672 
DE. C. W. SIEMENS ON DETERMINING THE DEPTH OF THE SEA 
Employment of Seconds' Pendulum. — The seconds’ pendulum has been the instrument 
employed in all cases to determine variations in the total attraction of the earth upon 
its surface, this being the method first proposed and adopted by Newton. 
Spiral Spring proposed by Heeschel. — Sir John Heeschel has proposed to use instead 
of the pendulum a weight attached to a spiral spring, and he has shown that with 
increase of the force of gravitation, the spring must be proportionately elongated. 
Sir John Heeschel writes, that “ the great advantages which such an apparatus and 
mode of observation would possess, in point of convenience, cheapness, portability, and 
expedition, over the present laborious, tedious, and expensive process, render the attempt 
to perfect such an instrument well worth making ” *. It appears, however, that this 
proposal by Sir John Heeschel has never been practically realized, and that, indeed, 
no serious attempt has been made to construct an instrument of such delicacy as to 
show statically minute variations in total gravitation, notwithstanding the great oscilla- 
tions to which a weight so suspended would be liable, and notwithstanding the influence 
of changes of temperature and atmospheric density. 
General Conditions. — Neither the pendulum nor the apparatus suggested by Sir John 
Heeschel would be applicable to the measurement of the height of a mountain or 
plateau above the sea-level, owing to the considerable error which would be caused by 
changes in gravitation, through the local attraction of the mass of the mountain itself 
above the horizon, nor would either instrument be serviceable on board ship for obvious 
reasons. But if an instrument could be devised which would be capable of indicating 
extremely slight variations in the total gravitation of the earth, subject only to compa- 
ratively slight causes of error, it would be found, I contend, that these indications would 
vary with the varying depth of water below the instrument, in such a definite ratio as 
would render it possible to construct a working scale, the divisions of which would 
represent depth of water. 
Attraction influenced by Depth of Water : General Statement . — The reason why the 
total attraction upon the surface of the ocean must be less than on the shore, is evident 
from the fact that the density of sea-water is nearly three times less than that of 
such calcareous, siliceous, and aluminous rocks as constitute the principal portion of the 
crust of the earth ; and it is also evident that, although the total mass of the earth and 
the distance of the instrument from its centre remains the same in gliding along the 
liquid surface of the sea, the total gravitation must be influenced in a greater measure 
by the mass near at hand, and that in proportion to the thickness of the layer of the 
substance of inferior density the total gravitation must be affected. 
Ratio of decrease of Gravitation with Depth. — The ratio of decrease depends, in the 
first place, upon the ratio of the density of sea-water to that of solid rock. The mean 
density of sea-water may be taken at 1-026, and the density of the rock composing the 
crust of the earth may be taken to be the mean of the following densities : — 
* Herschel’s ‘Astronomy,’ Cabinet Cyclopaedia, footnote p. 125. 
