1864.] 



Prof. Erman — Magnetic Elements at Berlin* 



219 



Gregorian epoch, T the absolute value of horizontal intensity with milli- 

 metre, milligram, and the second of mean time as unities, w the same in 

 unities of the Gaussian constants; the two values of T for 1805-5 and 

 1828*31 have been deduced from observed w, by T=0-00349216 . w. 



T and denote the observed time of oscillation of two magnets which, 

 since 1853-523 were carefdly guarded from the influence of other magnets ; 

 and therefore, marking by C, a, (d, C, a', unknown constants, e the basis 

 of hyperbolic logarithms, and taking ^j=^— 53*523, each value of t and 

 r' had to fulfil the equations 



(1+ae-^^i) . T' (1 + aW^i) .T* 



In the following list of observed values, the first is due to Humboldt ; 

 the twenty-eight following were obtained by Erman : — 



Date of 

 observation. 



Horizontal intensity, 

 T. 



Times of oscillation of 



Magnet I. 

 r. 



Magnet II. 

 r'. 





Observed. 



Calculated. 



Observed. 



Calculated. 



Observed. 



Calculated. 



1805-5 

 1828-31 

 1846-13 

 1849-59 



1853- 89 



1854- 59 



1856- 57 



1857- 54 



1858- 58 

 185960 

 1360-63 



1861- 52 



1862- 52 



1863- 80 



1-6452 

 1-7559 

 1-7751 

 1-7784 



1-6452 

 1-7437 

 1-7827 

 1-7867 



































3-i'696 

 3-1072 

 3-1168 

 311Co 

 3-1158 

 31229 

 3-1043 



3-1090 

 3-1141 

 3-1134 

 3-1131 

 3-1130 

 3-1129 

 31129 







1-7900 

 1-7900 

 1-7879 

 1-8035 

 1-7933 



1-7904 

 1-7913 

 1-7916 

 1-7917 

 1-79^2 



80082 

 8-0954 

 8-1193 

 8-1364 

 8-1223 

 8-0870 

 8-1258 

 8-1100 

 8-0975 



8-0056 

 8-1036 

 8-1104 

 8-1126 

 8-1132 

 8-1135 

 8-1138 

 8-1142 

 8-1151 



1-7972 

 1-7900 

 1-7929 



1-7917 

 1-7915 

 1-7911 







3-1148 



3-1135 



The calculated values result from the following most probable expressions 

 for T, and for those values of r and t which agree best with the contem- 

 poraneous T. 



I. T=l-61892 + 0*0057689 ^-0-0000481 19 



„ 2_ 17*3633 



• ' -{l + 0-07;592.e-B-^««-^x}.T \^.^^ 



TTT ,2_ 117*956 ( 



-|1 +0.09733 . c-ii6927.^t| J 



The expression I. appears liable to the probable errors, 



in first term, ±0*00126 "j 



in coefficient of t, +0'000065 V of a magnetic unity 

 in coefficient of t\ ±0*00000074 J 



53-523. 



