190 Dr. C. Chree on Applications of Physics 



treating the direct effect by itself. It must, however, be borne 

 in mind that the luni-solar influence is not confined to the 

 pendulum bob, but extends to the material of the earth itself. 

 Consequently the result calculated by Lord Kelvin and Prof. 

 Tait is part only of a composite effect, which there is no very 

 obvious way of analysing in practice into its components. 



In the actual earth the most obvious consequence of luni- 

 solar action is the ocean tides, and, as we saw in § 4, any 

 station near the sea-shore has its apparent level affected by 

 these in two distinct ways. Even at an inland station ocean 

 tides must exert some influence, though presumably it is very 

 small. 



In addition, however, to ocean tides there must be tides in 

 the earth's mass, whether solid throughout or not, and it is 

 to these I shali now call attention. 



The potential term (39) is only one of a series. The 

 numerical values of the coefficients diminish rapidly as the 

 order of the harmonic increases ; still it is desirable not wholly 

 to neglect the higher harmonics, if only to make sure that the 

 comparative smallness of the disturbing forces answering to 

 them is not compensated in any instance by great effectiveness. 

 I shall thus consider in the first place the results of the general 

 problem when the degree of the harmonic appearing in the 

 disturbing forces is unrestricted, making use of the results 

 contained in a paper communicated to the Cambridge Philo- 

 sophical Society* in 1887. 



§ 23. Before entering, however, on this investigation, it is 

 desirable to consider briefly the relation between the re- 

 sults of theory and the phenomena we may expect to en- 

 counter in direct observation. 



Surface-points on the undisturbed surface, regarded as 

 spherical, transform into surface-points on the strained sur- 

 face ; thus a very small surface-area, e. g. a square decimetre, 

 may be regarded as a tangent plane in both conditions. 



Suppose, now, tins area to have rigidly attached to it a 

 spirit-level, consisting of part of a circular arc filled with 

 liquid and with a minute air-bubble. In the undisturbed 

 condition suppose the bubble exactly at the central division 

 of the arc, while in the disturbed condition it is at an angular 

 interval S9 from 0. This an observer would naturally attri- 

 bute to a change SO of level. The true interpretation is that 

 in the disturbed condition the resultant of the forces at the 

 surface makes with the normal the angle SO. In a rigid 

 earth SO would be the angle of Thomson and Tait's calcula- 



*Sce the Society's Transactions, vol. xiv. p. 278. 



