TIDAL OBSERVATIONS. 



161 



southern point of Baffin Bay would probably enable us to trace its course north- 

 wards through this channel 



Investigation of the Form of the Tide Waves. — The compound character of the 

 wave requires a separate investigation of the forms of the diurnal and of the semi- 

 diurnal wave. We have seen that the diurnal wave undergoes smaller fluctuations 

 of range than the semi-diurnal, in which latter the spring and neap tides are fully 

 developed. To obtain the average slope of these waves the time between two suc- 

 cessive low waters was divided in six equal parts, for each of these phases the 

 ordinates were measured from the low water level. The ordinates of 20 diurnal 

 waves and of 38 corresponding semi-diurnal waves, Avere thus ascertained and their 

 mean values taken. Applying to these measures Bessel's circular function'^ the 

 average forms of these waves, from twenty days of observation, are given by the 

 following expressions : — 



For the diurnal wave 



r'.50 + 1.56 sin {0 + 270°) + 0.08 sin (2d + 135°) 



For the semi-diurnal wave 



3.75 + 3.79 sin (0 + 275°) + 0.21 sin {2d + 19i°) 



The observed and computed values agree as follows : — 



Diurnal wave. 



Semi-diurnal wave. 



Observed. 



Computed. 



Difference. 



Observed. 



Computed. 



Difference. 



O^'.O 

 0.6 

 2.3 

 3.1 

 2.2 

 0.1 

 0.0 



of'.o 



0.5 

 2.5 

 3.1 

 2.4 

 0.6 

 0.0 



0".0 

 + 0.1 

 —0.2 



0.0 

 —0.2 

 + 0.1 



0.0 



of'.o 



1.9 



6.2 

 T.4 

 5.3 

 l.Y 

 0.0 



— 0".l 

 + 2.2 

 + 6.1 

 + -7.5 

 + 5.2 

 + 1.8 

 —0.1 



+ 0'''.l 

 —0.3 

 + 0.1 

 —0.1 

 + 0.1 

 —0.1 

 + 0.1 



In the above expressions the angle 6 counts from low water (0°) to the following 

 low water (360°), for the first wave it passes through its values in a day nearly, for 

 the second in twelve lunar hours ; the ordinates are expressed in feet. The diurnal 

 curve appears to be nearly symmetrical, but the preceding slope of the semi-diurnal 

 wave appears steeper than the following slope ; the difference, however, is slight. 



The difference in the establishments of high and low water is 6"^ 05"". 7, which 

 represents the duration of fall, the duration of rise consequently is 6'' 18". 7; the 

 rise occupies therefore more time than the fall; the difference is 13". At Van 

 Rensselaer Harbor this difference was 16™, the water also rising longer.^ This 

 appears to be the rale for all localities which receive the direct ocean tide wave ; 

 the form of the wave, however, changes when ascending a shallow bay or a river, 

 and reverses the duration of the tide, making the rise the shorter. 



* Development of Bessel's function for the effect of periodic forces, etc , U. S. Coast Survey Report 

 for 1862, Appendix No. 22. 



^ In the discussion of the Van Rensselaer Harbor tides, p. 80, the reverse is inadvertently stated. 

 21 August, 1865. 



