68 REPORTS OX THE STATE OF SCIENCE. — ^1915, 



The sum of the times increases to a maximum of 852 sec, where there 

 is an accumulation which marks the trace (PiS,) and then diminishes 

 again. Since the time for S to travel 40° is by the same tables 847 sec, 

 this PiSi is later than S ; and it is easily found to be always lat«r. For 

 instance, at 



But in the above calculation for ii=40° the distance travelled as 

 P is only a few degrees ; and as we diminish the value of A this distance 

 contracts to zero, marking the limit determined by Mr. Walker in the 

 simple case of a homogeneous earth. 



The fact that P,Si is always later than S is an additional reason why 

 it cannot explain the mistakes in identif)dng S, which require a pheno- 

 menon sometimes preceding S, as will be seen from the examples quoted 

 below. But there is scarcely need of an actual example ; on general 

 principles it is pretty clear that something preceding S is more productive 

 of mistakes than something which follows ; for there is a strong tendency 

 to read the earliest movement in the suitable neighbourhood. 



Now, if the phenomenon is to precede S, it seems clear that it cannot 

 travel partly as P and partly as S, since even P,Si is later than S. We 

 cannot assign a smaller share to S than is represented by PiSi, except 

 no share at all. We are thrown back on P. 



A single reflection of P is well known as PK,, and there is no difficulty 

 in considering two, three, or more reflections of P. But when the appro- 

 priate neighbourhoods in the trace are examined, there seem to be no 

 conspicuous indications there ; certainlv nothing likely to be mistaken 

 for S. 



The suggestion now put forward is that of a large inimber of reflections 

 of P. When the number is large, the time of arrival tends to be inde- 

 pendent of the precise number, since the times near the origin, whether 

 for P or S, are sensibly proportional to the arcs. The printed tables 

 give an initial velocity to P of about 1° per 15'5s. The facts collated 

 below suggest that this should be altered to 1° per 14-9 s. and this will 

 be adopted for use provisionally. No large departure from the printed 

 tables is involved — the time at 4-0° would be 59 6 s. instead of 62 s. as 

 printed ; but the times will be assumed for a moment to be accurately 

 proportional to the arcs, at this rate. 



On this supposition it is clear that a total arc of 60° is described in 

 the same time by 



s. s. 



15 reflections of 4° each=lo x o9"6=894 

 30 „ ., 2° ,. =30x29-8=894 



60 „ „ r „ =60 X 14-9=894 



And indeed that any number of reflections greater than 15 have the same 

 total time of travel according to the tables. The simultaneity is only 

 limited by the accuracy of our assumption that the time near the origin 

 is directly proportional to the arc. 



There is a difficulty attending this supposition of a theoretical kind. 

 It is remarked by Mr. G. W. Walker on p. 45 of his ' Modern Seismology ' 

 that ' it is impossible to propagate along a plane boundary . . . longi- 

 tudinal waves with displacement parallel to the surface.' Now, when 



