SOUND-RANGING 73 



this would be what would be recorded on the timing device 

 electrically connected with M x and M 2 . This interval alone 

 would not serve to locate the position of the gun for there is 

 a whole series of positions which the gun might occupy and 

 still send the sound to M x a tenth of a second earlier than to 

 M 2 ; in fact G might lie anywhere provided G M 2 were greater 

 than G M x by 33.7 meters in the example chosen. Stated 

 more mathematically, G must lie on a particular hyperbola hav- 

 ing M! and M 2 as foci, for an hyperbola is a curve drawn in 

 sych a way that the difference of the distances from any point 

 of the curve to two fixed points, or foci, is a constant (33.7 

 meters in this case). Now if G is not close to M and M 2 

 compared to the distance between M x and M 2 , which is the 

 practical case on the battle front, the hyperbola on which G 

 must lie is practically a portion of a straight line which, if pro- 

 longed, goes through a point midway between M t and M 2 and 

 thus it is possible to determine the direction from this mid- 

 point to the gun. A plotting board may be prepared in ad- 

 vance which has a string pivoted on the mid-point A, and a 

 scale on the edge of the board marked with hundredth and 

 tenth seconds intervals. In the example taken this string 

 would have to be set at the interval marked one-tenth of a 

 second and the gun would be determined to lie on the ground 

 at some point represented on the plotting board as a point 

 lying under the string. Similarly, if the observed interval be- 

 tween the times of arrival of the report at M 2 and M 3 be laid 

 off on a second scale for a string pivoted on the mid-point B 

 the intersection of the two strings would locate on the plotting 

 board the position of the gun on the ground. Naturally the 

 plotting board must be very carefully prepared from an ac- 

 curate survey of the positions of the listening instruments on 

 the ground. 



The location found on the plotting board will only be exact 

 without correction if the temperature of the air is 10 degrees 

 centigrade and if there is no wind. If there is no wind but 

 the temperature is greater than 10 degrees centigrade the sound 



