[Reprinted from the PROCEEDINGS OF THE Royau Soctxty, A, Vol. 108.] 
Studies in Wave Resistance: the Effect of Parallel Middle Body. 
By T. H. Havetocg, F.R.S. 
(Received February 20, 1925.) 
Introduction and Summary. 
1. If a ship is altered by inserting different lengths of parallel middle body 
between the same bow and stern, the main features of the variation in the 
wave resistance may be inferred from the principle of wave interference, and 
may be expressed in terms of a certain length, sometimes called the wave- 
making length of the ship. The problem proposed for examination is the 
alteration in this length with varying length of parallel middle body at the 
same speed, and, further, its variation for a given ship at different speeds. 
Recent discussions have attracted renewed attention to this problem. It 
may be said that there are two approximations based on experimental results 
of various kinds obtained from ship models. On the one hand the wave-making 
length is supposed to be approximately independent of speed for a given ship, 
and to increase directly with the increase of parallel middle body ; on the other 
hand, an empirical formula which agrees with experimental results over a 
certain range makes the length increase with velocity, the increase beimg one- 
quarter of the increase in the wave-length of regular transverse waves. 
The following contribution to the solution of this problem is mathematical, 
and necessarily deals with a simplified form of ship. It is true that one cannot 
compare absolute values of the wave resistance with those of actual ship models ; 
but it has been shown in former studies of the dependence of wave resistance 
on ship form that one obtains a rather remarkable agreement, at least in the 
character of the results and in the positions at which changes occur. Leaving 
detailed discussion of the present extension till later, it may be stated that 
as regards the two approximate formule mentioned above the results are 
intermediate ; after an initial decrease the wave-making length increases with 
velocity, but not so rapidly as in the quarter wave-length formula. 
In §2 an expression is developed for the wave motion due to any distribution 
of doublets in a vertical plane in a uniform stream, and in §3 this is associated 
with the form of the ship’s surface. Applying the formule to a ship of infinite 
draught, with parabolic curves for the entrance and run and with parallel middle 
body, we obtain a general expression for the wave resistance (§4). After com- 
putation of the functions involved (§5), a detailed numerical study is made for 
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