Vol. 62.] CONSTITUTION OP THE INTEEIOR OF THE EAETH. 465 



It should be noted that the intervals and resulting rates must 

 not be taken too literally : the result of averaging observations is, 

 indubitably, to increase the interval and lessen the apparent rates ; 

 but, besides this, an allowance ought to be made for the reduced 

 rate of propagation of the disturbance through the outer crust of 

 the earth. The amount of these corrections is not accurately 

 determinable, but as they are in the same direction in every case, 

 and as both together would, probably, not amount to a minute of 

 time, they may be neglected so far as the conclusions drawn below 

 are concerned. 



III. The Deductions. 



Wave-motion originating at any point in the earth will be pro- 

 pagated in all directions from it, and whatever the nature of these 

 waves their wave-paths will be straight lines so long as the velocity 

 of propagation remains constant ; but, if this varies, the course of 

 the wave-paths will be altered according to the laws of refraction, 

 which are to be found in every text-book of physics. These laws 

 hold good whatever be the nature of the wave-motion, although, in 

 the case of elastic waves, the rate of propagation is dependent on 

 two factors — the elasticity and density of the medium through which 

 they are propagated. From this it will be seen that any information 

 that we can get regarding the form of the wave-paths will indicate 

 the changes, if any, in the rate of propagation, and thence in the 

 physical condition, of different parts of the earth traversed by the 

 wave-paths which emerge at different parts of its surface. 



It will not be necessary to enter into details as to the manner in 

 which the wave-paths can be determined from observations of the 

 time of arrival of the disturbance ; for the subject has been fully 

 dealt with as a mathematical problem by Dr. Eudzki l of Cracow, 

 and it will only be necessary to apply his conclusions. 



In the first place, if waves are propagated along the surface of 

 the earth, or at a short distance below but parallel to it, the mean 

 apparent rate of propagation, as measured along the surface of the 

 earth, will be constant for all distances. This is the case, or nearly 

 the case, for the third-phase waves, which are, consequently, 

 accepted as surface-waves, and can, therefore, give no information 

 regarding the central portions of the earth. In the first and second 

 phases this is obviously not the case : in the first phase there is a 

 continuous increase in the apparent rate of propagation, and although 

 there is irregularity in the rates calculated for the second phase, 

 these are higher for distances beyond 90° than for lesser distances. 

 These facts lead to the conclusion that the first and second-phase 

 waves cannot be surface-waves, nor waves propagated a short 

 distance below the surface, but must be mass-waves propagated 

 through the body of the earth. 



In considering the form of the paths along which these waves 

 are propagated, it will be convenient to consider each quadrant 



1 Beitrage zur Greophysik, vol. iii (1898) pp. 495-518. 



