166 TJ. S. COAST AND GEODETIC SUEVEY. 



hourly speeds of the components as given in Table 3. The differ- 

 ences refer to the uniformly varying portion V of the argument, it 

 being assumed that for practical purposes the portion u is constant 

 for the entire year. 



The approximate Greenwich (Fq + u) for any desired Greenwich 

 hour may be obtained by applying the appropriate differences from 

 Tables 16, 17, and 18 to the value for the first of January of the 

 required year, as given in Table 15. To refer this Greenwich (Vq + u) 

 to any local meridian, it is necessary to apply a further correction 

 equal to the product of the longitude in degrees by the subscript of 

 the component, which represents the number of periods in a com- 

 ponent day. West longitude is to be considered as positive and 

 east longitude as negative, and the subscripts of the long-period 

 components are to be taken as zero. This correction is to be 

 subtracted. 



The iVo+u) obtained as above will, in general, differ by a small 

 amount from the value as computed by Form 244, because in the 

 former case the u refers to the middle of the calendar year and in 

 the latter case to the middle of the series of observations. 



Table 19. Products for Form 194- — This is a multiplication table 

 especially adapted for use with Form 194, the multipliers being the 

 sines of multiples of 15°. 



Table 20. Augmenting factors. — ^A discussion of the augmenting 

 factors is given in section 27 of the text. The tabular values for the 

 short-period components are obtained by formulas (329) and (330). 

 For the long-period components the augmenting factors were com- 

 puted by formula (423) . 



Tables 21 to 26. — These tables represent perturbations in Kj and 

 S2 due to other components. They are based upon formulas (379) 

 to (384), inclusive. 



Table 27. Critical logarithms for Form 245- — This table was de- 

 signed for quickly obtaining the natural numbers to three decimal 

 places for column (3) of Form 245 from the logarithms of colmnn (2) . 

 The logarithms are given for every change of 0.001 in the natural 

 number. Each logarithm given in this table is derived from the 

 natural number that is 0.0005 less than the tabular number to which 

 it applies. Intermediate logarithms, therefore, apply to the same 

 natural number as the preceding tabular logarithm. For example, 

 logarithms less than 6.6990 apply to the natural number 0.000 and 

 logarithms from 6.6990 to 7.1760 apply to the natural number 0.001, 

 etc. 



Table 28. Component speed differences.— The component speeds as 

 given in Table 3 were used in the computation of this table. 



Table 29. Elimination factors. — These tables provide for certain 

 constant factors in formulas (409) and (410). Separate tables for 

 each length of series and different values for each term of the formulas 

 are required. The tabular values are arranged in groups of three;, 

 determined as follows : 



First value = logarithm of w^ — \ — - 



Second value = natural number ttt \ — always taken as 



positive. ^ Hi-a)r 



