HAUGHTON.— TIDES. 7 



All these tidal waves are complex, and consist of four well 

 marked waves. 



1. Lunar semidiurnal. 



2. Solar semidiurnal. 



3. Lunar diurnal. 



4. Solar diurnal. 



This tidal wave cannot, therefore, for a moment be confounded 

 with the Behring Strait wave, which is a simple lunar semi- 

 diurnal wave. 



The western branch moves (as I believe) across Melville Sound, 

 and meets the Behring Strait tidal wave in Maclure Strait. The 

 northern branch proceeds reguhxrly through Penny Strait to 

 lat. 76°, showing no sign of meeting an opposing tide although it 

 would probably meet tlie Behring Strait tide somewhere about 

 80°. The southern branch, as I have proved meets the Pacific tide 

 at the north entrance of Victoria Channel, where the Franklin 

 expedition was abandoned. If the statement of the meeting of 

 two tidal waves in Kennedy Channel be confirmed, it will diminish 

 the chance of reaching the North Pole by that route, even though 

 the northern tidal wave be not the Behring Strait wave which is 

 highly improbable. 



It is not at all unlikely that the Behring Strait tidal wave may 

 meet the united Atlantic waves to the north of Greenland, and at 

 this side of the Pole ; in which case it is probable that sledges 

 will do more work than ships. 



As it may be of use to determine quickly the character of the 

 tidal wave, I now give a method of doing so. 



II. — Method of determining quickly the existence op a 

 Diurnal Tide. 



Hourly observations of the height of the tide made for 48 

 successive hours, will determine accurately the diurjial tide for 

 every hour of the middle 24 hours. Let Aj, /^2, ^3, be three 

 heights of tide separated from each other by intervals of 12 hours, 

 then the diurnal tide, at the period corresponding to the middle 

 observation h^ is given by the formula : — 



-Q_ ^i — 2^2 + ^3 ,, V 

 4 ^ '^ 



The time selected for making the 48 hours observations should 

 be when the Moon's declination is great (either north or south) 

 because the diurnal tide vanishes with the declination of the Moon 

 or Sun respectively. The expression for the diurnal tide is of the 

 form, — 



D=M sin 2/x cos (m) + S sin 2a- cos (S) (2.) 

 Where |U= Moon's declination. 

 <r= Sun's declination. 

 m=A.n angle that goes through all its changes in a 



lunar day. 

 5= An angle that goes through all its changes in a 

 solar day. 



