78 THE PRINCIPLES OF SCIENCE. 



of heat from one part of the bar to another. All these 

 effects are utterly inappreciable in a practical point of 

 view, if the bar be a good stout one ; but in a theoretical 

 point of view they entirely prevent our saying that we 

 have solved a natural problem. The faculties of the 

 human mind, even when aided by the wonderful powers 

 of abbreviation conferred by analytical methods, are utterly 

 unable to cope with the complications of any one real pro- 

 blem. And had we exhausted all the known phenomena 

 of a mechanical problem, how can we tell that hidden 

 phenomena, as yet undetected, do not intervene in the 

 commonest actions. It is plain that no phenomenon 

 comes within the sphere of our senses unless it possesses 

 a certain momentum or magnitude capable of irritating 

 the appropriate nerves. There may then, and, in fact, 

 must be indefinite worlds of phenomena too slight to rise 

 within the scope of our consciousness. 



All the instruments with which we perform our measure- 

 ments are fallible and faulty. We assume that a plumb- 

 line gives a perfectly vertical line ; but this is never true 

 in an absolute sense, owing to the attraction of mountains 

 and other inequalities in the surface of the earth. In an 

 accurate trigonometrical survey, the divergencies of the 

 plumb-line must be approximately determined and allowed 

 for c . We assume a surface of mercury to be perfectly 

 plane, but even in the breadth of 5 inches there is a cal- 

 culable divergence from a true plane of about one ten- 

 millionth part of an inch ; and this surface further diverges 

 from true horizontality as the plumb-line does from true 

 vertically. That most perfect instrument, the pendulum, 

 is not even theoretically perfect, except for infinitely 

 small arcs, and the delicate experiments performed with 

 the torsion balance proceed on the assumption that the 

 force of torsion of a wire is proportional to the angle of 



e Pratt, ' Philosophical Transactions/ vol. cxlvi. p. 31. 



