72 PHILOSOPHICAL TRANSACTIONS. [aNNO 1776. 



tide. This difference in the rise and fall of the tide was uniformly the same on 

 each of the 3 springs which happened while they lay in the place, and was 

 apparent for about 6 or 7 days ; that is, for about 3 days before and after the 

 full or change of the moon. During the neap, the tide was very inconsider- 

 able, and if there was any difference between the rise of the tide in the day and 

 in the night, it was not observed ; but to the best of Captain C.'s recollection 

 none was perceptible. Excepting '2 or 3 mornings, when they had a land-breeze 

 for a few hours, they had the winds from no other direction than s. e., which is 

 the same as this part of the coast, and from which quarter he judged the flood- 

 tide came. The wind, for the most part, blew a brisk gale, and rather stronger 

 during the day than the night. How far this last circumstance might affect the 

 evening-tide, he pretends not to determine ; nor can lie assign any other cause 

 for this difference in the rise and fall of the tide, and therefore must leave it to 

 those who are better versed in this subject. T 



XXVII. An Experimental Examination of the Quantity and Propoition oj 

 Mechanic Power necessary to he employed in giving Different Degrees of 

 Felocity to Heavy Bodies from a State of Rest. By Mr. John Smeaton, 

 F. R. S. p. 450. 



About the year l6s6 Sir Isaac Newton first published his Principia, and 

 conformably to the language of mathematicians of those times defined, that 

 " the quantity of motion is the measure of the same, arising from the velocity 

 and quantity of matter conjointly." Very soon after this publication, the truth 

 or propriety of this definition was disputed by certain philosophers, who con- 

 tended, that the measure of the quantity of motion should be estimated by 

 taking the quantity of matter and the square of the velocity conjointly. There 

 is nothing more certain, than that from equal impelling powers, acting for equal 

 intervals of time, equal increases of velocity are acquired by given bodies, when 

 unresisted by a medium ; thus gravity causes a body, in obc) ing its impulse 

 during one second of time, to acquire a velocity which would carry it uniformly 

 forward, without an additional impulse, at the rate of 32 It. 2 in. per 

 second ; and if gravity be suffered to act on it for 2 seconds, it will have in 

 that time acquired a velocity that would carry it, at a uniform rate, just double 

 of the former ; that is, at the rate of 64 ft. 4 in. per second. Now, if in con- 

 sequence of this eijual increase of velocity, in an equal increase of time, by the 

 continuance of the same impelling power, we define that to be a double quan- 

 tity of motion, which is generated in a given quantity of matter, by the action 

 of the same impelling power for a double time ; this will coincide with Sir Isaac 

 Newton's definition abovementioned ; whereas, in trying experiments on the 

 total effects of bodies in motion, it appears, that when a body is put in motion, 



