ON THE MEASUREMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 109 



ratio is independent of the "wave-length 2Trh 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 valleys. 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* cm., o = 5§; and ^ao = 12-03 x 10* grammes 

 per square centimeter. The rigidity of glass in gravitation units ranges 

 from 1-5 X 10* to 2'4 X 10*. Therefore 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*), 

 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 disturb- 

 ance, whilst we were unable to assert positively that the attraction of 

 weights placed near the pendulum was perceptible. It also gives emphasis 

 to the criticisms we have made on M. Plantamonr'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 centimeter) is vjg. In the problem of the mountains, %vh is the mass 

 of a column of rock of one square centimeter in section and of length equal 

 to the heio-ht of the crests of the mountains above the mean horizontal 

 plane. In the barometric problem, ivh must be taken as the mass of a 

 column of mercury of a square centimeter 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 cm. 



The specific gravity of mercury is 136, and therefore wh = 34 grammes. 



The rigidity of glass is from 150 to 240 million grammes per square 

 centimeter ; that of copper 540, and of steel 843 millions. 



I will take vjg = 3 x 10*, so that the superficial layers of the earth 

 are assumed to be more rigid than the most rigid glass. It will be easy 

 to adjust the results afterwards to any other assumed rigidity. 



With these data we have^-- = -—- ; also^ ^— x -q-— = '-0117, 



2v 10* TT 10* 



lb seems not unreasonable to suppose that 1500 miles (2'4 x 10* cm.) 

 is the distance from the place where the barometer is high (the centre of 

 the anti-cyclone) to that where it is low (the centre of the cyclone). 

 Accordingly the wave-length of the barometric undulation is 4'8 X 10* cm., 

 and 6 = 4'8 X 10* -^ 6-28 cm., or, say, 6 = -8 x 10* cm. 



Thus, with these data, 3^h = 4-5 cm. 



Zv 



