642 EEV. S. HATJGHTON ON THE TIDES OF THE 



h m 

 Solitidal interval at Springs 7 36 



Solitidal interval at Neaps 7 14 



Mean 7 25 



Hence we find 



i»=2 53J (III.) 



i.=7 25 (IV.) 



We are now in a condition to calculate, according to received theories, from the pre- 

 ceding data, the eccentricity of the Moon's path, her mass as compared with that of the 

 earth, and the mean depth of the ocean canal traversed by the tide previously to its reaching 

 Frederiksdal. 



1. Eccentricity of the Lwnar Orbit. 



It appears from equations (3) that the mean height of the High Water of the Lunar 

 Tide is 



Mcos' (14°)= ^=3-477 feet. 



Adding to this, and subtracting from it half the maximum parallactic inequality, we 

 obtain, with the aid of equation (1), 



^3 3-48 + 0-70 _4-18 

 '3-48— 0-70~2-78' 



or 



l+e 



(i^:)' 



,_. =1-1466: 

 and, finally, 



^=2^=0-06786 (V.) 



2. Mass of the Moon. 



The ratio of the mass of the Earth to the mass of the Moon is found from the equation 



Mass of Earth _ Mass of Earth Mass of Sun _ 1 / 2xl2032 y S^ 



Mass of Moon— Mass of Sun ^ Mass of Moon" 359551 ^ \ 59-964 ) ^M' " ' (4) 

 or 



#SHSS=i'^-^5xS=im5xl|i; 



and, finally. 



Mass of Earth ^yi «qq /\tt \ 



MassofMoon =6^^^^ ^^■) 



3. Depth of the Sea deduced from Heights. 

 The depth of the Sea, determined from heights, is found from the equation 



1=0-47288 xJlil^*. (5) 



