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LXV. The Measurement of Time and oilier Magnitudes. 

 By ^"okman Campbell, Sc.D* 



IN your September issue Dr. L. Silberstein opens a dis- 

 . cussion of the measurement of time by the statement that 

 all systems in common use involve the assumption that some 

 body is moving or rotating uniformly, and therefore depend 

 on the measurement of space. I believe this statement to 

 be untrue, and still more untrue the statement implied, 

 that time-measurement independent of space-measurement 

 is impossible except by some such artificial and elaborate 

 method as he proposes. In passing I may say that all 

 systems of measurement which, like his, depend upon 

 " mental " experiments appear to me supremely unsatis- 

 factory: it was by relying on mental experiments that the 

 ancients succeeded so admirably in confusing themselves and 

 their successors. It is quite possible to measure time without 

 any measurement of: space by the use of experiments which 

 can be performed and not merely thoughtf . 



Let us consider first the measurement of another mag- 

 nitude, " weight in air at a certain time and place/' briefly 

 called weight. Three definitions are required: — (1) A certain 

 definite body is stated to have the weight 1. (2) Bodies are 

 defined to be equal in weight if, when placed on the opposite 

 pans of a balance of certain construction, they balance. 

 (3) A body C is defined to have a weight which is the 

 sum of the weights of A and B when, if A and B are 

 placed together in one pan, C, placed in the other, balances 

 them. 



We can now proceed to find bodies of weight 2, 3, ... . 

 By (2) we find a body of which the weight is equal to that of 

 the unit, i. e. 1. We place this body in the pan with the 

 unit, and by (3) find a body which has the weight 2— and 

 so on. To find a body of weight q/p we have to find p 

 bodies, such that their weights are equal by (2), and such 

 that, when all placed in the same pan, they balance the 

 weight q. 



Such is the method actually used for making a standard 

 series of weights. (The consideration of the subsequent 

 adjustment of the weights to " correct errors " would lead us 



* Communicated by the Author. 



f In a treatise which 1 hope will be published early next year I shall 

 discuss in full the theory of measurement. The remarks offered here 

 neglect many important and interesting considerations, but I believe they 

 are sufficient to throw doubt on Dr. Silberstein's views. 



