MAGNETIC OBSERVATIONS. 



53 



Let A" 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. 7T T = K + (t — 79°.5) AA" 

 we have 



= A" — log. K T + (t — 79°.5) AA" 



and each value of log. A" T , given in the table above, will furnish one equation of 

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

 units of the fifth place of decimals. 



o = — 241 — 3.3 AA' 



o = — 142 — 6.5 aAT 

 0= + 73 + 8.2AA' 

 o = — 307 + 10.5 aA" 

 = — 157 + 1 0.0 aA~ 

 o = + 50 + 18.5 aA' 

 o = + 5 + 7-7 ^AT 



o = — 95— S-S^AT 



0= + 25 2+ 5- 2 ^ A" 

 o = + 263 — 95 aAT 

 ° = + 2 53— 9-5 ^ K 

 0=+ 49 — 26.0 aA' 



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

 the normal equation 



= — 5856.2 -f 1646.0 AK 

 whence 



Log. A K— 0.55119 



AA= + 3.56 

 and finally 



Log. K r = 1.18320 + (r — 79°.5) 0.0000356 ± 0.000368 

 or 



K T = 15.248 + (r — 79°.5) 0.00125 ± 0.0129 

 Hence we have 



n-K* = 150.49 + (<r — 79°.5) 0.01234 

 or 



Log. tvIu = 2.17750 + (r — 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. n"K~ to the argument t. 



5°° 

 60 



70 

 80 

 90 



Log. 7r'jT T 



2.17645 

 2.17681 

 2.17716 



2.17752 

 2.17787 

 2.17823 



1° 



4 



2 



7 



3 



11 



4 



14 



5 



18 



6 



21 



7 



25 



8 



28 



9 



3 2 



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 



P= 



A' 



