276 Col. Beaitfoy on the Resistance of Water, [April, 



Article III. 



Experiments and Observations on the Resistance of Water, with 

 Remarks on the Apparatus, By Col. Beauioy, FRS. 



(To the Editor of the Annals of Philosophy.) 



DEAR SIR, Bushcij Heath, March 4, 1822. 



In the third volume of the Annals of Philosophy, Dr. Thom- 

 son pubhshed several of the experiments made at Greenland 

 Dock, between the years 1793 and 1798, on the resistance of 

 water to variously shaped bodies. Among these were the direct 

 and oblique resistance of two square iron planes, whose united 

 surfaces measured 2*972 superficial feet, the centre of each plane 

 being immersed three feet beneath the surface of the water. On 

 reference to the original papers, I am persuaded that an error 

 was committed in placing the planes obliquely to the impulse of 

 the fluid, instead of diminishing the angle of incidence from 50 

 to 40 degrees ; for it appears that when the planes formed the 

 angle of 50 degrees with their path, the motive weight of 134 

 pounds produced a velocity of 4*575 feet in a second, and that 

 the same weight gave exactly the same result when the planes, 

 obliquity was reduced to 40 degrees. That this statement is 

 incorrect is proved by a motive weight of 33^ pounds, which, 

 when the angle was 50 degrees, drew the planes with the velo- 

 city of 2,283 feet per second, and at an angle of 40 degrees, 

 2,366 feet. In consequence, in the annexed Table I, I have 

 rejected the experiment at the angle of 40 degrees, and com- 

 bined those at tae other angles, with some experiments not pre- 

 viously inserted in the Annals. The experiments were reduced 

 to the same velocity, six feet in a second, by finding the expo- 

 nent m of the resistance : according to this formula, m = 



^' _ ^^' ^ , R and r representing the motive weights 134 and 



33 .!r, and V and v the corresponding velocities. By calculating 

 the exponent m for every angle of obhquity from 90 degrees to 

 10, nine values are obtained, the mean of the whole is 2*0154, or 

 somewhat greater than the square of the velocity. The exponent 

 m being found, the various resistances the planes met with at 

 the different angles of incidence, and moving with different velo- 

 cities, are reduced to the same velocity six feet per second by 



making R = r x — , and the motive weights calculated by 



this formula are written down in Table I. To compare the 

 experiments with more facility, the resistance of the two planes 

 are reduced to the area of a square foot, or 42,885 pounds, and 

 beneath these reduced resistances are placed the sines to radius 

 42,885 pounds, by wliich it appears that the sines exceed the 



