358 THE SCIENTIFIC PAPERS OF 



ON DETERMINING THE DEPTH OF THE SEA 

 WITHOUT THE USE OF THE SOUNDING-LINE. 



BY C. W. SIEMENS,* F.E.S., D.C.L., M. lust. C.E. 



INTRODUCTION. It occurred to me some years ago that the in- 

 ferior density of sea-water as compared with solid rock, such as 

 that composing the crust of our earth, might be taken advantage 

 of to devise a method of determining the depth of sea below a 

 vessel. If an instrument could be constructed which, when sus- 

 pended 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 divi- 

 sions 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 regard- 

 ing 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. f 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' (1 + '005133 sin 2 X), 

 in which g signifies gravitation at a place in latitude X, and 

 g' ( = 32*088) gravitation at the Equator. 



RECENT RESEARCHES : STOKES AND AIRY. The recent re- 

 searches by Stokes and others have shown that these determina- 

 tions are correct only approximately, and that the actual total 

 attraction of the earth at any one point, even if taken upon the 



* Excerpt Philosophical Transactions of the Royal Society, 1876, pp. 671-692. 

 f Newton's "Principia." P>ook III. proposition xx. problem iv. 



