C Davison — Vorticose Earthquake Shocks. 261 



Yibrations would produce the attendant up-and-down, or " sussulta- 

 tore," movement of greater range." ^ 



Prof. J. Milne remarks that some of the Japanese earthquakes are 

 compounded of direct and transverse vibrations, and he gives as an 

 example the instance already quoted from his letter to Nature. It 

 is quite possible, especially if the seismic focus be at no great depth 

 and yet of some magnitude, that the direct and transverse waves 

 may not have completely separated before reaching the surface of 

 the earth,^ in which case tbe vibrations of one wave will combine 

 with those of the other, and will certainly produce shocks similar to 

 those described above, provided the transverse vibrations are com- 

 parable in magnitude with the direct vibrations. 



We come now to the theory which it is the principal object of 

 this paper to explain, and we shall confine ourselves at first to the 

 wave consisting of direct vibrations. If the seismic focus, or centre 

 of disturbance, be a mathematical point, and the earth be supposed 

 homogeneous and isotropic, the earthquake-wave at the surface will 

 be of a circular form (because every plane section of a sphere is 

 a circle), and the shock at any point will seem to come along the 

 surface from the centre of the circle, i.e. from the seismic vertex. 

 Hence, it follows that, if during an earthquake consisting of direct 

 vibrations, the shock appears to one observer to come successively 

 from different directions, there must be a seismic vertex correspond- 

 ing to each direction, and a centre of disturbance to each seismic 

 vertex, and therefore that the seismic focus cannot in this case be 

 a mathematical point. (See also p. 259.) 



Let us, then, investigate the effect at a point P on the surface of 

 the earth, of a disturbance proceeding from a seismic focus of any 

 form and magnitude, and acting simultaneously throughout its 

 whole extent, P being within the area vertically above the seismic 

 focus. With P as centre imagine an infinite number of spheres, 

 indefinitely near one another, and intersecting the focus, so that it 

 may be supposed made up of the portions of the spheres included 

 within it : and consider any one of these spherical portions. The 

 disturbances from every point of it will reach P at the same instant 

 and will affect it simultaneously. 



Now as, at any instant, the particle of rock at P must be moving 

 in some definite direction and with some definite velocity, we 

 may suppose the disturbances from the corresponding sphere to be 

 replaced by a disturbance at some equivalent point, the effect of 

 which at P will be exactly the same as that of all the disturbances 

 together proceeding from the spherical portion considered ; and the 

 shock at F will appear to come in the direction from a point (which 

 we may call the apparent seismic vertex) vertically above the 

 equivalent centre, 



1 Mr. R. Mallet. " Neapolitan Earthquake of 1857," vol. i. pp. 76-78. 



^ It a and b be the distances of the nearest and furthest points of the seismic 

 focus from any place, V the velocity of the direct wave, v that of the transverse 

 wave, and A the length of the former ; the two waves will not have separated before 



reaching the given place if — p— is greater than — • 



