382 IVlr. W. J. Macquoen Rankine on the Science of Energetics. 



niena, and an axiom states a mutual relation amongst such notions, or 

 the names denoting them ; while in a physical science, a definition states 

 properties common to a class of existing objects, or real phenomena, and 

 a physical axiom states a general law as to the relations of phenomena ; 

 and, secondly, — That in an abstract science, the propositions first disco- 

 vered are the most simple ; whilst in a physical theory, the propositions 

 first discovered are in general numerous and complex, being formal laws, 

 the immediate results of observation and experiment, from which the 

 definitions and axioms are subsequently arrived at by a process of rea- 

 soning differing from that whereby one proposition is deduced from 

 another in an abstract science, partly in being more complex and diffi- 

 cult, and partly in being to a certain extent tentative, that is to say, 

 involving the trial of conjectural principles, and their acceptance or 

 rejection according as their consequences are found to agree or disagree 

 with the formal laws deduced immediately from observation and ex- 

 periment. 



II. The Absteactive Method of forming a Physicai. Theoey, dis- 

 tinguished FROM THE HtPOTHETICAL MeTHOD. 



Two methods of framing a physical theory may be distinguished, 

 characterized chiefly by the manner in which classes of phenomena are 

 defined. They may be termed respectively the abstractive and the 

 HTPOTHETICAL methods. 



According to the abstractive method, a class of objects or phenomena 

 is defined by describing, or otherwise making to be understood, and 

 assigning a name or symbol to, that assemblage of properties which is 

 common to all the objects or phenomena composing the class, as perceived 

 by the senses, without introducing anything hypothetical. 



According to the hypothetical method, a class of objects or pheno- 

 mena is defined according to a conjectural conception of their nature, as 

 being constituted in a manner not apparent to the senses, by a modifica- 

 tion of some other class of objects or phenomena whose laws are already 

 known. Should the consequences of such a hypothetical definition be 

 found to be in accordance with the results of observation and experiment, 

 it serves as the means of deducing the laws of one class of objects or 

 phenomena from those of another. 



The conjectural conceptions involved in the hypothetical method may 

 be distinguished into two classes, according as they are adopted as a pro- 

 bable representation of a state of things which may really exist, though 

 imperceptible to the senses, or merely as a convenient means of expressing 

 the laws of phenomena ; two kinds of hypotheses, of which the former 

 may be called objective, and the latter siihjective. As examples of objec- 



