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XXXIII. On the Measurement of Time — a Rejoinder to 

 Dr. N. Campbell. By L. Silberstein, Ph.D., Lecturer 

 in Math. Physics at the University of Rome *. 



Tf 1HE paper on " A Time-Scale, etc.'' by the present 

 JL writer, published in the September issue of this 

 Magazine, opens the investigation by a statement that the 

 principle of common time-scales amounts to this : — -A certain 

 kind of motion (translatory or rotatory) is declared to be a 

 uniform motion ; the path is then cut up by means of 

 compasses etc. into a series of equal segments (or angles) and 

 the instants of passage of the mobile through the divisions 

 of this metrical scale are taken as £ = 0, 1, 2, 3, and so on. 



Dr. N. Campbell, in the November issue of the Phil. Mag. 

 (pp. 652-4), believes "this statement to be untrue. " It will 

 be my duty to show that it is true. In the second place, 

 Dr. Campbell believes "still more untrue" (as if truth were 

 liable of gradations) " the statement implied, that time- 

 measurement is impossible except by some such artificial and 

 elaborate method as he [Silberstein] proposes/' Now, 

 concerning this second point, I have not said nor meant to 

 imply that other methods independent of space-measurement 

 were impossible. I simply proposed one, without excluding 

 the possibility of other methods being invented by others. 

 Thus I have nothing more to say about this second point. 

 A third point, however, is that Dr. Campbell offers us his 

 own views on the measurement of time, and these are so 

 palpably unsatisfactory as to require but a few words to 

 be refuted. : 



But let me first attend to the first point. Now, my state- 

 ment, quoted at the outset, is not only logically true (that 

 is to say, that a theory of chronometry based on " uniform " 

 motion and paths or angles carved up into " equal " parts 

 would be a possible logical theory), but also, which is 

 of great importance, historically true, the two principles, 

 uniformity and rigid subdivision or transfer, being the 

 dominant and basal features of every practical chronometry 

 since times immemorial and up to, and including, our own 

 days. In fact, the most ancient measurement of time, as 

 practised by Babylonians, Assyrians, Egyptians, and whom 

 not, was based on the assumption of uniformity of rotation 

 of the heavenly sphere round the Earth, and on a rigid, 

 metrical subdivision of the angles involved in this pheno- 

 menon. Massive columns were erected and carefully kept 



* Communicated by the Author, 



