532 FOURTH REPORT 1834. 



increase with the square of the velocity ; that this law is sub- 

 ject to a remarkable exception at some point where the re- 

 sistance suddenly ceases to increase in the former ratio, and 

 appears to follow a new and unknown law. To this subject 

 the author has been recently induced to pay considerable at- 

 tention, and he has enjoyed some facilities of observing these 

 phaenomena on a large scale, as well as of making experiments 

 on a more limited one, which have induced him to take a view 

 of the subject considerably different from any with which he 

 has had the good fortune to meet. 



In regard to the point of velocity at which the phaenomenon 

 occurs, he states that it is in the transition from 8 to 9 miles 

 an hour ; and that after passing that point, the force required 

 to propel the boat at the higher velocity is less than at the 

 lower. It is also consonant with his observations and with exact 

 measurement, that the vessel at this point rises out of the 

 water, so that a vessel drawing 12 inches of water when at 

 rest, I'ises 2 inches out of the water when brought up to a ve- 

 locity of 9 miles. 



Such is the fact; and it is equally a fact, as Mr. Challis 

 remarks, that theory never predicted anything of the kind. 

 It appears to the author that the reason why theory has 

 hitherto been so ineffectually applied to this subject is that 

 the theory of immersed bodies has been confounded with the 

 theory of floating bodies. The immersed and the floating 

 body are in circumstances totally different. He has therefore 

 considered them apart from each other, and has arrived at the 

 following conclusions, which are entirely different from the 

 principles hitherto received, and which perfectly coincide with 

 the facts noticed, and readily account for them. 



The following are the results of the investigation. 



1. That in all cases and at all velocities the displacement of 

 water by a floating body is diminished by communicating ho- 

 rizontal rectilineal motion to it : that this effect is not con- 

 fined to velocities of 8 and 9 miles an hour, but extends from 

 the bottom of the scale of velocity to the top of it. 



2. That this emersion is independent of the form of the 

 body, and will take place equally with the worst and best form 

 of vessel, the only difference being that the other elements of 

 resistance will render more force necessary to conmiunicate 

 the required velocity in the former than in the latter case. 



3. That for the velocity of one mile an hour, the section of 

 immersion when compared with that section when at rest, con- 

 sidered as unity, will be diminished by '0228, or -^^y nearly ; at 

 5 miles an hour, the emersion becomes •114 = y^ nearly ; and 



