106 EEPOET — 1882. 



tioned in the Report of last year, is in the ' Trans. Roy. Soc' of Edin- 

 burgh, 1857, vol. 21, pp. 559-70, See also Bessel's ' Abhandlungen,' 

 vol. 2, p. 42, vol. 3, p. 304. In ' Nature ' for January 12, 1882 (p. 250), 

 there is an account of the work of the Swiss Seism ological Commission. 

 The original sources appear to be a text-book on Seismology by Professor 

 Heim, of Bern, the ' Annuaire ' of the Physical Society of Bern, and the 

 * Archives des Sciences ' of Geneva. I learn from M. d'Abbadie that 

 Colonel Orff has been making systematic observations twice a day with 

 levels at the Observatory at Munich, and that Colonel Goulier has been 

 doing the same at Paris, with levels filled with bisulphide of carbon. 



Appendix. 



On Variations in the Vertical due to Elasticity of the Earth's Surface. 

 By G. H. Darwin, F.R.S. 



1. On the Mechanical Effects of Barometric Pressure on the Earth's Surface. 



The remarks of Signore de Rossi, on the observed connection between 

 barometric storms and the disturbance of the vertical, have led me to 

 make the following investigation of the mechanical effects which are 

 caused by variations of pressure acting on an elastic surface. The results 

 seem to show that the direct measurement of the lunar disturbance of 

 gravity must for ever remain impossible. 



The practical question is to estimate the amount of distortion to which 

 the upper strata of the earth's mass are subjected, when a wave of baro- 

 metric depression or elevation passes over the surface. The solution of 

 the following problem should give us such an estimate. 



Let an elastic solid be infinite in one direction, and be bounded in the 

 other direction by an infinite plane. Let the surface of the plane be every, 

 where acted on by normal pressures and tractions, which are expressible 

 as a simple harmonic function of distances measured in some fixed direc- 

 tion along the plane. It is required to find the form assumed by the 

 surface, and generally the condition of internal strain. 



This is clearly equivalent to the problem of finding the distortion of 

 the earth's surface produced by parallel undulations of barometric elevation 

 and depression. It is but a slight objection to the correctness of a rough 

 estimate of the kind required, that barometric disturbances do not actually 

 occur in parallel bands, but rather in circles. And when we consider the 

 magnitude of actual terrestrial storms, it is obvious that the curvature of 

 the earth's surface may be safely neglected. 



This problem is mathematically identical with that of finding the state 

 of stress produced in the earth by the weight of a series of parallel 

 mountains. The solution of this problem has recently been published in 

 a paper by me in the ' Philosophical Transactions ' (Part II. 1882, pp. 

 187-230), and the solution there found may be adapted to the present case 

 in a few lines. 



The problem only involves two dimensions. If the origin be taken in 

 the mean horizontal surface, which equally divides the mountains and 

 valleys, and if the axis of z be horizontal and perpendicular to the moun- 



