SHIP BUILDING. 39 



must be considered as firm, and the inclination to curvature which tends to 

 displace the points H, C, G, andB, as well as the action on the supports 

 AC and AB, according to the weight applied, will operate to stretch the 

 timbers, which can be prevented only by the application of these bands. 

 But the action of the bands is entirely in the direction of their length, and 

 hence tends to prevent any change of form, so that the force which tends to 

 displace the point C, is removed by the resistance of the brace, AC, and of 

 the band to the firm point F, and thus an additional strength is given also to 

 the point E ; the action of the force which tends to displace the point H, 

 in common with C, is set aside by the firmness of the long internal timber 

 AH, and the resistance of the band HF ; so that if the materials are sound, 

 no displacement or change of form can take place. If we now consider the 

 opposite construction {pi. 7, fig. 26), it appears from what has been said, 

 that the braces, AC and AB, are exposed to a pressure ; and since the point, 

 A, according to the supposition, is neutral, and therefore firm, the pressure 

 must bear upon the point C, and produce a curvature. But the tendency to 

 press upon the point C is not set aside by the action of the band FE, and 

 consequently, since the point F, according to the supposition, is firm, the 

 tendency to extension in the brace must press upon the point, and still 

 more, consequently, upon the point C. The point E, thus acted on, must 

 communicate its own inclination to the band EH, and produce a sinking at 

 the point H. Every part of the framework, from C to H, is thus subjected 

 to pressure, and a change in the form of the ship must be the effect. 



According to Dupin, the main principles in regard to the curvature of 

 vessels are the following. 1. If a vertical plane divides the ship into two" 

 parts, so that the weight of each part is equal to the weight of the water 

 which it displaces, then the elements of these parts in respect to this plane, 

 that is to say, the tendency to curvature, will be either a maximum or a 

 minimum. 2. This inclination will be a maximum, when the infinitely 

 small part which lies on the plane of the element is directly opposite to the 

 plane of the total element. 3. The inclination will be a minimum, when 

 the element on the plane acts parallel to the total element. Let the lines 

 AO {fig. 27) coincide with the surface of the water, the different sections 

 AC, CE, EG, GH, HK, KM, and MO lying in the same. On some of these 

 segments take the triangular surfaces which represent the difference between 

 the weight of the transverse sections and their pressure on the water. On 

 the segment AC = 49, the right-angled triangle = +72 will lie under the 

 water-line, because the weight exceeds the pressure ; on CE = 20, the equi- 

 lateral triangle CDE = — 108, stands above the water-line, because here 

 the pressure exceeds the weight ; on EG = 50 stands the triangle EFG = 

 + 118 ; GH = Q.Q is too small to be taken into account ; on HK = 13.4 is 

 the right-angled triangle HIK = —119, and finally on KM and MO ^ 17.5 

 and 19.5, the triangles [KM and NOM = — 115 and +192. Now add 

 together the lines, and we have 176 feet as the length of the ship, and foe 

 the sum of the diflferences + 37, so that 37 tons must be removed from the 

 forward part of the ship on account of the pressure, in order to set aside 

 the tendency to curvature. 



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