94 TRANS. ST. LOUIS ACAD. SCIENCE. 



Reduction of Intensity Observations. 



The units used were foot, grain, second. 



The reductions for oscillations are indicated by the formulte, 



7T-k 



[.+^]r..(._o.] 



where t' z= temperature of the oscillation series ; 

 / ^ " " deflection " 



h . . . r 



\ -\ — -; IS the correction for torsion ; 



T' =: observed time of oscillation ; 



k = moment of inertia of the magnet ; 



m z=. the magnetic moment of the oscillating magnet ; 



H =1 the horizontal intensity of terrestrial magnetism ; 



T z=i the corrected time of oscillation ; 



g =z the constant of temperature. 



For the deflection series, 



-— = J j^3 tan z< (i_ — ), 



H r- 



where r ^=. the distance between the magnets ; 



u z=L angle of deflection, corrected for torsion and 



temperature ; 

 Z' ^ a constant, depending upon the distribution of 

 magnetism in the two magnets. 



At each station the mean of values log. —were taken, and the 



Jri 

 mean temperature of the two series was taken as the tempera- 

 ture of the deflecting magnet, to which temperature the oscilla- 

 tion series was reduced. This is sufliciently accurate when the 

 differences in temperature are small. 



For the Canton observations, however, the following reduction 

 was made : 



Calling u and u^ angles of deflection at temperatures / and /q, 



then 



sin u^ 

 sin u z= — 7- — 



