604 



On the Bates of a Rocking Watch. 



measure variations of the attraction of gravitation, fig. 3 

 shows at once that the short period of the above watch would 

 be unavailable for such a purpose, the changes of rate within 

 the range of observation being too small. The conditions 

 for the long period, however, are worth a statement. The 

 effect of adding; ballast is an increment both of the moment 

 of inertia and of the torque acting on the compound pendulum. 

 The following table contains the decrements of the acceleration 

 •of gravitation Sg/g, corresponding to the increments of 

 ballast for each of the series of experiments made. 



Table III. — Equivalent decrements of Gravitation. 



Sk/7c 



fylff- 



Eates, sec/hour, 

 long period. 



+ •000 

 •013 

 •023 

 •030 

 •046 

 •091 

 ■240 

 •380 



-•ooo 



-•004 

 -•008 

 -■009 

 -•016 

 -•033 

 - 071 

 -•104 



-39-81 

 -397 



-46-0 



-58-3 



-75-3 y 



-135-Ot 



-1993^ 





These data show that the long period passes toward in- 

 finity at an accelerated rate with Sg/g ; for if the observations 

 be grouped as suggested by the brackets, the successive 

 increments of rate are 11 s./h., 16 s./h., and 19 s./h., respec- 

 tively, for each per cent, of decrement of Sg/g. If the mean 

 value be taken, the loss of a second per day on the rocking 

 w r atch is equivalent to a decrement of gravitational accelera- 

 tion of &g/g = '00003. Even if one second per day is 

 trustworthy on a good watch, this datum is about 200 times 

 as large as the differential effect of a olobe of lead 50 centim. 

 in diameter, on the watch swinging immediately above and 

 immediately below it. 



The case is somewhat more favourable when the variations 

 of acceleration met with in a gravitational survey are in 

 question. Quoting from the interesting digest of a survey 

 across North America due to Prof. Mendenhall,* it appears 

 that the surface variations encountered lie within an interval 

 of 13/10 4 , or 43 seconds per day on the above rocking watch ; 

 while the variations reduced to sea- level lie within 32/10 5 , 

 about 11 seconds per day on the watch. 

 Brown University, 

 Providence, IL'S.A. 



* Mendenhall, American Journ. xlix. p. 81 (1895). 



