APPROXIMATE TIDE-CONSTANTS FOR TABLE BAY 



AND ALGOA BAY. 



By W. H. Finlay, M.A. 



[Read 31st August, 1887.] 



At the suggestion of H.M. Astronomer, D. Gill, Esq., self- 

 registering tide-gauges of the most approved pattern were erected in 

 3880 at Cape Town and Port Elizabeth by the respective Harbour 

 Boards : and the tracings of several years' tides are now available for 

 reduction. It is to be hoped that arrangements will soon be made for 



- a complete discussion of these curves and for an accurate prediction of 

 future tides. Meanwhile I have thought it would be of considerable 

 interest to obtain some preliminary results with regard to the moi*e 

 important of the tidal constituents, and to see in the case of Table 

 Bay whether any correction is indicated to the data published in the 

 Shipping Gazette, 1853, and used for the formation of the tide-tables 

 to the present day. These data were derived from 4,099 observations 

 of the time of high water at the Naval Yard, Simon's Town, during 

 the years 1840-1848. From previous observations in 1834 and 1835 

 with two temporary gauges, one at Simon's Bay and the other at the 

 South Jetty, Table Bay (near the Imhoff Battery), the conclusion 

 was arrived at that there was no sensible difference between the time 



. of high water in Simon's Bay and in Table Bay ; and the results of 

 the Simon's Bay observations were adopted without alteration. No 

 information, however, is given in the Shipping Gazette about the 



rlieights of the different high waters. Tide-gauge diagrams have, I 

 ibelieve, been regularly filed for many years previous to 1880, but no 



•attempt (so far as I know) has ever been made to discuss them. 



The height of the tide at any place may be expressed as the sum of 

 3. number of simple harmonic functions of the time, the periods of the 

 functions being the same as the periods of certain terms in the theory 

 of the Sun and Moon. The analytical expression for such a function 

 is 



A cos nt -f- B sin nt, or R cos (fit — e), 



^•where t denotes the time elapsed from some starting-point, n is the 

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