54 



MB 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 tAVO 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 duninution 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 Tlate III. Fig. 4, having a 

 mass of 12,579 lbs. All the cuxumstances 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 11. 



Space Described. 



1000 feet 

 1000 feet 



117.5 

 93.5 



Velocity In Feet. 



8.61 

 10.69 



Resistance in lbs. 



233. 

 426. 



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 ri-^ers, the motion of winds, and the resistance of fluids to bodies 

 m 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 



