16 KEPORT 1869. 



girth only. The forcbody must have for its level sections curves of siucs 

 (harmonic curves) whose equation may be written as 



0.'=—, ?/=|/j(l+cos6), 



b being the half breadth of the ship at any level, and 1 the length of the 

 forebody, which must not be less than the length of the " solitary wave," 

 which has the same speed as the ship is intended to have, in order that the 

 resistance may be the least possible. The afterbody is to have trochoids 

 for its level lines, their equation being 



.r=— , +|6 sin e, 7j=^h{l + cos 0), 



TT 



Z' being the length of the afterbody, which is not to be less than that of one 

 half of the oscillating or trochoidal wave of the same speed as the ship. The 

 straight middlebody may be of any length whatever, as it will only affect the 

 resistance by increasing the surface for friction ; or, subject to these condi- 

 tions, the resistance of the ship will be expressed by 



where © represents the area of midship section, and S the wetted surface, 

 K and K^ are coeiRcients, the former of which may be roughly stated at j'^j 

 of that due to a flat plate drawn flatwise through the water, and the latter 

 depending upon the condition of the surface. For a pure wedge bow, whose 



angle is e, Mr. Scott Eussell considers that the resistance varies as I s | , 



e Ij'ing between the limits of 12° and 144° ; and where the bow is compounded 

 of this and of the wave form, he gives, as a rough measure of the resistance, 

 a formula obtained by compounding this, in such proportion as may properly 

 represent the geometrical combination of form, with the resistance due to the 

 wave form. 



As far as can be judged by Mr. Scott Russell's published writings, there 

 appears to be some unsettled ground in his theory relatively to the shape of 

 the afterbody. The form of the bow is simply that of one-half the profile 

 of a solitary wave of translation, laid horizontallj- instead of vertically. The 

 form of the stern is also taken from the form of the wave, which is set up 

 when a hollow in the surface of water has to be filled up ; but it is nowhere 

 made clear whether this form ought to be given to the level sections, or to 

 the vertical longitudinal sections, or whether some compromise should be made 

 between the two ; and it seems probable that the author himself was doubt- 

 ful on the subject. The experiments recently made under the direction of the 

 Committee of the British Association appointed to make experiments on the 

 difference between the resistance of water to floating and immersed bodies 

 (Report for 18G6, p. 148) seem to indicate that that doubt is still unsettled. 



Without hazarding an opinion as to whether this form is really that of 

 least resistaiice, it appears certain that the cui-ves used are among those 

 along which fluid particles can glide smoothly, without causing supernume- 

 rary diverging waves in the liquid. 



The general formiila for the length of a ship given by this theory is : — 



Forebody in feet= — V^ in feet per second; 

 Afterbody=— V- in feet per second. 



