Bat it may be asked, in attempting to extend the investigation of these elements beyond the limits at tained by Chapman, how are these derived functions to be obtained? We answer, by experiment and ob servation; by inquiring into the properties of the most approved models that have hitherto been pro duced; by grouping together facts, and drawing from their united testimony, legitimate results; pouring into the very heart of shipbuilding the genuine spirit of induction, and throwing over the whole of the inquiry the mantle of a pure philosophy; viewing facts, not as detached and insulated fragments, but as parts of a system which the progress of inquiry must eventually blend into one perfect and harmoni ous whole.
To those who may be disposed to deny the possi bility of tracing, in the extended manner alluded to, the connexion of these different elements, we would observe, that some ships of war, and some vessels of our mercantile marine, possess confessedly better qualities than others. Some, indeed, possess a more than ordinary proportion of good qualities, and as such, become proper objects of philosophical examina tion. Suppose for example, that two or more ships of a particular class were selected, whose properties were generally recognised as good, might not many important conclusions be deduced from an analysis of their different elements? Each ship, for example, would have a given displacement, a length, a breadth a main sectional area, a certain stability, a particular position of the metacentre, a corresponding position of the centre of gravity, and indeed many other elements, each of which it would be highly proper to ascertain, and the relation of all of which to some primary element, it would be of the first importance to determine. These elements would, of course, at first possess a numeri cal character; but the generalizing eye of a philoso pher would soon trace the existence of laws among the apparently unconnected arithmetical results; and order, and a system of definite relations, assume the place of irregularity, apparent accident, and chance.
To draw an example from the first of the tables before given, Chapman shows, in the case of a frigate, that the displacement is so related to the burthen es timated in cubic feet, as to present tne conditiona! equation D PN; or, in the second table, that the length is related the displacement by an equation of the form wherein / and D represent the elements referred to, and x, y, are unknown or indeterminate quantities, which it is the proper business of well-directed ex periments to disclose.
In like manner we may draw from the investiga tions of the same able engineer, that the breadth is related to the length by the expression B where 1 the length may be obtained from the condi tional equation before given, in terms of the displaco ment, and x',y' are empirical quantities, owing their origin entirely to experiment and observation.
Hence we may perceive how important it must be to the interests of naval architecture, to obtain from ships of approved character and value, every element that may be desired; not however by theoretical in quiry, but by courses of experiment, and long trains of observation; tabulating all the results that successful industry may obtain, in approved, and intelligible forms; entering every conclusion not as a detached and insulated quantity, but as an ele mcnt which bears some relation to every other step of the inquiry.
Hitherto it has been the practice of those connect ed with naval inquiries, to view the various elements of shipbuilding, too much in the light or detached and insulated quantities, and not as parts of a system which possess the most perfect and intimate relations, and incapable of separation from each other. How often, from the imperfect condition of our knowledge, arc we obliged to give to our most laborious disqui sitions on stability, on displacement, on the metacen tre, and indeed to most of the elements of naval archi tecture, a detached and insulated character; unable to trace the gradually inductive steps by which one branch of' the inquiry is led on to another; how one individual element of a system is related to the ele ments that surround it, and it stands connected with the great whole, of which it forms a part. And in no view of the subject before us, is this remarkable circumstance more apparent, than when we speak of the dimensions of' ships, and endeavour to connect to gether the elements which compose them.
No one we will venture to say, who investigates the present condition of naval architecture, can for a mo ment allow, that it has been benefited in any material degree, by the example which the great reformer of philosophy exhibited to the experimental world. There has been little of what may he truly termed in ductive inquiry, displayed in its history; and it stands 110 NV almost as a solitary monument of the fully which guided the predecessors of Bacon, in the paths of ex perimental investigation. Vet, in no subject is there greater room for the application of the most rigid principles of the inductive logic, than this. Millions of ships have been constructed, but only here and there a successful example has been offered for our contem plation, as if to mock the implicit obedience we pay in the practice of naval architecture, to uncertain and ill-defined rules.