MAGNETIC OBSERVATIONS. 



53 



Let K represent the mean of all the logarithms of K in the above table ; then 



K = 1.18320 

 at a temperature of 79. 5. Now, assuming 



Log. 7f T = K, + (T 79.5) AK 

 we have 



= K log. K v + (* 79.5) AK 



and each value of log. A' T , given in the table above, will furnish one equation of 

 condition for the determination of AK, as follows : the absolute terms being in 

 units of the fifth place of decimals. 



o = 142 6.5 

 =+ 73+ 8.2 

 = 37 + IO -5 

 o = 157 4- 10. 

 o = + 50 4- 18.5 

 0=4- 5 + 



o = 241 3.3 



o = 95 5-5 

 o= + 25 2+ 5.2 

 0=4-263 9 5 

 = + 253 9.5 

 0=4- 49 26.0 



From these equations of condition we obtain, by the method of least squares, 

 the normal equation 



= 5856.2 + 1646.0 AK 

 whence 



Log. AK= 0.55119 



and finally 



or 



Hence we have 



or 



Log. /C = 1.18320 + (r 79.5) 0.0000356 0.000368 



K T = 15.248 + (t 79.5) 0.00125 _|- 0.0129 



n-Kv = 150.49 -f (T 79.5) 0.01234 



Log. 7t 2 /f T = 2.17750 + (T 79.5) 0.0000356 



In Order to facilitate the reduction of the observations of vibrations, the follow- 

 ing table has been computed from the formula last given. It furnishes the value 

 of log. 7i 2 Kv to the argument T. 



. The Constant P, depending upon the distribution of the magnetism in the mag- 

 nets C 32 and S 8, was determined by means of the formula 



A- A 

 ~'A_A 



r~ z ~r 72 



