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



bodies in this method is as follows. As a matter of fact we 

 find that in many cases the bodies with which we deal 

 undergo deformations so slight that they may for many 

 purposes be ignored. When this is the case the fundamental 

 principles of Statics, obtained in the above way, are sufficient, 

 and enable us, in virtue of known kinematical theorems, to 

 obtain all the information we care about. In other cases 

 (fluids and flexible solids) these principles are equally valid, 

 but they are no longer sufficient, and additional experimental 

 knowledge has then to be sought for. 



A possible objection to the above method may be here 

 anticipated. It may be urged that, even granting its soundness, 

 it is altogether too difficult and abstruse for the purposes of 

 elementary teaching. I believe that, on examination, much 

 of this supposed difficulty will disappear, and that, on the whole, 

 the method will be found to be really much simpler than that 

 at present in vogue. The main difficulty is at the outset. 

 When the foundation of the method has once been laid, a 

 whole series of propositions, now usually obtained each by a 

 separate and often a complicated proof, follow as immediate 

 corollaries. It is, I think, now coming to be generally 

 admitted that some knowledge of Kinetics ought to precede 

 the study of Statics. Now the principles of linear and 

 angular momentum can be deduced (as in c Thomson and 

 Tait,' § 267) with great ease from the second and third laws 

 of motion, and constitute of themselves a valuable intellectual 

 acquisition. The first of these principles leads directly to the 

 parallelogram of forces as far as the magnitude and direction 

 of the resultant is concerned ; and the second principle, with 

 the help of Varignon's geometrical theorem of moments, fixes 

 its line of action. The rules for the composition of parallel 

 forces, the equivalence of couples of the same moment in 

 parallel planes, the reduction of a system of forces in one 

 plane, the various forms of the conditions of equilibrium, &c. 

 need no longer to be deduced by laborious processes from the 

 parallelogram of forces, but are simple and almost self-evident 

 corollaries from the fundamental principles of momentum. 

 It may be noticed, too, that the " transmissibility of force " 

 now receives an exact and perfectly general meaning, although 

 as a separate principle it has no proper place in our method. 



It seems unlikely that the views here advocated should be 

 altogether novel ; but the only approximation to them (a 

 remarkable one, however) which I have been able to discover 

 is in Professor Minchin's ' Statics,' § 94 (second edition). 

 If Professor Minchin had followed out to its legitimate con- 

 clusion the line of thought there indicated, and made it the 



