618 DR W. PEDDIE ON 



numbers, 46*1 has to be added to the first five positive elongations, and then 20 has to 

 be subtracted from all positive readings ; and the first negative reading must be 

 called —1*5, all the negative readings being then subtracted from 20. 



The waves which are observed on the experimental curves in fig. 1 are due to slight 

 pendulum- wise oscillations of the wire, which could not be avoided when the torsional 

 oscillations were large. They do not appear in the middle curve. 



Test of the Accuracy of the Formula. 



In Table VIII. a comparison of the results of observation with the results obtained 

 by calculation is given for all the experiments in the three series. The upper row 

 contains values of x, and succeeding pairs of rows contain the logarithms of observed 

 and calculated values of y corresponding to the given values of x — the calculations 

 being made from the formula 



//"(.'• + a) = b, 



and the values of a, n, and b being those given in Tables IV., V., and VI. In the first 

 series of experiments the observed value of y usually exceeds the calculated value at 

 the end of the first oscillation (x=l) by more than a possible error of observation, and 

 sometimes, at the end of the second oscillation, the difference considerably exceeds one 

 per cent, of the value of y. But it must be recollected that the above formula, from 

 the point of view of theory (see former paper), can only be regarded as strictly applic- 

 able when two or three oscillations have taken place. With these exceptions, the results 

 of observation and calculation may be regarded as being within the limits of possible 

 observational error. When x is large, y is small, and the difference between observed 

 and calculated values of y sometimes exceeds one per cent, of the value of y, but then 

 so also does the possible observational error. 



Critical Angle of Oscillation. 



We have found that, in the present series of observations, the product of the 

 quantities n and b may be regarded as being constant. Yet it is easy to see that this 

 is a mere accidental circumstance depending on the particular unit in terms of which 

 the angle of oscillation was measured. In terms of the unit here used we may write 

 the equation in the form 



ny"(.c. + a) = H, 



where B is an absolute constant. Suppose now that we choose the unit k times smaller. 

 Then the new y (y f say) is k times the old, and we get 



iil:"y"(.c + a) = B' = B/,'", 



bo that the most general form in which the equation can be put is 



>/"(,■ + a ) = U" (1) 



