Mathematical theory of sound ranging

The development of the art of concealing large guns so that they can not be easily seen by hostile airmen or observers in kite balloons has brought into prominence the study of methods of locating powerful guns by means of observation of the time of arrival of their gunfire at one or more observing stations. There are really two distinct problems to be discussed. (1) The simple case when the flash is seen and the distance of the gun is to be determined from the observed interval of time between the instants when the flash is seen and the report is heard at a single station. (2) The more complex case when the flash is not seen. The sound of the report must now be timed at three or four observing stations and the position of the gun estimated from the observed differences in time. A small error in the timing of the sound is more disastrous in the second case than in the first, consequently an accurate method of timing the arrival of the sound is very necessary for the successful application of the second method.