[ 671 ] 
XXV. On determining the Depth of the Sea without the use of the Sounding-line. 
By C. William Siemens, F.B.S., D.C.L., Mem.Inst.C.E. 
Received January 20, — Read February 24, 1876. 
Introduction. 
It occurred to me some years ago that the inferior density of -sea-water as compared 
with solid rock, such as that composing the crust of our earth, might be taken advan- 
tage of to devise a method of determining the depth of sea below a vessel. If an 
instrument could be constructed which, when suspended on board ship, would indicate 
extremely slight variations in the total attraction of the earth, those indications might 
be referable to the depth of sea, and a scale be obtained whose divisions would give the 
depth in fathoms, or other units, without having recourse to the laborious process of 
sounding by means of the sounding-line. 
Terrestrial Attraction : Newton. — Our knowledge regarding terrestrial attraction dates 
from Newton, who proved that “ the attraction of a spherical shell on an external 
particle is the same as if the mass of the shell were collected at the centre,” and that 
the earth might be considered as consisting of an aggregate of such shells. Bearing in 
view, however, the fact of the earth’s rotation he proved its ellipticity, and that partly 
in consequence of that form, and partly on account of the centrifugal force engendered 
by its rotation, the total attraction of the earth in reference to a point on its surface 
must vary with latitude*. He determined the ratio of increase on the supposition that 
the earth is homogeneous, and showed that it varies as the square of the sine of the 
latitude. It is actually represented by the formula 
g—g'(l -p -005133 sin 2 ^), 
in which g signifies gravitation at a place in latitude X, and y=32'088 gravitation at 
the Equator. 
Decent Besearches : Stokes and Airy. — The recent researches by Stokes and others 
have shown that these determinations are correct only approximately, and that the 
actual total attraction of the earth at any one point, even if taken upon the sea-shore, 
is influenced by the rising land of continents, or by cavities in the interior of the earth. 
He also established a reason for an observation made previously by Airy, that total 
gravitation is greater on an island than it is near the sea-shore of a continent, and 
greater on the sea-shore than on an estuary inland f. 
* Newton’s 1 Principia,’ Rook iii. proposition xx. problem iv. 
t Cambridge Philosophical Transactions, vol. viii. pp. 672-695. 
