the Mean Depth of the Ocean, 



35 



of the mean depth obtained from soundings is calculated from 

 data given by Prof. Milne. 



Station. 



Mean Depth in Fathoms obtained from 



f 

 Velocity of Sea-waves. 



Soundings. 



Geinitz. 



> 

 Milne. 



Wellington 



1430 

 2319 

 1930 

 2182 



1028 

 1635 

 1662 

 1563 



2473 

 2495 

 2500 



2584 



Honolulu 



Samoa 



Xamaishi 





Both Captain Wharton and Prof. Milne notice the discre- 

 pancy between the calculated and observed mean depths, and 

 both offer a partial explanation of it. According to the latter, 

 " the common error in actual soundings is that they are 

 usually too great, it being difficult in deep-sea sounding to 

 determine when the lead actually reaches the bottom." Captain 

 Wharton remarks that " any unknown ridges would diminish 

 the speed ; but these must be large, or the portion of the wave 

 overlapping them would still travel at the speed due to deeper 

 water, and over a very slightly longer course." 



But even if the soundings were absolutely exact, and if 

 there were no unknown ridges, the discrepancy would still 

 exist ; for, as will be shown below, the assumption that the 

 mean depth of the sea is given by the equation \Z(#H) = A/T 

 is incorrect. 



Taking the tide-gauge as the origin, the horizontal line 

 joining the gauge and the epicentre as the axis of x, and the 

 axis of y vertically downwards, then, neglecting the curvature 

 of the earth, 



T= J_ f A *L, 



VgJo Vy 



and therefore 



/ A *» 

 H= 



Also, D being the true mean depth, 



D =*5j v dx > 



D 2 



