422 Mr. G. H. Darwin on Variations in the Vertical 



Distance of Amplitude of 



observatory from apparent oscillation 



mean water-mark. of the vertical. 



10 metres 0"-126 



100 „ -101 



1 Idiom '076 



10 „ -050 



20 „ -042 



50 „ -035 



100 „ -025 



It follows, from the calculations made for tracing the curve, 

 that halfway across the continent (that is to say, 3142 kilo- 

 metres from either coast) the slope is 



648 ' 0Q0 x 85* x -2703 second of arc =0"-00237, 



7T 1TV 



and the range of apparent oscillation is O^'OOG. 



In these calculations the width of the sea is taken as 6283 

 kilometres. If the sea be narrower, then, to obtain the same 

 deflections of the plumb-line, the observatory must be moved 

 nearer the sea in the same proportion as the sea is narrowed. 

 If, for example, the sea were 3142 kilometres wide, then 

 at 10 kilometres from the coast the apparent amplitude of 

 deflection would be // '042. If the range of tide is greater than 

 that here assumed (viz. 80 centim.), the results must be aug- 

 mented in the same proportion. And, lastly, if the rigidity 

 of the rock be greater or less than the assumed value (viz. 

 3 x 10 8 ), the part of the apparent deflection depending on 

 slope must be diminished or increased in the inverse propor- 

 tion 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 sea- 

 side gravitational observatory*. 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 



* Thomson and Tait's ; Natural Philosophy,' § 818. 



