HARMONIC A:N-ALYSIS AIS^D PREDICTION" OF TIDES. 167 



rr^T • -, 1 1 /x \ ., sin ^(6 — a)r . ... 



Third value =^{b-a)T, if w^_ x — is positive, 



or i (6 - a) r + 180, if — ^4 n — is negative. 



Table 30. Products for Form ^4-^.— This table is designed for 

 obtaining the products for columns (6) and (7) of Form 245. 



Table 31. For construction of primary stencils. — This table gives 

 the differences to be applied to the solar hours in order to obtain the 

 component hours to which they most nearly coincide. Each differ- 

 ence applies to several successive solar hours, but for brevity only 

 the first solar hour of each group to which the difference applies is 

 given in the table. 



An asterisk (*) indicates that the solar hour so marked is to be used 

 twice or rejected according to whether the component speed is greater 

 or less than 15p, when in the summation it is desired to assign a 

 single solar hour to each successive component hour. For the 

 nsual summations in which each solar hour height is assigned to the 

 nearest component hour no attention need be given to the asterisk. 



The table is computed by substituting successive integral values for 

 d in formula (264) and reducing the resulting solar hour series (slis) 

 to the corresponding day and hour. The solar hour to be tabulated 

 is the integral hour that immediately follows the value the {shs) of 

 the formula. If the fractional part of (sTis) exceeds 0.5, the tabular 

 solar hour is marked by an asterisk (*) . The successive values of d, 

 although used positively in formula (264), are to be considered as 

 negative in the application of the table when the speed of the com- 

 ponent is less than 15p. When the component speed is greater than 

 15p, the difference is to be taken as positive. All tabular differences 

 are brought within the limits +24 hours and —24 hours by rejecting 

 multiples of ±24 hours when necessary, and for convenience in use 

 all differences are given in both positive and negative forms. 



The following example will illustrate the use of the table: To find 

 component 2Q hours corresponding to solar hours 12 to 23 on 16th 

 day of series. By the table we see that solar hour 12 of the 16th day 

 of series is within the group beginning on solar hour 8 of the same day 

 with the tabular difference of + 19 or — 5 hours, and that the differ- 

 ence changes by —1 hour on solar hours 15 and 21, the latter being 

 marked by an asterisk. Applying the differences indicated, we have 

 for these solar hours on the 16th day of series: 



Solar hour 12, 13, 14* 15, 16, 17, 18, 19, 20, 21* 22, 23 



Difiference -5 -5 -5 -6 -6 -6 -6 -6 -6 -7 -7 -7 



Component 



2Q hour____ 7, 8, 9* 9, 10, 11, 12, 13, 14, 14*, 15, 16 



In the results it will be noted that the component hours 9 and 14 are 

 ■each represented by two solar hours. If it should be desired to limit 

 the representation to a single solar hour each, the hours marked 

 with the asterisk should be rejected. 



To find compcment 00 hours corresponding to solar hours O to 18 

 on the 22d day of series. The O hour of the 22d day is in the group 

 beginning on solar hour 14 of the preceding day with the tabular 

 difference of +14 or —10 hours, and changes of +1 hour in the 



