538 ADDITIONS. 



which au Engine usually does, is Duty ; but as this word naturally 

 signifies what the engine ought to do, rather than what it does, we 

 should at least distinguish between the Theoretical and the Actual 

 Duty. 



The difference between the Theoretical and Actual Duty of a Ma- 

 chine arises from this : that a portion of the Laboring Force is ab- 

 sorbed in producing effects, that is, in doing work which is not reck- 

 oned as Duty : for instance, overcoming the resistance and waste of 

 the machine itself. And so lon<j as this resistance and waste are not 

 rightly estimated, no correspondence can be established between the 

 theoretical and the practical Duty. Though much had been written 

 previously upon the theory of the steam-engine, the correspondence 

 between the Force expended and the Work done was not clearly made 

 out till Comte De Pambour published his Treatise on Locomotive En- 

 gines in 1835, and his Theory of the Steam-Engine in 1839. 



Strength of Materials. 



Among the subjects which have specially engaged the attention of 

 those who have applied the science of Mechanics to practical matters, 

 is the strength of materials : for example, the strength of a horizontal 

 beam to resist being broken by a weight pressing upon it. This was 

 one of the problems which Galileo took up. He was led to his study 

 of it by a visit which he made to the arsenal and dockyards of Venice, 

 and the conclusions which he drew were published in his Dialogues, 

 in 1633. In his mode of regarding the problem, he considers the 

 section at which the beam breaks as the short arm of a bent lever 

 which resists fracture, and the part of the beam which is broken off 

 as the longer arm of the lever, the lever turning about the fracture as 

 a hinge. So far this is true ; and from this principle he obtained re- 

 sults which are also true ; as, that the strength of a rectangular beam 

 is proportional to the breadth multiplied into the square of the depth : 

 — that a hollow beam is stronger than a solid beam of the same mass : 

 and the like. 



But he erred in this, that he supposed the hinge about which the 

 breaking beam turns, to be exactly at the unrent surface, that surface 

 resisting all change, and the beam being rent all the way across. 

 Whereas the fact is, that the unrent surface yields to compression, 

 while the opposite surface is rent ; and the hinge about which the 

 breaking beam turns is at an intermediate point, where the extension 



