"68 XJ. S. COAST AND GEODETIC SURVEY. 



hour of the component day {cJi) requked for the construction of the 

 stencils may be obtained b3' rejecting multiples of 24 from the (chs). 



In the application of the above formula it 'svill be found that the 

 integral component hour will differ from the corresponding solar 

 iour by a constant for a succession of solar hours, and then, with 

 the difference changed by one, it will continue as a constant f )r 

 another group of solar hours, etc. This fact is an aid in the prepara- 

 tion of a table of component hours corresponding to the solar hours 

 of the series, as it renders it unnecessary to make an independent 

 calculation for each hour. Instead of using the above form \lx for 

 each value the times when the difference between the solar and com- 

 ponent hours changes may be determined. The application of the 

 differences to the solar hours will then give the desired compone.it 

 howcs. 



Formula (262) is true for any value of (sJis), whether integral or 

 fractional. It represents the component time of anv instant in the 

 series of observations in terms of the solar time of that same instant, 

 Tooth kinds of time being reckoned from the beginning of the series 

 as the zero hour. The difference between the component and the 

 «olar time of any instant may therefore be expressed by the folbwing 

 formula : 



Difference = tn^(s7is) ~ (shs) = , _ ^ {slis) (263) 



Ibp lop 



If the component day is shorter than the solar day, the speed a 

 iviU be greater than 15p, and the component hour as reckoned from 

 the beginning of the series wiU be greater than the solar hour of the 

 same instant. If the component day is longer than the solar day 

 the component hour at any instant will be less than the solar hour 

 of the same instant. At the beginning of the series the difference 

 l)etween the component and solar time will be zero, but the difference 

 will increase uniformly with the time of the series. As long as ttie 

 difference does not exceed 0.5 of an hour the integral component 

 hours will be designated by the same ordinals as the integral solar 

 hours with which they most nearly coincide. Differences between. 

 0.5 and 1.5 will be represented by the integer 1, differences between 

 1.5 and 2.5 by the integer 2, etc. If we let d represent the integral 

 difference, the time when the difference changes from (d—l) to d, 

 will be the time when the difference derived from formula (263) 

 equals {d — 0.5). Substituting this in the formula, we may obtain 



{sTis)= ^^f, id -0.5) (264) 



a~15p 



In which (sJis) represents the solar time when the integral difference 

 between the component and solar time will change by one hour from 

 (d—l) to d. By substituting successively the integers 1, 2, 3, etc., 

 for d in the formula (264) the time of each change throughout the 

 series may be obtained. The value of {sTis) thus obtained will 

 generally be a mixed number; that is to say, the times of the changes 

 will usually come between integral solar hours. The first integral 

 solar hour after the change will be the one to which the new difference 

 will apply if the usual system of distribution is to be adopted. In 

 this case we are not concerned with the exact value of the fractional 



