-9- 21 



formula {l2o) now jives 



T = 18.6 mill iseconJs 

 The corresponJing value oDtaineJ by Jirect measurement is 



T = 17 mill iseconJs 



By the same mtthod the interval T can tie calculated for the case of a 3opth charge. For 

 this purpose .-;quation (l2c) is more convenient. Consider for example the case of a 300 lb. charje 

 of T.N.T. The heat value of T.N.T. is given as 1040 calories/gm., from which the total energy W^ 

 of the entire charge is found to oe 5.9 10 ergs. At a depth of (say) 30 feet? ^ 1.9 atm. = 

 1.9 10* 3ynes/cm^. Equc-.tion (l2c) th!!n gives 



T = 1.2 seconds. 

 An experirrental value 



T = 0.6 seconds 

 has been quoted for a 300 lb. mine exploding at a depth of 30 feet. 



(d) Variation of T with pressure f. 



As already pointed out, the dependenct of T upon P expressed by equation (l2b) implies that 

 T Should vary with the depth at which a charge is fired. Values of T for the detonators have been 

 worked out for various depths up to 300 feet just as in the example worKea out abov'j for 15 f-et. 

 The rrsulting values define the continuous curve drawn in Figure 5. To test these values, direct 

 rreasurements of T w.ire carried out at sea down to a depth of 245 f=et. These experimental values 

 are set out in Table 1 and ^re marked by the circles in Figure 5. These values lie close to the 

 theoretical curve, showing that equation (l2b) gives a reliable figure for the absolute value of T 

 under external pressures/' ranging from 1 to B atmospheres, 



Tneoret icilly T should vary inverseley witn? . To test the accuracy with which the 

 index 5/6 is oper.-.tive the ixporimentil values for T dhd P have been plotted on a logarithmic scale 

 in Figure 6. « stnignt line of slope -5/6 has been orawn passing through these points. For 

 purpos.' of comD->rison lines with slopes -2/3 ind -1 nave jlso been indicated. It is evident that 

 the --xperiment ;1 values discrimireite quite she.rply in favour of the index -5/6. 



(e) Time intervals between successive pulses . 



As was mentioned earlier, it is found experimentally that the tim; intervals between successive 

 pulses get shorter a.id shorter, and this effect is in qualitative agreement with theory. It is 

 now possible to mike quantitative comparison. 



Equation (l2a) shows that tne time interval between the first and second pulses is 

 proportional to r^ c^ ' where r^ and p^ refer to the initial values of r and p at the first explosion. 

 For a given mass of gas, Dy virtue of equation (4), r is proportional to P~ (assuming 7= 4/3) 

 so that T depends on the initial pressure of tne gas according to the relation 



T - p 1/12 







But from equations (4) =na (25) 



p - n ^'3 



p being the internal and the external pressure, so that 



1/9 



This is strictly accurate only if the vibrations are unaamped, XI being then the^same for the first 

 and secono pulses. For a damped train of pulses it is not quite legitimate to apply this formula 

 to the pressure amplitude for the first pulse; it is more accurate to regard the first half of the 



