150 THIRD REPORT — 1833. 



applied, instead of once and a half. M. Poisson thinks that 

 the calculations of M. Bessel leave some room for doubt, and 

 objects to the discordance of the values obtained for air and 

 watei', which, according- to his own theory, ought to agree. 

 More recent experiments of Mr. Baily *, which, from their num- 

 ber and variety, and the care taken in performing them, are 

 entitled to the utmost confidence, give the value 1*864 for 

 spheres of different materials one inch and a half in diameter, 

 and 1 '748 for spheres two inches in diameter, the latter being 

 nearly the size of those for which M. Bessel obtained 1*946. 

 The theory of M. Poisson does not recognise any difference in 

 the value of the coefficient for spheres of different diameters. 

 The discrepancies that thus appear between theory and expe- 

 riment, and between the experiments themselves, show that 

 there is much that requires clearing up in this important sub- 

 ject. As far as theory is concerned, it is easily conceivable that 

 much must depend upon the way in which the law of trans- 

 mission of the motion from the parts of the fluid immediately 

 acted on by the sphere to the parts more remote is to be deter- 

 mined : and, as it is the province of this Report to point out 

 any possible source of error in theory, I will venture again 

 to express my doubts of the correctness of the principle em- 

 ployed in the solution of this problem, of making the deter- 

 mination of the law of transmission depend on the arbitrary 

 discontinuity of the functions introduced by integration, the law 

 itself not being arbitrary f. 



A singular fact, relating to the resistance to the motion of 

 bodies partly immersed in water, has been recently established 

 by experiments on canal navigation, by which it appears that a 

 boat, drawn with a velocity of more than four or five miles an 

 hour, rises perceptibly out of the water, so that the water-line 

 is not so distant from the keel as in a state of rest, and the re- 

 sistance is less than it would be if no such effect took place. 

 Theory, although it has never predicted anything of this na- 

 ture, now that the fact is proposed for explanation, will proba- 

 bly soon be able to account for it on known mechanical prin- 

 ciples. 



The foregoing review of the theory of fluid motion, incom- 



* PhHosophlcal Transactions for 1832, p. 399. 



t In an attempt at this problem made by myself, and published subsequently 

 to the Meeting of the Association, the value of the coefficient is found to be 2, 

 without accounting for any difference for spheres of different diameters. See 

 the London and Edinburgh Philosophical Magazine and Journal for Septem- 

 ber 1833. 



