44 KINEMATICS. [87. 



simplicity, as a practical working hypothesis, and it was found to work 

 well. From the logical point of view we may strengthen its probability 

 by the following considerations. 



87. The origin of our notion of time as a measurable quantity lie 

 in the subjective sensation that teaches us instinctively to distinguish 

 between shorter and longer intervals of time. This feeling of time is 

 of course (just as in the analogous case of muscular force) far too vague 

 and indefinite to admit of measurement. But it is sufficient to convince 

 us that, approximately, the lengths of successive days are equal. With? 

 far greater approximation can we judge by our time-feeling that the 

 oscillations of the pendulum of a clock are nearly isochronous. Let us 

 combine these two entirely independent facts. Careful observation will 

 show that the number of oscillations made by the pendulum in the 

 interval between two culminations of the mean sun is almost precisely 

 the same for every mean day. Moreover, the agreement becomes the 

 more perfect the more we eliminate any causes that tend to disturb 

 the isochronism of the pendulum. It will therefore be reasonable to 

 conclude that the mean solar day must have a very nearly constant 

 length. 



But it is to be kept in mind that this is an empirical fact and hence 

 not absolutely true, but only within the limits of the errors of observa- 

 tion. Indeed, certain considerations concerning the friction caused 

 by the tides make it probable that the angular velocity of the earth is 

 diminishing very slowly.* 



* See O. RAUSENBERGER, Analytische Mechanik, I., Leipzig, Teubner, 1888, p. 14; i 

 H. STREINTZ, Physikalische Grundlagen der Mechanik, Leipzig, Teubner, 1883, p. 

 8 1 sq.; E. BUDDE, Allgemeine Mechanik, I., Berlin, Reimer, 1890, p. 33; THOMSON 

 and TAIT, Natural philosophy, I., London, Macmillan, 1879, p. 460; J. C. MAXWELL, 

 Matter and motion, New York, Van Nostrand, 1878, p. 27 and p. 60.; K. PEARSON,. 

 Grammar of science, London, Scott, 1892, pp. 217-^230. 



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