On the SubjcSl of Navigation. 313 



they be made to diverge as they defcend, fo that they may be 

 equal at the bottom, the unequal fcale will be changed into 

 a fcale of equal parts, the fand received into it will be fo dif- 

 tributed thereby, when lodged at the bottom, that the diftance 

 of each portion of it from the end of the receiver will be as 

 the fliip's velocity when it fell ; and, confequcntly, the fum of 

 the products arifing from the multiplication of the quantity 

 in each compartment, by its diltance from the end of the re- 

 ceiver, will be as the diltance failed. But the fum of thefe 

 products is equal to the fingle product of the diftance of the 

 common centre of gravity of the fallen fand from the ex- 

 tremity of the receiver, by the weight of all the fallen land; 

 and, if the receiver be furniflied with a falling handle, this 

 centre of gravity may be found at any time by finding tenta- 

 tively that point of the handle by which it may be fufpended;^ 

 fo that the receiver containing the difcharged fand may not 

 incline to either fide : and if this experiment be made with 

 the hook of an ounfcl containing a fcale graduated for the 

 purpofe, the weight or quantity of fand difcharged may be 

 known; alfo, if the faliing handle be graduated into equal 

 parts, correfponding with the divifions of the compartments 

 at the bottom of the receiver, and marked with numbers re- 

 prcfcnting the rate of failing which thele divifions denote, 

 the number on this handle at the centre of gravity, multiplied 

 by the number on the fcale of the ounfel, will ihow the di- 

 ftance failed at any time. 



In order to adapt this inftrument to the feaman's ufe, it is 

 neccU'ary to confider the irregularities of motion occafioned 

 by the waves, and to provide againft their effecls. Thefe are 

 of three forts. Firft ro//i;/^, or a motion about the longitu- 

 dinal axis of the thip, which does not feem capable of dif- 

 turbing the operation of the inftrument. Secondly, he-zuay^ 

 which takes place when a fliip moves in any direction except 

 that of her keel :■ in this cafe, the ftring, being drawn tranf- 

 verfcly, will not have its full efl'ecl on the pulley at the bot- 

 tom of the ftern-poft, but will a«il as an oblique force, and 

 conicquenlly the diftance will be reprefcuted too little; to 

 remedy which, the lower pulley muft be formed fo as to have 

 a motion like that of a caftor on the foot of a table, whereby 

 it may be turned bv the line into its own direction, and then 

 the action of the ball u ill produce the required effect. Thirdly, 

 pitcbing, or a vibrating motion about the tranfvcrle axis, 

 which, if the ftring to which the ball is faftened be ftiort, iii 

 ail high fea, would give a Icrpentiiie motion to the ball, that 

 would rcprefeul the diftance greater than it fliould be ; to 



prevent 



