94 Dr. C. V. Burton on a 



density. The radial stress at any point, reckoned as a pres- 

 sure, is 



and, equating the value of this for 7i = to — P given by (5), 

 we readily find 



p _ SikgA ,£. 



u -&*mV{(*+*»)ft}' • • * • W 

 where n=/>/27r, the frequency of the periodic variation of 

 gravity. 



9. The rigidity fi of the earth as a whole is not very dif- 

 ferent from that of steel *, and if we assume the com- 

 pressibility also to be something like that of steel, we may 

 take as roughly approximate numerical values 



k = 1-5 X 10 12 dynes/sq. cm., fj, = *82 x 10 12 dynes/sq. cm. ; 



moreover, p the density is about 6*6 grams per cc, and 

 thus (8) gives for the semi-amplitude of the apparent motion 

 of the earth's surface in centimetres 



•OOG8A/71 3 . 



10. As an example, take A equal to unity, and n equal to 

 one second. The gravitative attraction between any two 

 bodies would then vary between zero and twice its mean 

 value, the period of the variation being one second. The 

 actual periodic displacement of the earth's surface would 

 amount to about 25 cm. above and below its mean position ; 

 but the observable effects would, with our assumptions, be the 

 same as if (with gravity invariable) the earth's surface were 

 pulsating with a period of one second and with a semi- 

 amplitude of *0068 cm. The maximum acceleration involved 

 in this apparent pulsatory movement would be about 

 *35 cm./sec 2 , or roughly 1/2500 part of the mean acceleration 

 of gravity ; and refined observations would be required to 

 discern any periodic effects. If the frequency n of the 

 fluctuations were changed in a given ratio m (their amplitude 

 remaining the same), the amplitude of the apparent surface 

 pulsation would be changed in the ratio ??i~ 3 , and the 

 maximum acceleration involved in that pulsation would be 

 changed in the ratio wi _1 f. 



11. It appears, then, that the interaction of the earth with 



* A somewhat vague statement, though definite enough for the purpose 

 in view. 



f The amplitude and extreme acceleration of the apparent motion are 

 of course proportional to A, which, according to any pulsatory theory of 

 gravitation, would be a large number. The value unity has here been 

 given to A merely by way of illustration. 



