ON THE PARABOLIC SYSTEM OF CONSTRUCTING SHIPS VENTED By ADMIRAL F. H. CHAPMAN.
The system which is at present used by the Swed ish engineers, in the construction of ships, was the result of the labours of the latter years of Chapman's life; it is called the parabolic method, and is explain ed in a work entitled, Forsok till en Theoretisk hand ° ling att gifea at Linie Shen) deras rdtta Slorlek och Form Likalcdes fur Fregatter och mindre Bevarade Far tyg. of F II. of Chapman. Carlskrona, 1806.
The following paper, drawn up by Lieut. A. G. Carlsand of the Swedish navy, is an outline of this description, with some few alterations, which the writer considers may perhaps render the calculations more simple.
By making calculations on a number of ships which have been found to possess good properties, and sub jecting the result to scientific investigation, we are enabled to state what displacement and what dimen sions a well-constructed ship should have; we can also determine where the centre of gravity, in respect to length, should be placed; but we cannot by the usual methods of construction, without very great labour, determine the area of the midship section, its distance before the middle of the length, and the areas or forms of the other sections, so as to ensure having this re quisite displacement, nor that it shall be so distribut ed that the centre of gravity shall be in the required situation. It was to supply these deficiencies that Chapman invented the method which is the subject of this paper.
As the above-mentioned elements depend upon the areas and situations of the several transverse sections, Chapman endeavoured to discover whether ornot these areas, in well-constructed ships, followed any law; and if so, to find the law. For this purpose, he calculated the areas of the sections of several ships; and, in order to make the numbers more convenient, he divided the areas by the breadth of the midship section; then setting off from the water line, at the respective sta tions on the drawing, distances equal to the quotients, he traced a curve representing the areas, which he called the curve of sections. He then endeavoured
to find the equation to the curve, or rather that of another curve which would coincide with this for the greatest length; and he found that if the power and parameter of a parabola were so determined as to allow that curve to pass through three given points of the curve of sections, the two curves would nearly coincide. In the fore body the three points were taken, one forward, one at the midship section, and one midway between. In the after body the points were similarly situated. In some ships the exponent to the curve was higher in the after body than in the fore body, in some it was the same for both: it was also found that there were ships in which the curve of sections almost exactly agreed with the parabola, and these ships invariably bore excellent characters. Chapman consequently concluded, that if the areas of the several sections of a ship were made to follow the law of the abscissas of a parabola, a vessel pos sessing good sailing qualities might be formed, and the process of construction much simplified.
This account shows that this method is deduced from experience by theoretical investigation; it is ap plicable to all sorts of constructions, as it only re quires that the relative areas of the sections shall de crease from the midship section towards the extremi ties, in a certain relation which can be varied to in finity; it is therefore equally useful in constructing the sharpest man-of-war, as the fullest merchantman.
It may perhaps be objected, that the alterations which have taken place in the forms of the bottoms of ships, since the introduction of this method by Chapman in 1806, would probably give different re sults; it is therefore desirable that this should be as certained by a series of calculations on the bodies of some of the most modern ships which have been found to answer.