March 2, 1899] 



NATURE 



415 



the intervals of time which elapse between the arrival of the 

 first tremor^and the largest wave or waves corresponding to the 

 originating impulse and the duration of the very first series of 

 preliminary tremors. As measured on seismogranis for disturb- 

 ances which have originated at different distances from the 

 Isle uf Wight observing station, these two intervals are given 

 in the following table : — 



These figures are too few in number to be used as a found- 

 ation for any certain conclusions, but they may possibly indicate 

 results to be sought for in future records. With regard to the 

 first set of intervals, we know that for distances up to S° from 

 an origin the time by which tremors outrace the main move- 

 ment may be reckoned by seconds. Adding this fact to our 

 list, it seems that here we have a table which indicates that as 

 an earthquake travels the tremors outrace the large waves at 

 a very slow rate on the first part of its journey : but as its 

 distance from the origin increases, this rate increases. This 

 goes on until a point between 48' and 62° distant from the 

 origin has been reached, after which the rate at which the large 

 movements are left behind decreases. 



< )ne explanation for this is to suppose that the first precursors 

 came through the earth with an average velocity which observ- 

 ation shows to increase approximately with the square root of 

 the average depth of the chord joining the centrum and the 

 observing station, whilst the large waves travelled round the 

 surface. An objection to this view is that observations exist 

 which show the large waves have apparently travelled over paths 

 varying between 20° and 110°, at rates which rather than being 

 constant have increased from 2'i to 3 3 km. per second. 



The velocities giving this comparatively slight difference were, 

 however, determined on the assumption that the times at which 

 various earthquakes originated were known, and there is, there- 

 fore, a possibility that they may be apparent rather than real. 



Also it must be remarked, as pointed out by Dr. C. G. Knott, 

 that if we regard the speed of propagation of the large waves as 

 depending on a coefficient of elasticity, mainly distortional and 

 not appreciably influenced by change of pressure and density, it 

 is quite conceivable that the large waves should also pursue a 

 brachistochronic path through our earth. The question then 

 arises whether these larger movements would be left further and 

 further behind their precursors in the manner indicated. 



When we come to our second set of intervals which indicate 

 the duration of the first preliminary tremors before they are 

 eclipsed by groups of vibrations which usually grow in size and 

 appear from their periods to be distortional, we see that up to 

 a point about 62° from an origin these figures increase, but 

 beyond that point they grow less. 



What we have to explain in addition to this fact is that of the 

 practical continuity and growth in magnitude of what very often 

 forms a long and continuous series of preliminary motions. As 

 I have already stated, their very appearance indicates that they 

 have travelled on different paths. The first have followed a 

 path entirely through our earth, whilst the successors may have 

 travelled shorter and shorter distances through the earth to meet 

 a crust through which they have completed their journey to the 

 observing station. The first followed Knott's brachistrochronic 

 path, or that of least time, whilst the successors took paths the 

 latter parts of which were along arcs of increasing length. The 

 result of this would be that at an observing station vibrations 

 would arrive in series, each group corresponding to an origin- 

 ating impulse. The last of the rabble would be the series repre- 

 senting the main shock which, although it sent waves on 

 brachistochronic paths, may in part have travelled as a surface 

 undulation through the crust. 



To illustrate this hypothesis I here reproduce a sketch given 

 to me by Dr. C. G. Knott, showing the probable form of wave- 



NO. I 53 I, VOL. 59] 



fronts and paths of compressional vibrations passing through 

 our earth. 



The assumption on which this has been drawn is that the 

 square of the speed of the movements is a linear function of the 

 depth, which closely corresponds, as already indicated, with 

 observation. 



The result at which Knott arrives indicates that the square of 

 the speed increases at o'9 per cent, per mile of descent in the 

 earth, the formula being ' 



z;- = 2'9 -t- '026 (/ in mile second units. 



With an initial velocity of I 7 miles per second, the velocities 

 at depths of 400, 800, 1200 . . . 4000 miles become 37, 4-9, 

 5-8, 67, 7-4, 8-1, 87, 9-3, 9-8, and 10-3 miles per second. The 

 times taken for wave-fronts to reach the positions shown are 

 indicated in the sketch ; the time taken to pass through the 

 earth being 22 minutes. 



I assume that when a wave has passed from its origin beyond 

 the region vaguely referred to as the crust of our earth, it then 

 spreads in all directions through a mass in which there is only an 

 extremely gradual change in elasticity and density with regard to 

 its centre. All wave-paths, however, before they emerge at the 

 surface, encounter at varying obliquities the under-surface of 

 this crust. For purposes of illustration, we will assume this 



region of abrupt change to lie on the 400-mile circle. The 

 path /i meets this surface nearly at right angles, whilst p., p-^ 

 meet it at decreasing angles less than right angles. After each 

 of these incidences a condensational wave will be refracted and 

 split up into condensational and distortional rays. Now it will 

 be observed that these two waves, which I will call < and d, 

 will have different distances to travel before actual emergence, 

 which distances will increase from /, towards /j. At any station 

 P, the first arrival will be c, but as this will be eclipsed on the 

 arrival of d, its duration will always be short, and unless the 

 originating shocks are well separated, seismograms, as we know- 

 them, can never show more than one set of condensational 

 tremors. 



At some point, like p.^, the duration of the preliminary 

 tremors should reach a maximum, but from this point on to- 

 wards the origin this quantity will decrease, if only on account 

 of the fact that the velocity along the brachistrochronic ray 

 differs less and less from that of the distortional wave within the 

 crust. Such a view may possibly explain not only the short 

 duration of the first precursors, but also the rise and fall in the 

 values of our last column. 



The growth in amplitude of the groups of tremors maybe due 

 to the fact that they are usually the outcome of originating im- 

 pulses which increase in intensity until they culminate in a 

 violent shock. 



' See Scottish Geogra/'ttUal Masazuu- for January 1S99. 



