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



The manner in which the fundamental propositions are 

 presented by all but the most recent writers is too familiar to 

 need any long recital. Certain principles are assumed as the 

 result of experience ; and the parallelogram of forces and the 

 other leading propositions of Statics are then deduced from 

 these by purely mathematical reasoning. Conspicuous among 

 these principles is that of the " transmissibility of force," 

 which asserts that a force acting at any point A of a body 

 may be supposed applied indifferently at any other point B in 

 its line of action. This principle is usually stated with a 

 certain amount of hesitation and qualification. We are told 

 that it is not generally true, unless B be " rigidly " connected 

 with A ; and when, as sometimes happens, we wish for 

 mathematical purposes to transfer the force to points not so 

 connected, we are (in effect) told to conjure up before our 

 minds the vision of an imaginary " rigid " framework attached 

 to the body with which we are dealing. When the desired 

 conclusion has been reached, this framework is conveniently 

 dismissed to the void whence it came. Of a piece with this 

 artifice is that which, in the application to Elasticity, Hydro- 

 statics, &c, consists in imagining certain portions of matter 

 to become " solidified." Now all this seems very unnatural. 

 In the first place there are no " rigid " bodies, in the sense in 

 which the word is defined by the writers here criticised. The 

 fundamental propositions of Statics ought surely to admit of 

 being stated in such a way that they shall be true, accurately 

 and without any manner of qualification, of matter such as we 

 find it. Again, it ought to be possible to establish the law T s of 

 equilibrium &c. of one body A without introducing, even in 

 imagination, another body (framework) B, even if the proper- 

 ties attributed to B were real and not fictitious. 



Since the publication of Thomson and Tait's i Natural 

 Philosophy ' the methods here recalled have fallen into some 

 discredit. These writers first pointed out that a sufficient 

 appeal to experience having been made once for all in the 

 Laws of Motion, it was unnecessary and unphilosophical to 

 introduce a fresh set of experimental data as a basis for Statics, 

 which is after all but a branch of Kinetics. Although the 

 propriety of this view has been universally acknowledged, no 

 subsequent writer has, so far as I know, ventured to follow 

 resolutely the path thus indicated, and to develop a thoroughly 

 consistent doctrine of Statics based solely on the Laws of 

 Motion and their consequences. Thus in a text-book otherwise 

 admirable we find that although the truth of the parallelogram 

 of forces is asserted* to be an immediate consequence of 



* Attention seems hardly to have been sufficiently directed to the fact 



