4()0 PHILOSOPHICAL TRANSACTIONS. [aNNO J 754. 



will be greater in proportion as the time of continuance of this action is greater; 

 and therefore the log will follow the ship twice as far in going one knot, when the 

 ship is twice as long in running it. The consequence of this is, that a vessel always 

 runs over a greater space than is shown by the log-line ; but that this error is 

 greater, in [)roportion as the vessel moves slower. It is this reason probably that 

 has induced the practical seamen to continue the distance between their knots 

 shorter than they are directed by the theory. 



Afterwards, in the same summer, Mr. S. made such another expedition, in a 

 sailing vessel, along with Capt. Campbell of the Mary yacht, and Dr. Knight. 

 Having prepared two of these machines as near alike as possible, he determined 

 to try, how far they were capable of agreement, when exposed to the same in 

 conveniencies, and used together. During the trial of these machines, one 

 made 86,716 revolutions, and the other made 88,184. During this space, they 

 were compared at 10 several intervals. The revolutions between each interval 

 differed from the proportion of these numbers, in the first comparison, -rV of the 

 whole interval. The errors of each interval, in the other comparisons, were, 

 in order, vVj tVj -sV) Vt, tt, ^, tt> -tt, tV; the greatest errors being where 

 the spaces were the shortest. In other respects, the plates seemed to perform 

 their duty in the water well enough, though the sea was as rough in this voyage 

 as our small vessel could well bear. 



Lastly, being for some time on board the Fortune sloop of war, commanded 

 by Alexander Campbell, Esq. in company with Dr. Knight, for the purpose of 

 making trial of his new invented sea-compasses, I had frequent opportunities of 

 making use of these machines, by comparing them with each other, with the 

 log, and with real distances; and having, by repeated trials, pretty well ascer- 

 tained the number of turns of the plate, equal to a given space, by the help of 

 the log, in the manner before described, when the ship was on a middle velocity, 

 he found the spaces, so measured, nearly consistent with themselves, and with 

 the truth; but all this while the winds and weather were very moderate. It 

 afterwards happened, that they ran 18 leagues in a brisk gale of wind, which 

 drove them sometimes at the rate of 8 knots an hour, as appeared by heaving 

 the log. During this run he observed, that the resistance of the water to the 

 line and plate, was very considerable, and increased the friction of the spindle so 

 much, as to prevent it from beginning to turn, till the plate had twisted the line 

 to such a degree, that when it did set a-going, it would frequently run 150 or 

 200 turns at once. He also observed, that the wind coming across the course 

 of the ship, blew the cord a good deal out of the direction of the spindle, and 

 caused the line to i-ub against the safeguard hole, for the button to stop against, 

 as above described; which undoubtedly occasioned considerable friction in that 

 place. But the most untoward circumstance was, that being in a rough, but 



