294 OF STEAM NAVIGATION. [SECT. x. 



with the length ; also when the body terminates either in cones or pyramids, the 

 angles being those the slant sides form with the length. 



616. If the section be a triangle, and the ends triangular pyramids, being 

 the angle the side of the triangle forms with the upper surface, then, if q be the 

 product of the sin. , by sin. Q, the resistance will be, 



v3 /a q + q ) + 0-0032 I c \ = the power in Ibs. raised one foot per second. 



The resistance of this figure is less than that of any convex curved solid, but its 

 capacity is also small ; and its stability depending on the form at the water lines, 

 it will be subject to roll at sea. Great capacity cannot be obtained with a 

 minimum of resistance. 



617. If the plan of the water lines be composed of circular arcs, the bottom 

 flat, and the radius be m times the half breadth of the boat, and z be the length 

 of the curved part, r = the radius, and a the depth, which is uniform ; then 3 z 

 = r (4 */ 2 m ^ 2 m z 2 ), and 



V 3 a /3z r(l-m)(3- 4m)./2m' + (2 2 (1 m) \ (1 - m) + 3 m\ r -0032 / c\ _ 

 a V 4 3 a / 



the power in Ibs. raised one foot per second, required to keep the vessel in motion 

 at the velocity v. 



618. In canal boats m = ^ = -125, or the radius is 4 times the breadth, 

 and therefore v 3 ('35 ab + -0032 Ic) = the power in Ibs. raised one foot per 

 second. 



If the radius be equal the breadth, then m = '5, and v 3 ('74 a b + '0032 / c) = 

 the power in Ibs. 



619. Mr. Bevan made some experiments with a canal boat of the form just 

 described, the results of which he has communicated to me for the purpose of 

 comparing theory with practice. 



The length of the boat was 69'57 feet, its width 6'83 feet, its floating depth 

 when tried 0'89 feet ; the bottom was flat, and the sides were parallel to within 

 about 13'75 feet of each end, but the ends were curved, the curves being circles 

 described by a radius of 8 times the half breadth of the boat. The whole 

 surface in contact with the water was 540 feet ; and the weight was 91 tons. 

 Putting these numbers in the equation (art. 618.) we have 



v- (-89 x 6-83 x -35 + -0032 x 540) = 3-8 v* = the resistance. 



