414 
ME. E. J. REED ON THE UNEQUAL DISTRIBUTION OE 
steel in shipbuilding — have added much to the urgency of the inquiry. A long armoured 
ship, say, like the ‘ Minotaur ’ or ‘ Agincourt ’ (400 feet in length, and with fine tapering 
extremities burdened with towering masses of armour), when pitching in Atlantic waves, 
undergoes a succession of stresses of great magnitude, undoubtedly requiring to be brought 
as much as possible within the grasp of calculation, the more so as these stresses undergo 
continual changes, sweeping through the fabric, so to speak, with prodigious velocity. 
The employment of iron and steel, and the improvements which the manufacture of 
both is undergoing, fortunately facilitate the concentration of the strength of the ship 
in those parts which are subject to the greatest stresses; and to further this object, a 
closer knowledge of these stresses than has hitherto been possessed is much needed. 
Bouguer, the author of the famous ‘ Traite du Navire ’ (174G), was one of the earliest 
authors who gave consideration to the strains brought upon ships by the unequal distri- 
bution of weight and buoyancy. The approximate and imperfect character of his theo- 
retical investigations will readily be seen from the fact that he assumes the immersed 
portion of the ship to be formed of the halves of two equal right cones, set base to base, 
with their common axis in the water-line. He then constructs a curve the ordinates of 
which represent the areas of the corresponding sections of the cones, and this he calls 
the curve of buoyancy for the body. It necessarily comes out a parabola for each cone. 
He next assumes that the weight of the ship and her lading is uniformly distributed 
throughout the length, so that it can be represented by a rectangle which stands on the 
same base as the parabolic curve, and includes an equal area, the latter condition being 
fixed by the necessity for the displacement equalling the total weight. His investigations 
have, however, the merit of exhibiting an early example of that graphical or geometrical 
method of illustrating the distribution of weight and buoyancy which has since been 
employed by many authors, which Professor Eankine in particular has recently used 
with great advantage, and which I have adopted throughout the following investigations. 
About ten years after the publication of Bouguer’s work, Daniel Bernoulli wrote 
his celebrated memoir “ Principes Ilydrostatiques et Mechaniques,” which obtained the 
prize offered by the Academy of Sciences in 1757 for the best essay on the means of 
preventing pitching and rolling. Being limited to the discussion of the one branch of 
the subject proposed by the Academy, Bernoulli did not discuss, as the title of his 
work might lead us to expect, the strength and strains of ships ; but two years afterwards 
the Academy, in order to supply this want, supplemented their previous question by 
another having reference to the strains caused by pitching and rolling, and this elicited 
Euler’s well-known memoir*. Although even this treatise says little of statical strains, 
and contains but a cursory notice of the longitudinal bending-strains of a ship afloat in 
still water, it is remarkable on the ground that it presents us with the first instance in 
which we find account taken of the bending effect of the longitudinal pressure of the 
* “ Examen des efforts qui ont a soutenir toutes les parties d’un vaisseau dans le roulis et dans le tangage ; 
ou recherches sur la diminution de ces mouvements.” Par M. L. Eulek, Directeur de l’Academie Royale des 
Sciences et Belles-Lettres de Prusse. 
