HAYES— U. S. NAVY MV TYPE OF HYDROPHONE. 381 



Moreover, the angle a which the sea-bottom makes with the keel 

 of the vessel, assumed to be horizontal, is given by the relation 



2a = <I>2 — $1. 



If <I>j = <?>., the formula reduces to the sounding equation, viz.: 



Z) = C-f Ltan$. 



In practice it has been found that shelving of the sea-bottom is 

 seldom rapid enough to cause any great error in the determination 

 of depth, especially for depths within 15 or 20 fathoms, and for 

 purposes of navigation a single hydrophone located in the bow of 

 the vessel and a sound-source located near the stern have been con- 

 sidered sufficient. Such an installation tends to err by giving too 

 great depths when approaching shallow water and too small when 

 approaching deep water. This error has been checked by taking 

 soundings out and in on same course and found to be negligible in 

 the most cases. 



Soundings taken on a shelving bottom with any of the various 

 types of sounding machines err in the some direction as do soundings 

 given by the simple hydrophone installation described, if the. sound- 

 ing weight is launched from the stern of the vessel. Since the lead 

 reaches bottom some distance behind the vessel, it will register too 

 great depths when approaching shoal water and too small depths 

 when entering deeper water. The hydrophone method has the 

 advantage that the error is independent of the speed of the vessel 

 while in case of the sounding machine the error increases with the 

 speed. 



Errors Introduced by Incorrect Determination of Sounding 



Angle. 



The MV hydrophone determines direction by measuring the dif- 

 ference in time between reception of the sound by the two groups 

 of receivers which connect with the two ears respectively ; or, what 

 amounts to the same thing, by determining the path difference be- 

 tween the sound-source and the two groups of receivers. This time 

 difference or path difference is measured by introducing sufficient 

 compensation into the paths connecting the receivers to the ears to 



