XL. Dimensional analysis

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Abstract
A re-examination is made of the physical assumptions underlying dimensional analysis, and suggestions are offered of a method of employing dimensional arguments which is less liable to error than those at present in vogue. The final conclusion is stated in § 10, the method advocated (which is not new, but the oldest method of all) in § 4. Incidentally some arguments by Jeans and Einstein, which seem to have been accepted as valid, are discussed. It is concluded that the former, while formally valid, are insignificant and do not really involve the conception of dimensions; and that the latter are completely fallacious.