the Stability of Ships. 267 
Mr. Chapman, an eminent author on the subject of naval 
architecture,* applies this theorem to naval mensurations, as a 
substitute, and certainly an useful one, to the less perfect rules 
which are employed for this purpose, in the works of M. Bou- 
guer and other authors. The example by which Mr. Chapman 
illustrates the use of this rule is the same with that which is 
given in Mr. Simpson’s Essays. 
This approximation to the measures of areas being applicable 
* The following observation on this theorem is inserted in the Report from the 
Committee of the French Royal Marine Academy, who were appointed to examine 
the translation of Mr. Chapman’s Treatise on Naval Architecture, by M. Vial 
de Clairbois; this report is prefixed to the French edition of Mr. Chapman’s 
work. 
“ Ce celebre constructeur commence par donner une nouvelle methoae de calcul de 
" Replacement, qui sans etre beaucoup plus longue que celle que l’on emploie com- 
et munement, donne un resultat infiniment plus exact. On considere ordinairement 
“ les parties curvilignes des plans de flottaisons, ou de gabarits, entre les extremites 
se des ordonnees, comme des droites; M. Chapman les regarde comme des parties 
<£ paraboliques ; et, de la nature de cette section conique, et du trapeze, il tire une 
expression sur laquelle il fonde un calcul assez simple,” &c. 
A comparison of the results derived from this rule, and from that which is em- 
ployed by M. Bouguer, does not seem to confirm the opinion of the very superior 
exactness which the committee here attribute to the former rule: that it is more exact 
there is no doubt, especially when the curvature is at all irregular in respect to its varia- 
tion, and the results inferred are data on which other computations are to be founded; 
but, in many of the cases which occur in practical mensurations, the latter rule ap- 
proximates to the required results sufficiently near the truth, as will appear by the 
instances in the subsequent pages. The expression « une nouvelle methode” can- 
not be understood to mean a rule of computation newly invented, but one which 
Mr. Chapman has first applied to naval mensurations. In this sense, the theorem 
inserted in the 265th and 268th pages of these papers would be entitled to the appel- • 
lation of a new method but it has already been shewn, that the three rules here 
described, and employed in the computations which follow, are only particular cases 
of the general method demonstrated in the works of Sir I. Newton, Stirling, 
Simpson, and other authors. 
Mm2 
