52 



REPORT ON 



t = time in which the magnet makes one vibration at the temperature <r (corrected 



for chronometer rate, arc of vibration, and torsion.) 

 t' = time in which the magnet, loaded with the inertia ring, makes one vibration 

 at the temperature <r (corrected for chronometer rate, arc of vibration, and 

 torsion) 

 Then 



' d? + d e 



ir T =-^[i + 2 £ (r-* )]j^±^ 2 } 



The inertia ring used in making my observations was of bronze. Mr. Joseph 

 Saxton, Assistant Superintendent of the Office of Weights and Measures, very 

 obligingly measured and weighed it, with the following result : 



Internal diameter == 2.385 inches = 0.19875 foot 

 External diameter = 2.947 inches = 0.24558 foot 

 Weight = 798.72 grains 

 the temperature of the ring being 74° Fah. 



Hence, assuming the coefficient of expansion for an increase of temperature of 

 1° Fah. in the metal of this ring to be 0.0000105, we find by the formula v given 

 above 



K\ = 9.9601 + (* — 50°) 0.000209 

 or 



Log. K\ = 0.99827 + (* — 50°) 0.0000091 

 The following table contains all the times of vibration which were observed for 

 the purpose of determining the moment of inertia of the magnet, together with the 

 computation of the corresponding values of log. K from them. The value of t' was 

 always observed either immediately before, or immediately after, the corresponding 

 value of t which was to be- used with it. This was done in order to have the tem- 

 perature in both cases as nearly as possible the same, so that the correction neces- 

 sary to reduce V to the same temperature as t was always very small. Then having 

 a sufficient number of values of E, obtained from observations made at widely 

 different temperatures, the value of A K was easily found. 



Date. 



- 



Log. ft 



Log. i* 



Log. {t'l—P) 



Log/JLJ) 



Log. K\ 



Log. K r 



Oct. 28, 1865 



73-o 



1.88210 



1.66424 



1.47811 



O.18613 



0.99849 



1. 18462 



Nov. 16, 1865 



87.7 



1.72767 



1. 50891 



1.32504 



CI8385 



0.99862 



1. 18247 



Nov. 28, 1865 



90.0- 



1-72835 



1.51108 



1-32345 



O.I8763 



0.99864 



1. 18627 



Dec. 13, 1865 



89-5 



1-74459 



1.52673 



1.34060 



O.18613 



0.99864 



1. 18477 



Dec. 27, 1865 



98.0 



1. 76681 



1. 54810 



1. 36412 



O.I8398 



0.99872 



1.18270 



Jan. 18, 1866 



87.2 



1.77770 



*-559 21 



1.37467 



O.18458 



0.99861 



1-18315 



March 19, 1866 



76.2 



1.75849 



1.54101 



1-3539* 



O.187IO 



0.99851 



1.18561 



April n, 1866 



74.0 



1.75824 



1. 54019 



1-35454 



O.18565 



0.99850 



1-18415 



May 30, 1866 



84.7 



I-673SI 



1-45405 



1. 27196 



O.18209 



0.99859 



1. 18068 



Nov. 2, 1866 



70.0 



1.90424 



1.68479 



1.50268 



O.I82II 



0.99846 



1. 18057 



Nov. 2, 1866 



70.0 



1. 90391 



1.68450 



1.50229 - 



O.I822I 



0.99846 



1. 18067 



Nov. 2, 1866 



53-5 



1.92843 



1.70989 



i-5 2 548 



0.1 8441 



0.99830 



1.18271 





79-5 













1. 18320 



