602 - 2 - 



The rtSsumDtt:ns .Ps:- 



(1) That the exclusive ;ressur=s are crciigatea with the ncrmal velocity 'C -' 

 s:una W3Vds in water. That velicity is 1U50 wtres ;or sec^nO, ana in r.-una 

 numDors we shall call it 1300 netres ;cr sccrn3. Measurements :f the 

 c:m;res3iDility cf water show th=.t exce;t within c-. few feet -f the iX:l;sion 

 there is n; reason t: excect any serious Jeoarture from the abcve s:ee3. 



(2) That the wave is scherically synmetrical aDout the source. 



From this it follows that the pressure at any Doint while fleoenaent on time varies inversely 

 as the aistanco r fron the source, that the velocity of aisolacement is entirely racial ana if 



p - density of water 



C = soeea of orocagation 



= cressure cf any Dcint 



V = raOial velocity at same Doint 



with very great accuracy. 



We may now oxolain tne spr=iy ohencmenon in genere.l terms. 



Let X y De tne free water surface of aeec water. 



M a submerosa mi neat aecth a 



m' ?n imagt: mine at the octical image of H in X Y. 



The whole -ffect at any Doint = is due to the orimary effect from m ccrroined with the 

 effect reflected from the surface X Y. (see Figure l). 



Now the surface is a free water surface and thus the resultant sressure there must be 

 cermanently zero. This can Oe secured ana the effect of the reflection at any ooint in the water 

 is reoresentea Dy an imaginary exDlosion at M of equal magnitude but in oDoosite sign to that at 

 M and starting at the same instant. 



This secures that at any ooint 3 on the surface the aressure is oerraanently zero, Out the 

 resultant velocity at Q is ccmcoundeo of two equal effects arriving at orecisely the same instant, 

 one airectea from M to 3 ana the other'from Q to M*. _ The resultant Is no horizontal comconent Out 

 a ourely vertical velocity. Calculation shows that this velocity 



V p_z 



Now is varying with time and we can further show that if the negative aressure which the 

 water will suooort i5 neglijiole then each aoint of tne water surface in succession must cart 

 ccmaany with the jeneral oody of water at the instant when t^ attains a maximum, and aroceeas 

 uowards with the corresoonaing initial velocity. In aarticular at vertically aOcve the mine 

 the initial velocity of the soray v^ = 2 a Ip^Z where a is the n«ximum aressure oevelooed at 

 distance d. Conversely if we can measure the initial velocity we can calculate a = i p^ v the 

 maximum aressure develoced at distance o. =ossibl-. corrections to this simale result will be 

 considered later. 



The saray aheno'^enon is so racio that a kinema record is required to show its develoament 

 ana enable us to estimate the initial velocity of aro>ection of tne saray. 



Cur kinema normally takes from 16 to 20 aictures ver second. The times are at oresenl 

 aeterminca by including at the corner of each aicture a ahotograah of the raaioly moving hana of 

 a chroncgraoh fixid in front of the camera. This hand moves through 120*' In 1 second. 



The distance scale is determined ^y including the ohotograoh of a measured base line of 

 60 feet marked at one end ^i an ematy mine case from which the mine oroaer is susoended ana at the 

 other end riy a fisherman's blob. 



