HAYES— DETECTION OF SUBMARINES. 15 



variation in angle requires but slight change in air path and as a 

 result a very slight error in determining the difference d in air path 

 lengths will result in a large error in determining the angle. Sec- 

 ondly, the direction so determined will be ambiguous. 



Fig. I shows that the time difference between the reception of 

 the sound at receivers R and L will, from conditions of symmetry, 

 be the same whether the sound comes from the direction indicated 

 by arrow i or that indicated by arrow 2. It is, then, impossible to 

 tell from the value oi d whether the sound comes from the direction 

 of 9 or from the direction 2Tr—d. 



Both of these weaknesses are readily overcome, as will be seen 

 by a consideration of Fig. 2, Plate III. Suppose the line connecting 

 the two receivers R and L is perpendicular to the direction from 

 which is measured and suppose the sound is proceeding from the 

 same angle 6 that is represented by arrow i in Fig. i. The time dif- 

 ference between the reception of the sound at the two receivers R 

 and L is represented by the water path R-C, Fig. 2. But sound pro- 

 ceeding from the direction represented by arrow 2, would, from con- 

 ditions of symmetry, give a time interval between reception at the 

 two receivers represented by the same length of water path. It 

 will be impossible then to tell from the value of d whether the sound 

 comes from the direction 6 or ir-O. 



The direction of the sound as determined by two receivers ori- 

 ented as in Fig. i is determined as being either 6 or 2Tr-9 whi;lel 

 the direction as determined from a pair of receivers oriented as in 

 Fig. 2 is determined as 6 or -n-d. It must follow that the angle 

 common to the two determinations, viz., 6, gives the true direction 

 and thus the ambiguity is removed. Moreover, it is to be noticed 

 that the angular range within which the determination of direction 

 is subject to most error when the two receivers are oriented as in 

 Fig. I is the region wherein direction is determined with greatest 

 accuracy when the receivers are oriented as in Fig. 2. It therefore 

 becomes possible to determine direction accurately at all angles pro- 

 vided that reliance is placed on the proper pair of receivers. 



The line connecting the second pair of receivers need not neces- 

 sarily be at right angles to that connecting the first pair, and the 

 second pair of receivers may utilize one receiver of the first pair. 



