164 MR. R. D. OLDHAM ON THE PROPAGATION OF 



of light passes the limit of photographic resist ration, and the record is lost. Thrsr 

 remarks do not apply to Professor MILNE'S pattern of instrument, where the displace- 

 mentof the pendulum is directly photographed without any reflection or magnification 

 of the movement, but, as the time of maximum displacement is not 1<> IK- found in the 

 published accounts of the records of this instrument, it has not l)een possible, except 

 in a few cases, to utilise the Shide records. 



The two types of instrument differ not only in detail but in the object aimed at in 

 their construction ; HORACE DARWIN'S bifilar pendulum, as well as the horizontal 

 pendula of REBEUR-PASCHWITZ, GERLAND and MILXE, were designed to register tilting, 

 and are not primarily intended to respond, by their inertia, to a rapid movement of the 

 ground in a horizontal direction. The heavily weighted pendula are, on the contrary, 

 intended to respond to horizontal shakes, the heavy mass acting as a steady point. 

 Professor GRABLOWITZ has shown,* from a comparison of the records of the instru- 

 ments at Ischia, which are under his charge, that during the first phase the record is 

 due mainly to inertia, and only to a small extent, if at all, to tilting, while in the 

 latter stage the opposite takes place, and the record is principally due to tilting. The 

 greater constancy of record of the heavy peudula in the case of the first phase, and 

 the greater sensitiveness of the light pendula to the motion of the third phase are, 

 consequently, in accordance with the objects specially aimed at in the construction of 

 each type of instrument. 



5. Taking up the consideration of the records of the first two phases, it will be 

 seen that, as plotted on the diagram on page 163, they all lie very close to two 

 curved lines, starting from the origin and proceeding with a regularly decreasing 

 curvature at any rate to a distance from the origin of 90 of arc. In both cases the 

 only serious divergence of a record from the curve is in a few cases of photographic 

 records, and this is most marked in the case of the first phase. The concordance is 

 so close that the curves drawn may be taken as, in the main, representing the true 

 time curvest. of these two phases. 



From the construction of these curves they represent graphically the apparent 

 velocity at any point, for this is directly proportional to the cotangent of the angle 

 of inclination. The relation of the apparent velocity to distance is consequently 

 exactly what is required on the assumption that the wave motion is transmitted 

 through the earth, and a simple calculation shows that the increase is markedly greater 

 than what would be due to rectilinear propagation. It follows, therefore, that for 

 the wave motion represented by these two phases, the rate of propagation increases 

 with the depth, and the wave paths are convex towards the centre of the earth. 



* ' Boll. Soc. Sismol. Ital.,' Part II, passim. Professor URABI.OWITZ only recognises two phases, corre- 

 sponding to the first and third of this paper. 



t Dr. A. SCHMIDT has proposed (' Jahresheft Ver. f. Vaterland. Naturk. in Wiirttemberg,' vol. 44, 1888), 

 to apply the term " hodograph " to these time curves, but as this term is already used in a very different 

 sense, I think it best to abandon the word, and use the simple expression " time curve." 



