48 MR RUSSELL'S RESEARCHES IN HYDRODYNAMICS. 



the action of that species of moving force was found too desultory and discontinu- 

 ous to furnish a measure of resistance sufficiently accurate to be used in compa- 

 risons of a delicate description, and therefore in 1835, means were provided for 

 rendering the action of the moving force more nearly continuous by using a pecu- 

 liar apparatus. With this apparatus experiments were made on the resistance 

 of four vessels of about 70 feet in length, at different depths of immersion, so as 

 to give comparative measures of resistance in reference to sixteen forms, at velo- 

 cities from three to fifteen miles an hour. 



The results of the investigations directed to the determination of the law 

 which connects the resistance of the fluid with the velocity of the motion of the 

 floating body, appear to establish the following conclusions, — that the resistance 

 does not follow the ratio of the squares of the velocities, excepting in those cases 

 where the velocity of the body is low, and the depth of the fluid considerable — 

 that the increments of resistance are greater than those due to the squares of the 

 velocities, as the velocity approaches a certain quantity, which is determined by 

 the depth of the fluid — ^that at this point the resistances attain a first maximum, 

 and that here, by certain elements of the form of the body, and of the dimensions 

 of the fluid, they may become infinite — ^that immediately after this, there occurs a 

 point of minimum where the resistance becomes much less than that due to the 

 square of the velocity, and after which it continues to receive increments, of which 

 the ratio is less than that due to the increment of the square of the velocity — that 

 according to the law of progression which has been established, the resistance will 

 reach a second point of maximum, when a velocity shall be attained of about 29 

 miles an hour, after which it will be rapidly diminished with every increase of 

 velocity. 



Extracts from the Experiments, shewing the connection between Resistance and 



Velocity. 

 Example I. Example II. 



Velocity. 



Resistance. 



Resistance. 



Squares of Velocities, 



3.7 



28.0 





14.3 



4.0 



33.76 



39. 



16. 



6.0 



61.0 





26. 



6.1 



91.0 



111. 



38.4 



7.1 



21 r 



266. 



61.6 



7.6 



266. 



330. 



67.3 





Point of First Maximum and Minimum. 





8.6 



216. 



210. 



72.6 



9.0 



234. 



236. 



81.8 



11.3 



246. 





129. 



12.3 





362. 



163.6 



16.1 





444. 



229.6 



