74 



U. S. COAST AND GEODETIC SUEVEY. 



aient A day after the coincidence of integral hours of components 

 A and B the component ^ hourly height will differ in time from 

 the integral component B hour to which it is to be assigned by 24 



/ ^ 11 component B hours. At the end of the third component 



A day this difference becomes 72 ( — 1 ) component B hours. The 



same difference with opposite sign will apply to the third component 

 .day before the middle day of the page. Now, taking account of the 

 fact that the component B hour on the middle day of the page may 

 ■differ by an amount as great 0.5 of a component B hour from the 

 integral component A hour, and that the integral component A hour 

 may differ as maich as 0.5 of a component A, or 0.5 yl/p^a of a compo- 

 nent B hour from the time of the actual observation of the solar hourly 

 height, the extreme difference between the time of observation of an 

 Jiourly height and the time represented by the component B hour 

 with which this height is grouped by the secondary stencils may be 

 represented by the formula. 



[72 (^ ~ l') + 0.5 (^ + l\ component B hours. (274 



The differences may be either positive or negative, and in a long 

 :Series it may reasonably be expected that the number of positive and 

 negative values will be approximately equal. 



The above formula for the extreme difference furnishes a criterion by 

 which to judge, to some extent, the reliability of the method. Testing 

 the following schedule of components for which it is proposed to use the 

 secondary stencils, the extreme differences as indicated are obtained. 

 The differences are expressed in component B hours and also in com- 

 ponent B degrees. It will be noted that one component hour is 

 equivalent to a change of 15° in the phase of a diurnal component, 30° 

 in the phase of a semidiurnal component, etc. 



±1 



