cmicernlng the Act-tons of Machines. 73 



raises it move over equal distances. The motion of the weight is 

 here mistaken for the distance through which its gravitation is 

 overcome ; its absolute motion, for its motion in altitude : now, 

 it is well known that the force requisite to drag a body up an in- 

 clined plane, is to the weight of that body as the height of the 

 plane is to its length ; and therefore the principle of virtual ve- 

 locity is here adhered to. This misconception is palpable and 

 easily corrected ; the motion of the machine does not alter the 

 proportions of the forces. But, in the case of the bent lever, the 

 error must be more involved, since it has crept from the work- 

 shop to the lecture-room, and has been promulgated where 

 sound knowledge and accurate ideas ought to have rewarded 

 the labours of the student. The arcs, we are told, which the 

 ends of the arms describe, are proportional to the lengths of 

 these arms, while the balancing forces are not proportional, in- 

 versely, to the same lengths. Here, again, the absolute motion 

 of the point of attachment is mistaken for the distance through 

 which the pressure is overcome. If, however, the objector's ca- 

 pacity be not entirely exhausted by the immense profundity of 

 this remark, he will reply, and with justice too, that even esti- 

 mating the motions in the directions in which the pressures act, 

 the rule does not hold good. 



For the removal of this mighty difficulty I must summon all 

 my strength. Accustomed to handle tools (I speak not for my- 

 self only, but for every devotee of true philosophy), accustom- 

 ed to handle tools admirably adapted for facilitating researches 

 of this nature, and now called upon by the circumstances of 

 the case to lay these tools aside and to venture on the question 

 with unappareled hands, I cannot altogether divest myself of 

 repugnance to the task. To render it, however, more inviting, 

 I shall make the question as general as possible, and, without 

 confining myself to this or to any other individual case, apply 

 my remarks to those machines generally, in which the forces 

 vary with the positions of the parts. 



Conceive that for a given position of such a machine, the 

 pressures are so arranged as to balance each other, and then 

 let the machine suffer a displacement. If this displacement be 

 considerable, the equilibrium will be materially disturbed, and 

 the estimate of the motions, far from giving information con- 



