A complete theory of the construction and properties of vessels; with practical conclusions for the management of ships, made easy to navigators. ... des vaissaux, of the celebrated Leonar

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1790 Excerpt: ...readily determine the Velocity which the Vessel will receive, by the aid of this Equality _i_ = 4 F. fI",,. 4£ zae Sin. p and, and, by this means, we know how to estimate the greatness of the acting Force: But with respect to the Place of application of this Force, that will be the Subject of Enquiry in the following Chapter. § 39 But before this Chapter is finished we shall take notice of a very singular Paradox in the Expression, V P Cos.p4-fQSin. p. which denotes the Force of the Resistance, and which becomes = P when p--and will be--Qjf p = 90. The first of these Cases will happen when the Vessel moves in the Direction of the great Axe B A; and the other when it moves in that of the lesser Axe C D, from whence it seems that since is several times greater than P, the least Resistance ought to take place in the direct Course, where the Lee-way p vanishes. But it is certain that the Resistance will become still less for a particular Angle of Lee-way, which is found by taking the P Tang. p--and must in consequence be very P small; and since we thenhaveSin.p= I 4 and--is less than Unity. Here is there's/ p-f c fore this great Paradox, that by giving to the Vef p sel a small Lee-way f, such that Tang. p----, the Resistance will be found less than in the direct Course but it is precisely the Case which we have already remarked, where the Angle XF Y vanishes, so that the Resistance is here directly contrary to the Motion F X. CHAP. CHAP. VI. CHAP. VI. Upon the Place of Application of the acting Force, % 40. FROM the Manner in which we have began this Research, by considering the Body as a rectangular Parallelogram, and the Force of the Resistance as applied to the Center of the Body pIate Ir F; and also when we have afterwards generalized Fig-&qu...