164 U. S. COAST AND GEODETIC SURVEY. 



sin 2v sin^ / 



Tan 2/' = 



_ . 2 J, 2 + 3eiV cV S . 2 



sin 21* sin^ / /r>o-i\ j? r-, 



" cos 2vsin^ 7+0.0728 (231) of p. 57. 



Table 7. Values of log Ra for amplitude of component Lj. — This 

 table has been computed by means of the followdng formula: 



i?a = [l-12 tan2 i/cos 2P + 36 tan* i/]"^ (177) of p. 48. • 



The argument P = p — ^. The value of p and N for any date 

 between 1800 and 2000 may be taken directly from Tables 4 and 5 

 and the values of ^ and / as functions of N may be obtained from 

 Table 6. 



Table 8. Values of R for argument of component L3. — This table 

 has been computed by the following formula : 



T^°'^ = cotMV-"6Tos2P ' (178) of p. 48. 



The argument of P=p — ^. The values of p and A^ for any date 

 between 1800 and 2000 may be taken directly from Tables 4 and 5, 

 and the values of ^ and / as functions of N may be obtained from 

 Table 6. 



Table 9. Values of log Qa. for amplitude of component M^. — The 

 formula upon which this table is based is 



^. = [5/2-9/2 tan2 ^7+9/4 tan* ^7+ 3/2(1 -tan^ i7) cos 2P]-i, 



(191) of p. 50. 



Attributing to 7 its mean value (co = 23.°452) from Table 2, the 

 above may be written 



Qa = [2.310 + 1.435 cos 2 P]-K 



By means of the latter formula a single argument table of the log- 

 arithms of Qa, has been prepared, which is applicable without serious 

 error to any series without regard to the exact value of 7. 



Table 10. Values of Q for argument of component M^. — The formula 

 for which this table is based is 



Tan Q =1^1^^^ tan P (195) of p. 51. 



Attributing to 7 its mean value (w = 23.°452) from Table 2, the 

 above formula may be written 



Tan Q = 0.483 tan P. 



By means of the latter formula a single argument table has been 

 prepared which is applicable without serious error to any series with- 

 out regard to the exact value of 7. 



Table 11. Values of u for equilibrium argument. — The values for 

 the table have been computed for each degree of iV by the formulas 



