32 Professors Perry and Ayrton on a neglected Principle 



If, however, instead of actually observing the lamp we merely 

 get a record of its greatest swing, then very little information 

 could be obtained of the strength of the shocks ; for the great 

 or small deflection of a slowly vibrating pendulum during an 

 earthquake will depend on whether the period of the earth- 

 quake is or is not some submultiple of the period of the pen- 

 dulum ; so that considerable mathematical knowledge and much 

 time would be requisite to deduce from the comparatively 

 small ripples on the larger vibrations the nature of the earth- 

 quake. In addition, as the length of the swings of the lamp 

 will generally be much greater than the earthquake vibrations, 

 they will, if recorded on paper, require a very large recording 

 apparatus. 



We now proceed to the principle which is to enable us to 

 record an earthquake-message. It must be evident that the 

 message can only be correctly recorded when we have obtained 

 the complete motion at every instant of time during the earth- 

 quake of a large portion of the rocky crust of the earth. Any 

 point P in the solid earth has a certain position, a certain ve- 

 locity, and a certain acceleration in a certain direction in any 

 instant of time during an earthquake ; and if we know these 

 elements we are said to know the motion of P. Now we have 

 a complete record of an earthquake when we know the motions 

 of all points P affected by the earthquake ; and if the earth 

 were rigid, this could be derived from a knowledge of the 

 motion of three of its points not in the same straight line. 

 Still, although the earth is not rigid, and although the condi- 

 tions of motion, of different parts of an elastic non-homoge- 

 neous solid are very complicated, we may say that the important 

 character of an earthquake, its origin and the media through 

 which it has travelled, as well as its rate of motion, are recorded, 

 and may perhaps be easily deduced from the known motions 

 of three well affected points in the solid earth. Believing this 

 to be the ease, and seeing how important it is to the whole 

 science of terrestrial physics that the earthquake-message 

 should be read, we have been led to investigate mathematically 

 the motion, during an earthquake, of a body attached to the 

 earth by springs. And we have come to the conclusion that 

 the centre of mass of a body fastened by means of springs 

 inside a metal box rigidly attached to the earth, has in certain 

 cases motions with respect to the box itself which in miniature, 

 with great exactitude, represent the motions of a point of the 

 box during the earthquake — this result being truly obtained 

 when the springs are exceedingly strong, so that the motion 

 of the mass relatively to the box is exceedingly small, and 

 practically obtained when the springs are so strong that the 



