-5- 605 



It may be snown tnat at 200 yards Horizontal distance from a mine 60 feet deeo, 

 r. - r would be equal to l metre at a depth of 16 feet beneath the surface, and equal to 3 cms. 

 at 3 deoth of 6 inches beneath the syrface. 



This is shown aia^rrimnBt ically in Figures 3 and U, 



In the s?ime way Figure i shows new reducing the deoth of the mine tends to lower its 

 damaging efficiency stceways. r. tenas to Decomo more nearly equal to r as the mine -iDoroaches 

 the surface, so that the oooosing actions ere more nearly equal in magnituae, and more nearly 

 equal -^s regarcs time cf drrivil, and n;;nc'; they tend to neutralise e=iCh otner. 



Those inferences sre in agreement with direct observaticn. For if we observe at say 

 20C yarcE fr^m an exolosion only ?, very Slight snock is exoerience- in a rcwing bjat jr a shalliw 

 draught meter launch, whereas in a deeo draught trawler the shock is very marked. 



In order to preserve slmc'icity in the preceding argument, we have not referred to a 

 modifying circumstance which must now De considered. 



The original surface layer breaks away from the lower water, out successive layars follow 

 as the reflected wwe spreods so that 3 saucer shaped depression should rapidly develop oownwarcs. 

 Between this saucer surface and the dome above there will be a continuous succession of spray, 

 moving however with smaller speed, so that it dees not break through, and we can learn nothing 

 about it by direct observation. 



Tne dovol-oing saucer boundary forr.s ^t e^ch instant the efectiv** reflecting surface tcr 

 the primary wave and thus the reflected nej-:itive wave underg.-.es aist.rti:!n in its later stages 

 without affecting anythinj that occurred earlier. The net result is that a body in the water will 

 experience the prirrary crushing pressure, which will be followed at the aoprcpriate time by the 

 creation of a vacuum on the side nearest the image mine and which will scread to the remote side. 

 The destructive effect of this on = submarine already crumcled oy the :;rimary wave may be very 

 important. 



Although the oriir^iry velocity ^icquired Oy the water at seme decth may be vory hijh, 

 e.g. 11 retres zcr sr.cend in th: Cis- ef i 300 lo. ch-'.rge at 50 feet yet the time is so shcrt that 

 the w^ter \-.'i£ n-:t frv-ve mer: than ^bjut * cm. 



Although we have discussed only the reflection from the surface, the effect of tne bottom 

 may also b: jxamined by the method of ima-jes, tf e,^. the bottom is rigid rock the corresponding 

 imjyC would h.ive the same sign as the true mine since the condition is now zerc resultant ncrmal 

 Velocity instead ,f zero resultant cressure. =^robiDly, h;?wever, the bottcm is s.ft and yields 

 at first and at greate' deoth becomes rigid so that the composite action may not Oe nearly so 

 simole as that of a free water surf-ics. tXDerifr,ents ?.re, however, in progress and further 

 discussion cf tne effect of the Oottom is reserved until these have been analysed, 



wc h:tvc- now t: consider p::5sib1e corrections to the simple formul.-. c, = i p Cv fjr the 

 maximum oressure. 



(1) we nov;; neglected ^ t^rm involving the squ^r.^ of v , it is f erder wjz comoared 

 witn the main term. At 50 fe^'t from a 30C Id, charge v is about 23 metres oer second, 

 whil: C is ibOC metres oer second. Thus the correction is of oroer i% in this case 

 ano rr.iy Oe nejlscted, ' For larger charges \r\a shorter distances the effect might rise 

 to a few oer cent and would have to oe alloweo for if the mer.surements ever attain such 

 ii dejrec jf iccuracy. Tne cerrection is negative in sign. 



(2) ^e nave assumed tnjl th? water cannat suooort negative cressure* 



NOW OsoornTe Reynolds found that air-free water might in favcuraolo conditions support a 

 negitiv:- oressuro- of 7^ lbs, c.r square inch. Since sea water nas pl=nty of air dissolved in it, 

 it w'juld seem dcuDtful i* it could sucoort anything like this -inount, on the other'hand certain 

 features in the scray oh^ihOiTicncn, /..g. the sharo boundary suggest tnat the water may support 

 negative or-.-sure i\s much -s a ton oc-r squ-^.re inch without breaking. The evidence Is, however, 

 still ambigj-js, out will be .xamined lat-ir. 



If it should jrove tnat the negative cressure must exceed say -» tons oer square inch 

 be'ore ruoture ta^iS clace, then the rraximum oressure p as calculated above is an under estimate 

 of tne correct value of 5 = aocrjximately. The result of a finite v/ilue of = is that the spray 



