TIDAL OBSERVATIONS 591 



The mean range of tide may also be obtained from the harmonic constants by the formula 



Mn = 2M, + ^j^[s^i», + N',«», + . . . . + K\k\ + O\o\ + . . . .] 



+ M, (cos z; + cos ze;) + Yg^ X 2M^ (v — w) sin (2M°, — M" J 

 + 2M„ cos (3M°, - M°J - 2M, 

 which by means of Table 22 *, becomes 



Mn = 2.04 X Table 22 * + .035M4 {v — w) sin (2M:°, — M°,) 



+ M, (cos V + cos ze/) + 2M, cos (sM", - M°,) — 2M, (40) 



in which v and w are the same as obtained for (11) and (12). By (40) the mean range of 

 tide from the harmonic constants is 



For Cape Flora Mn = 0.952 feet (41) 



For Teplitz Bay Mn=i. 100 feet (42) 



which agrees fairly well with the values given in (38) and (39). 



The spring and neap ranges of tide may be obtained from the harmonic constants by the 

 formulas 



Sg = Mn-.536|+[i.96-.o8(^)'] 



X [S, + A, cos (2M°, - S°,— A°,)] (43) 



Np = Mn-.536|-[r.96-.o8(l4^y] 

 X [S, + //., cos (2M°, - S°, - iJ.\y\ (44) 



in which the first and last letters of the words spring and neap are used as abbreviations. 



From (43) and (44) we obtain : 



Cape Flora Teplitz Bay 



Ft. Ft. 



Spring range = Sg 1.224 1-485 (45) 



Neap range =Np 0.628 0.625 (46) 



The heights of the tropic tides above mean sea level may be obtained from the harmonic 

 constants by the following formulas : 



Tropic HHW ^ 1.02 4, x Table 45 f (47) 



Tropic I,HW= 1.02 J, X Table 45 f (48) 



Tropic HLW = 1.02 /)j x Table 45 f (49) 



Tropic I,I,W= 1.02 ^j X Table 45 f (50) 



where 



J, = 1. 010 M, + o. 27 (S, -f- M,) - K, cos [(K°, - O",) (/> (K°, - M%)] 



• See note, p. 588. t See note, p. 588. 



