116 KEPOUT— 1882. 



water changes to low, there would be oscillations of the vertical 2^ times 

 as great. We thus get the practical results in the following table : — 



Distance of obser- Amplitude of 



vatory from apparent o-cillation 



mean water-mark of the vertical 



10 meters 0'-126 



100 m -101 



1 kilom '076 



lOkilom -050 



20 kilom -042 



50 kilom -035 



100 kilom -025 



It follows, from the calculations made for tracing the curve, that half- 

 way across the continent (that is to say, 3,142 kilometers from either 



coast) the slope is • x -^'' x '2703 seconds of arc, = 0"'00237 ; 



and the range of apparent oscillation is 0"'006. 



In these calculations the width of the sea is taken as 6,283 kilometers. 

 If the sea be nai'rower, then to obtain the same deflections of the plumb- 

 line, the observatory must be moved nearer the sea in the same pro- 

 portion as the sea is narrowed. If, for example, the sea were 3,142 kilo- 

 meters wide, then at 10 kilometers from the coast the apparent amplitude 

 of deflection is 0"-042. If the range of tide is greater than that here 

 assumed (viz., 80 cm.), the results must be augmented in the same 

 proportion. And, lastly, if the rigidity of the rock be greater or less than 

 the assumed value (viz., 3 X 10**) the part of the apparent deflection 

 depending on slope must be diminished or increased in the inverse pro- 

 portion to the change in rigidity. 



I think there can be little doubt that in narrow seas the tides are 

 generally much greater than those here assumed ; and it is probable that 

 at a gravitational observatory actually on the sea-shore on the south-coast 

 of England, apart from seismic changes, perceptible oscillations of the 

 vertical would be noted. 



Sir William Thomson has made an entirely independent estimate of 

 the probable deflection of the plumb-line at a seaside gravitational obser- 

 vatory.^ He estimates the attraction of a slab of water, 10 feet thick 

 (the range of tide), 50 miles broad perpendicular to the coast, and 100 

 miles long parallel with coast, on a plummet 100 yards from the low- 

 water mark, and opposite the middle of the 100 miles of length. He 

 thinks this estimate would very roughly represent the state of things say 

 at St. Alban's Head. He finds then that the deflection of the plumb-line 

 as high tide changes to low would be ^^jro^ooth of the unit angle, or 

 0"*050. The general theorem proved above, as to the proportionality of 

 slope to attraction, shows that, with rigidity 3 x 10" for the rocks of 

 which the earth is formed, the apparent deflection of the plumb-line would 

 amount to 0"-25. 



It is just possible that a way may in this manner be opened for deter- 

 mining the modulus of rigidity of the upper 100 or 200 miles of the earth's 

 surface, although the process would be excessively laborious. The tides of 

 the British Channel are pretty well known, and therefore it would be 

 possible by very laborious quadratures to determine the deflection of the 

 plumb-line due to the attraction of the tide at any time at a chosen station. 



' Thomson and Tait's Nat. Phil. § 818. 



