Mr. H. Lamb on the Basis of Statics. 189 



Newton's Second Law, yet the principle of the transmissibility 

 of force is retained, and employed in deducing the rules for 

 the composition of parallel forces, &c. In the method followed 

 by Thomson and Tait the particular dynamical principle 

 adopted as a basis is that of Work, in the form of Lagrange's 

 principle of virtual velocities. This is of course the method 

 most consistent with the plan of their book, which is to exhibit 

 the connexion between the various branches of mathematical 

 physics in the light of the doctrine of the Conservation of 

 Energy. But an alternative presentment of the subject seems 

 desirable, and, at all events for the purposes of elementary 

 teaching, even necessary. It should be remarked, too, that 

 Thomson and Tait follow the ancient practice of regarding 

 Statics as a subject which deals primarily with ideal " rigid " 

 bodies, and that accordingly, in their treatment of Hydrostatics 

 &c, they retain (as I cannot but think most unfortunately) 

 the artifice of an imaginary " so^dification " of the portions 

 of matter to which the fundamental propositions are to be 

 applied. 



It is with all due deference that I venture to suggest a new 

 point of departure in a subject which has been handled by so 

 many distinguished writers. I am of opinion that the true 

 and proper basis of Statics is to be sought for in the principles 

 of linear and angular momentum. Regarding Statics as the 

 doctrine of the equivalence of forces, I would define the word 

 "equivalent," and say that two sets of forces are "equivalent" 

 when, and only when, they produce the same effect on the 

 linear and on the angular momentum of any material system 

 to which they may be applied — i. e. when they produce the 

 same rate of change of momentum in any assigned direction, 

 and the same rate of change of moment of momentum about 

 any assigned axis. In the same way two sets of forces would 

 be said to be "in equilibrium" when they produce no effect 

 on either the linear or the angular momentum of any system. 

 On this basis the fundamental theorems of Statics can be 

 developed with great ease ; and there is of course no qualifica- 

 tion as to the physical nature of the system on which the 

 forces are supposed to act. The particular status of rigid 



that this assertion is only correct so long as we are dealing with forces 

 acting on a particle. When we have to do with a body of finite size, all 

 that the most liberal interpretation of the second law can tell us is that 

 two forces represented by two lines AB, AC are equivalent to a force 

 represented by some line equal and parallel to the diagonal AD of the 

 parallelogram constructed on those lines. To prove that the resultant 

 must act in the line AD we require the third law as well. A good deal 

 of confusion seems to have arisen here (and elsewhere in our subject) 

 from the vague way in which the word "equivalent" has been used. 



