due to Elasticity of the Earth's Surface. 413 



Therefore deflection bears to slope the same ratio as v/g to 

 \ah. This ratio is independent of the wave-length lirb of the 

 undulating surface, of the position of the origin, and of the 

 azimuth in the plane of the line normal to the ridges and val- 

 leys. Therefore the proposition is true of any combination 

 whatever of harmonic undulations ; and as any inequality may 

 be built up of harmonic undulations, it is generally true of 

 inequalities of any shape whatever. 



Now a=6'37 x 10 8 centim., 8 = 5% ; and £aS = 12"03 x 10 8 

 grammes per square centimetre. The rigidity of glass in 

 gravitation-units ranges from 1*5 x 10 8 to 2*4 x 10 8 . There- 

 fore the slope of a very thick slab of the rigidity of glass, due 

 to a weight placed on its surface, ranges from 8 to 5 times as 

 much as the deflection of the plumb-line due to the attraction 

 of that weight. Even with rigidity as great as steel (viz. 

 about 8 x 10 8 ), the slope is 1| times as great as the deflection. 



A practical conclusion from this is that, in observations 

 with an artificial horizon, the disturbance due to the weight 

 of the observer's body is very far greater than that due to the 

 attraction of his mass. This is in perfect accordance with the 

 observations made by my brother and me with our pendulum 

 in 1881, when we concluded that the warping of the soil by 

 our weight when standing in the observing-room was a very 

 serious disturbance, whilst we were unable to assert positively 

 that the attraction of weights placed near the pendulum was 

 perceptible. It also gives emphasis to the criticism we have 

 made on M. Plantamour's observations — namely, that he does 

 not appear to take special precautions against the disturbance 

 due to the weight of the observer's body. 



We must now consider the probable numerical values of the 

 quantities involved in the barometric problem, and the mode 

 of transition from the problem of the mountains to that of 

 barometric inequalities. 



The modulus of rigidity in gravitation-units (say grammes 

 weight per square centimetre) is v/g. In the problem of the 

 mountains, wh is the mass of a column of rock of one square 

 centimetre in section and of length equal to the height of the 

 crests of the mountains above the mean horizontal plane. In 

 the barometric problem, wh must be taken as the mass of a 

 column of mercury of a square centimetre in section and equal 

 in height to a half of the maximum range of the barometer. 



This maximum range is, I believe, nearly two inches, or, let 

 us say, 5 centim. 



The specific gravity of mercury is 13*6; and therefore 

 z«/i=34 grammes. 



The rigidity of glass is from 150 to 240 million grammes 



