518 Sir William Thomson on Stationary 



Esq., one of the proprietors of the works, took fright and 

 ran off, dragging the boat with it, and it was then observed, 

 to Mr. Houston's astonishment, that the foaming stern surge 

 which used to devastate the banks had ceased, and the 

 vessel was carried on through water comparatively smooth, 

 with a resistance very greatly diminished. Mr. Houston had 

 the tact to perceive the mercantile value of this fact to the 

 Canal Company with which he was connected, and devoted 

 himself to introducing on that canal vessels moving with this 

 high velocity. The result of this improvement was so valuable 

 in a mercantile point of view, as to bring, from the conveyance 

 of passengers at a high velocity, a large increase of revenue to 

 the Canal Proprietors. The passengers and luggage are con- 

 veyed in light boats, about sixty feet long and six feet wide, 

 made of thin sheet iron and drawn by a pair of horses. The 

 boat starts at a slow velocity behind the wave, and at a given 

 signal it is by a sudden jerk of the horses drawn up on the top 

 of the wave, where it moves with diminished resistance, at 

 the rate of 7, 8, or 9 miles an hour"*. 



The " diminished anterior section of displacement pro- 

 duced by raising a vessel with a sudden impulse to the 

 summit of the progressive wave" is no doubt a correct 

 observation of an essential feature of the phenomenon; 

 but it is the annulment of " the foaming stern surge which 

 [at the lower speeds] used to devastate the banks" that 

 gives the direct explanation of the diminished resistance. 

 It is in fact easy to see that when the motion is steady, no 

 waves can be left astern of a boat towed through a canal at a 

 speed greater than s/gT), the velocity of an infinitely long 

 wave in the canal ; and therefore (the water being supposed 

 inviscid) the resistance to towage must be nil when the velo- 

 city exceeds \/gT). This holds true also obviously for towage 

 in an infinite expanse of open w r ater of depth D over a plane 

 bottom. 



The formula (25) of Part II. for the whole horizontal com- 

 ponent force upon an inequality or succession of inequalities 

 on the bottom allows us to calculate the resistance on a boat 

 of any dimensions and any shape provided we know the height 

 of the regular waves which follow r it steadily at its own speed 

 in the canal, at a sufficiently great distance behind it to be 

 sensibly uniform across the breadth of the canal, according to 

 the principle explained in the middle of p. 354 of Part I. The 

 principles upon which the values of .£) [the h of formula (25), 

 Part II.] may be calculated are partly given in the remainder 



* Trans. Roy. Soc. Edinb. vol. xiv. (1840) p. 79. 



