14 



Fishery Board for Scotland. 



added a number of Professor Geelmuydeii's Norwegian results (re- 

 duced to feet), and also the various English and Scotch co-efficients 

 which I owe to the Idndness of Mr. E. Roberts. We may now use 

 the symbols commonly employed in treatises on the Tides, viz., H 

 for the half-range (or semi-amplitude), and k for the phase-angle, 

 in the annual (Sa) and semi-annual (Ssa) tides, respectively. 



Table F. — Harmonic Constants for the Annual (Sa) and Semi-armual 

 (Ssa) Tides (in feet ; to the epoch of the Sun's mean longitude). 



H. 



Sa. 



Ssa. 



H. 



These are the constants of cosine formula^, reduced to the epoch of mean 

 sohxr longitude, as used by students of tidal phenomena. By our first analysis 

 of a series of twelve monthly mean values, we obtain a formula m such terms as — 



A|, -f Aj cos (t + ei) + Ao cos (2t + e2), 



where the phase is reckoned from the epoch of mid- January, say 15th Januaiy. 

 For reduction to the epoch of the sun's longitude {h), which may be taken as 

 295°, or 295 days, before the 15th January, we have merely to substitute {h~e) 

 for e in the above formula, which new constant is usually known as k. If we 

 continue to call mean sea level, Aq, our formula then becomes 



Ay -I- Hs,, cos (h-k,) + Hssu cos (2 h-k,). 



