BUCKINGHAM: PHYSICALLY SIMILAR SYSTEMS 



347 



and a, b, and c the observed values, respectively, for the next 

 preceding, the actual and the next succeeding year. 



Fig. 1. 



The results of this study are represented graphically by the 

 two ''smoothed" curves of the accompanying illustration, the one 

 of American (eastern United States) temperatures, the other of 

 European (Gemian) rainfall, or, rather, water equivalent of the 

 total precipitation. Obviously, as the curves show, in this case 

 at least, the statistical results fully support and confirm the pre- 

 vious logical deduction, namely: That high annual average tem- 

 peratures in America must lead to correspondingly heavy precipi- 

 tation in Europe and, conversely, that persistently low average 

 American temperatures must be accompanied by more or less 

 correspondingly light European precipitation. 



In addition to the rainfall of Germany that of the north slope 

 of the Alps, and also of Holland, were independently examined, 

 and, as might have been suspected, all three found to vary in 

 substantially the same manner. 



As above implied, this result is only an earnest of the many 

 important meteorological inter-relations which the complete 

 investigation may reasonably be expected to reveal. 



PHYSICS. — Physically similar 

 Bureau of Standards. 



systems. E. Buckingham, 



1. Let n physical quantities, Q, of n different kinds, be so 

 related that the value of any one is fixed by the values of the 

 others. If no further quantity is involved in the phenomenon 

 characterized by the relation, the relation is complete and may be 

 described by an equation of the form 



(1) 



y^MQ'",Q\- 0> = 



