310 



Prof. G. H. Darwin. 



[June 19, 



For M 2 and S 2 . 



Semi-lunations numbered 1, 2, 3, &c. 

 234 



No. of semi-lunation 1 



No. of last H.W. in the semi- 

 lunation 29 



No. of last L.W. in the semi- 

 lunation 28 



Total No. of tides up to end of each 

 semi-lunation . . 57 



57 



67 



86 

 85 



114 

 114 



5 6 

 143 171 

 142 171 



114 171 228 285 342 



For Annual and Semi-annual Tides. 

 Months, or T V h parts of a year, numbered 1, 2, 3. 



The epoch for the second quarter year should be 91 days after first 

 epoch, that for the third 92 days after the first, for the fourth 91 days 

 after the third, except in leap year, when the last should also be 92 

 days. 



There are six tides (or about thirty-seven hoars) more in a quarter 

 year than in xiii quarter-lunar-anomalistic periods ; the times of these 

 six tides (or ten tides in one of the quarters) are to be omitted from 

 the reduction, and their heights are only required when the annual or 

 semi-annual tides are to be found. 



F. Cosine and Sine Factors for all the Tides. 



These are the cosines and sines of 2 30', 7 30', 12 30', &c. They 

 are as follows : 



Cosine and Sine Factors. 

 Bead downwards for cosines, upwards for sines. 



1. 



2. 

 3. 

 4. 

 5. 

 6. 

 7. 

 8. 

 9. 



0-999 



0-991* 



0-976 



0-954 



0-924* 



0-887 



0-843 



0-793* 



0-737 



10. 

 11. 

 12. 

 13. 

 14. 

 15. 

 16. 

 17. 

 18. 



0-676 



0-609* 



0-537 



0-462 



0-383* 



0-301 



0-216 



0-130* 



0-044 



cos 



In the evaluation of S ^ ' 4F and S*" fF, only the factors 



Sill S1H 



marked * are required. 



