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locality, affords a full explanation of curious phenomena which have 

 been observed by many in failing to repeat Foucault's admirable 

 pendulum experiment. When the mode of suspension is perfect, we 

 have \=0 ; but in many attempts to obtain Foucault's result, there 

 has been an asymmetry in the mode of attachment of the head of 

 the cord or wire used, or there has been a slight lateral unsteadiness 

 in the bearings of the point of suspension, which has made the 

 observed motion be the same as that expressed by the preceding 

 solution, where X has some small value either greater than or less 



than w, and n has the value * /^. The only case, however, that 



need be considered as illustrative of the subject of the present com- 

 munication is that in which o> is very great in comparison with n, 

 To obtain a form of solution readily interpreted in this case, let 



-ll- J* 



The preceding solution becomes 



) +B cos {(w-< 



To express the result in terms of coordinates I, /, with reference 

 to fixed axes, instead of the revolving axes OX, OY, we may assume 



> =xcos tat y sin ut, jj=a?sin w+y cos ut. 



Then we have 



= A cos (p* + a) + B cos (W-/3) 



/Bsin{(w-< 



i}4/Bsin{(w a)t + P\)coswt. 



When w is very large, e and / are both very small, and the last two 

 terms of each of these equations become very small periodic terms, 

 of very rapidly recurring periods, indicating a slight tremor in the 

 resultant motion. Neglecting this, and taking a = and /3=0, as 

 we may do without loss of generality, by properly choosing the axes 



