3T3 0« the SuhjeSl of Navigation. 



with a praftical contrivance for finding the diftance at any 

 time by thefe data, are aimed at in the following fcheme. 



Let a fmall globe of metal be attached to the end of a line 

 which is to be palled over pulleys fixed in the ftern-poft of a 

 fhip, in fuch a manner that this globe may be drawn through 

 the water after the fhip at fo low a level as not to be aflefted 

 by the fhip's wake or the motion of the rudder, and fo that 

 the other end of the line muv be conduced into the veflol,, 

 •where it is to be joined to the end of a ftronu: fpiral fpring ot 

 fufficient fizc and elafticity to exprefs, by diiiiuil expanfions 

 and contratlions, every variation of reliliance which may 

 affeft the immerfed globe. If a fliip, furnifhed with fuch an 

 inftrument, move at fea with an afcertaincd degree of velo- 

 city, and if the expanfion of the fpring, at the fame time, be 

 marked on a fcale annexed, this degree of expanlion will be 

 peculiar to that degree of velocity ; and if the fcale be filled 

 ■with all the ufeful graduations taken from aftual experiment, 

 the fliip's rate of motion may be known thereby at any time, 

 whatever the law of hydrodynamic refinance may be. 



Then fuppofe a cup, with a fmall perforation in the bot- 

 tom, containing that fort of metallic fand which is ufed for 

 hour-glaffes, to be joined to the extremity of the fpring, the 

 ftream of fand which iffues from it will have a common mo- 

 tion with the fpring, fo that the point of the fcale on which 

 this ftream falls will mark the rate of progrefs, and (fince 

 fand* flows equably) the quantity which falls upon that point 

 will mark the time, the produ6l of which quantities is the 

 diftance paflfed over during that time. Therefore, if there be 

 a receiving veflel for the fand, divided tranfverfely into feveral 

 compartments, fo that the partitions between them may be 

 at the fame diftances afunder as the graduations of the fcale, 

 the fum of the produfts arifing from the multiplication of the 

 quantities of fand received in all of them, by the velocities de- 

 noted by the compartments which hold them refpeiSlivcly, 

 will be the diftance failed at any time. 



However, though this method furniflies quantities from 

 which the diftance may be computed, confiderable delay 

 mud arife from the mcaiuremrnt of each feparate portion of 

 fand, and the multiplication of each of thele by its refpedive 

 degree in the fcale ; which difficulty may be removed in the 

 following manner : 



It is evident, from the nature of the fcale, that the orifices 

 of the compartments of the receiver muft be unequal ; but if 



* Tt hiS been proved, hy experiment, that the clifcharge of rand in this 

 cafe will be liic (a^Tifc in ic|uhI times, wiurher the fu(-eriiicnnibciit weight 

 be great or fmali, — contraiv to the eilablilhetl laws oi jiuuh. 



thev 



