 immediately follow the time indicated by the last formula. The 

 numerical value of this formula will usually be a mixed number. 

 Let /equal the fractional part, and let m be an integer representing 

 the number of any integral component hour according to its order in 

 the middle component day of each page. For each page m will have 

 successive values from 1 to 24. The integral component A hours 

 falling within the middle component day of each page of tabulations 

 will then be represented by the general formula 



[(168 71-84.5) ~--12-f+m] component A hours (268) 



from the beginning of the series. 



The relation of the lengths of the component A and component B 



hours is given by the formula 



vb ' 

 1 component A hour = ^ component B hours. (269) 



The component B hour corresponding to the integral component A 

 hour of formula (268) is therefore 



[(168 n-84.5) j^-12-/+m] ^ component 5 hours (270) 



from the beginning of the series. 



The last formula will, in general, represent a mixed number. The 

 integral component B hour to which the sum for the component A 

 hour is to be assigned will be the nearest integral number represented 

 by this formula. Let g be a fraction not greater than 0.5, which, 

 applied either positively or negatively to the formula, will render it 

 an integer. 



The assignment of the hourly page sums for component A hours to 

 the component B hours may now be represented as follows, multiples, 

 of 24 hours being rejected: 



[(168 n — 84.5) :j-= 12— /+m — multiple of 24] component A hour 



^^P (271) 



sum to be assigned to 



[{(168 n-84.5) ^ 12 -/+ m} ^ - i^r- multiple of 24] compo- 



nent B hour. (272) 



The difference between the component A hour and the component 

 B hour to which the A hour sum is to be assigned is 



[{ (168 n- 84.5) ~ 12 -/+ m}{^~-l}±g- multiple of 24] (273) 



By means of the above formula Table 33 has been prepared, giving- 

 the differences to be applied to the component A hours of each page 

 to obtain the component B hours with which they most nearly 

 coincide. 



For the construction of secondary stencils the forms designated for 

 the compilation of the stencil sums from the primary summations. 



