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LXXIX. Notes on the Method of Dimensions. 

 By E. Buckingham *. 



1. Introduction. 



THE dimensional method of analysing problems in 

 Physics, which we owe to the late Lord Rayleigh, 

 somewhat resembles the methods of Thermodynamics in 

 being very simple in principle but sometimes a little 

 puzzling in practice. To the initiated, all the information 

 obtainable from dimensional considerations is often evident 

 upon mere inspection, so that any formal and detailed 

 account of the reasoning appears quite superfluous ; and 

 Lord Rayleigh's numerous applications are sometimes so 

 concisely described that the results seem rather like magic. 

 But while a closer study of his solutions can only increase 

 our admiration, it will certainly lead the average reader to 

 wish for a less intuitive and more systematic procedure for 

 obtaining the same sort of result. 



Such a routine procedure is provided by formulating 

 the requirement of dimensional homogeneity as a general 

 algebraic theorem, which was first published by Ria- 

 bouchinski -\, and which will be referred to as the 

 IT theorem. It may be stated as follows : — 



(I.) Let it be assumed that n quantities Q h Q 2 , . . . Q w , 

 which are involved in some physical phenomenon 

 as variables, or as potentially variable though 

 actually constant, are connected by a complete 

 relation, i. e. by an equation 



F(Qi, Q a , . . • , Q„) = .... (1) 



containing these quantities and nothing else but 

 pure numbers. 



(IL) Let k be the number of fundamental units required 

 for specifying the units of the Q's. 



* Communicated by the Author. 



t VAerophile, Sept. 1, 1911 , and Koutchino Bulletin, No. 4, Nov. 1912. 

 A reference to the first of these papers appeared in the Annual Report 

 of the British Advisory Committee for Aeronautics for 1911-12, p. 260, 

 abstract 134. Guided, no doubt, by the hint contained in this abstract, 

 the present writer came upon substantially the same theorem and 

 described it, with illustrative examples, iu the ' Physical Review ' for 

 October 1914 (vol. iv. p. 345). The statement of the theorem given in 

 the present paper does not differ materially from Riabouchinski's, 

 except in that he confined his attention to mechanical quantities. 



