54 



MR RUSSELL'S RESEARCHES IN HYDRODYNAMICS. 



in the inverse ratio of some of those powers. In addition to the examples at the 

 end of this paper, I may here adduce two very obvious illustrations, the one shew- 

 ing an increase of resistance corresponding to a very high power of the velocities, 

 and the other exhibiting a diminution of resistance with an increase of velocity 

 greater than the former. The experiments were made on the 18th of October 

 1834 with the floating body, whose form is given in Plate TIL Fig. 4, ha\dng a 

 mass of 12,579 lbs. All the cncumstances attending the performance of the two 

 experiments were alike, and the last column shews the comparative resistances 

 as obtained by a dynamometer. 



Example I. 



Experiment I. 

 Experiment II. 



Space Described. 



1000 feet 

 1000 feet 



Time. 



117.5 

 93.6 



Velocity in Feet. 



8.51 

 10.69 



Resistance in lbs. 



233. 

 426. 





Example XL 







Experiment III. 

 Experiment IV, 



Space Described. 



Time. 



Velocity in Feet. 



Rcsisunce in lbs. 



2640 feet 

 600 feet 



302.' 

 35. 



8.76 

 14.28 



261. 

 261. 



In the first of these examples, the velocities being in the ratio nearly of 85. 

 to 106., the resistances are nearly as the third powers of the velocities ; and in 

 the second case, the velocity being increased from about 5.9 miles an hour to 9.6 

 miles an hour, the resistance is found to diminish in a ratio of 26.1 to 25.1. 



To the imperfection of this branch of science, I may also adduce the testi- 

 mony of two eminent individuals, to whose exertions we owe much that is now 

 being accomplished for its improvement. In the Essay towards an approximation 

 to a Map of Cotidal Lines, in the Philosophical Transactions of 1833, Professor 

 Whewell remarks, that " the phenomena of waves, the motion of water in tubes 

 and canals, in risers, the motion of winds, and the resistance of fluids to bodies 

 in motion, are aU cases in which we are yet far from having drawn our analytical 

 mechanics into a coincidence with experiment, or even a close approximation to 

 it ;" and Mr Challis has made the same admission at the end of his Report on 

 the state of the Theory of Hydrodynamics, made for the British Association, where 

 he says, that his " review may serve to shew that this department of science is 

 in an extremely imperfect state, and that possibly it may on that account be the 

 more likely to receive improvement ;" and he adds, that " a singular fact relating 



