20 REPORT — 1869. 



that any specific mathematical form is to be preferred in respect of its total 

 resistance to a long, fine, fair ship, either drawn or modelled by eye by a 

 practised draughtsman or modeller. 



A possible connexion between the resistance of ships and their depths of 

 immersion has been pointed out by ilr. Eankine in some papers published in 

 the ' Proceedings of the Eoyal Society' for 1868, p. 3-1-4, in the ' Reports of 

 the British Association ' for 1868, in the ' Transactions of the Institution of 

 ISTaval Architects ' for 1868, and in the ' Engineer' of the 28th August and 

 30th October, 1868. He shows from theory, corroborated by his own obser- 

 vations, and by those of ilr. John Inglis, junior, that every ship is accompa- 

 nied by waves, whose velocity of advance is V ^ k, g being gravity, and h 

 the mean depth of immersion, found by dividing the displacement by the area 

 of water-section. So long as the speed does not exceed V gk, these waves 

 cannot produce any additional resistance ; but when the speed exceeds 

 that limit, the waves are made to diverge from the ship at the angle whose 



cosine is ^ , and thus to carry away energy, like the other diverging 

 speed 



waves previously mentioned. 



The form of the midship section does not appear to exercise any influence 

 on the resistance to propulsion in still water, except so far as it affects the 

 extent of wetted surface exposed to the action of the water. If the wet 

 girth and the breadth at the water-line be given, the form of greatest area 

 will be a segment of a circle ; but this will not be the solution of the ques- 

 tion which usually presents itself, namely, given the breadth and the draught 

 required, the form for which the ratio of area to surface shall be the greatest 

 possible. In the particidar case in which the di-aught is half the breadth, it 

 is easily seen that the ratio of area to girth is the same for a semicircular as 

 for a rectangular section, and therefore that the solution lies between these 

 extreme cases. It does not appear that the general problem has yet been 

 solved, and perhaps, as the really practical problem relates to the ship and 

 not to the midship section, it is of secondary interest. A restricted solution 

 has been given by Mr. James Robert Napier in a paper read before the Glas- 

 gow Philosophical Society, and reprinted in the ' ilechanics' Magazine ' for 

 24th April, 1863, vol. ix. p. 311, and in the ' Engineer ' for 1st May, 1863, 

 vol. XV. p. 24.5. 



The best ratio for good propulsion of length to breadth and draught, even 

 when it is assumed that the length exceeds Scott Russell's limit, is not yet 

 known. This is not perhaps of practical importance, inasmuch as considera- 

 tions of economy, capacity, and handiness generally settle these proportions, 

 without much reference to a theoretical maximum of efficient propulsion. 

 But the extent to which an increase of breadth or depth, lea\'ing other things 

 unaltered, affects the propulsion itself can hardly be regarded as within oiir 

 settled knowledge. 



The resistance of the air to a ship's hull is not a point to be neglected in 

 practice or in experiment; but it is not one which we propose to discuss 

 here. 



The above contains an abstract of nearly all that is known concerning the 

 TOTAL RESISTANCE of a ship in smooth and deep water. We do not consider 

 it necessary in this Report to enter into the question of the increased resist- 

 ances due to shallow water, narrow channels, or a rough sea. We may sum 

 up the result in the broad statement that there exists no generally recognized 

 theory or rule for calculating the resistance of a ship. Many such rules 



