TIDES AND CURRENTS. 663 



The value of (^^ — >.i) is a maximum or minimum when 



cos 2(^ — a) = 



^1 



hence tan 2(^1 -Xi)=- ^^ - or sin 2(6 j^-K^)= ^ 



a/-(I; 





The height y of the tide above the mean surface is given by the 

 equation y = \^h? + h^^ -\- 2 hh^ cos 2(^ — a) 



To determine the variations in the mean level accurately 

 requires very great care, and the observations made in Dr. Kane's 

 or Dr. Hayes' Expeditions do not at all determine them, as the 

 zero was several times shifted during the series of observations. 



The height of the tide is affected by the barometric pressure, 

 and also by the wind. 



The effect of pressure may be tested by grouping the mean 

 levels for days below the average pressure, and those for days 

 above the average pressure, in two separate columns ; the dif- 

 ferences from the average value are then taken, and the mean of 

 the whole series gives the change of level due to a given change 

 in the height of the barometer. 



Similarly the effects due to opposite local winds may be deter- 

 mined by an arrangement of the observations according to the 

 direction of the wind. 



9. Obsehvations on Tides and Currents in '^ Polaris Bay '* 

 by Dr. Bessels (Bulletin Soc. Geographique, March 1875). 



As soon as the ice was strong enough an Observatory was 

 erected on it for the observations on the sea and on ice. 



Observations on the tides were generally made hourly and 

 extended over seven lunations ; during three or four weeks they 

 were made every ten minutes, and the following results were 

 obtained. 



The Establishment of Polaris Bay is 12h. 3m. 



The highest spring tide - -8-0 English feet. 



The lowest spring tide - - 2* 5 ft. 



Mean height of low tides ■• 3*8 ft. 



Mean height of high tides - 5-47 ft. 



Mean of neap tides - - 1 • 83 ft. 



Observations were also made on the specific gravity of the sea, 

 the depth, and the temperature at different depths. 



After entering Smith's Sound a current to the south was met 

 with varying from 1 "5 to 5 miles, and this current brought drift 

 wood into Polaris and Newmann Bays. The wood was pine-wood, 

 and the different layers showed that it had grown in northern 

 latitudes. 



