64 Professor Forbes's Experiments on 



Table II. 



Initial Semi. Arc = « = 10°. Initial Semi- Arc -a.- 20°. 



No. of Vibrations observed = n = 100. No. of Observations observed = n = 300. 



m Additive Log. m Additive Log. 



70 9-99978 70 9*99969 



80 « 9-99975 80 9*99960 



90 9-99972 90 9*99953 



100 9-99970 100 9*99946 



110 9-99967 110 9*99939 



120 9*99965 120 9*99933 



130 9-99962 130 9*99926 



I have every reason to think this correction to be accurate 



on the whole : the agreement of the two modes of observation 



being in general very close. 



15. III. Temperature. — This extremely important correc- 

 tion it is very difficult to determine. Without an accurate 

 estimation of it, it would be vain to attempt to decide whether 

 or not the magnetic energy varies with height ; because at great 

 elevations the temperature being always diminished, the inten- 



M = 1 + - l + r2 + r * + r * - r * (l '~ 1) = 1 + "* 



16 * n i ' 16 (1 ~r z )n 



Hence the mean duration of n vibrations, 



~2 1 r 2n . / ct \2 . 



Fromthe Oth to the nth is 1 + -^ . !_ = l + ( — ).A 



16 (1 — r 2 n) V 4 / 



10th to the (n+ 10th) is =1 + /_* Y r iox2.A 



(because the initial arc instead of ct is ct r 10 ) 

 I 20th to the (n+ 20th) is =1 + (— V r 20*2. A 



60th to the (n+ 60th) is = 1 +(.fLY ,6o*e a 



And the mean value of these deviations is 

 1 I /"Y A l+r 20 +^...-r-r^ / * x 1 - r'« 



1+ Vi7 a 7 =1+ VT) 2<A -7 (i-^) 



The concluding factor may be called B ; and substituting the value of r 

 from the text, or (j})" 1 * we have 



2 ft 140 



A = _ a, B -~ » 



r being independen 

 Corrected time = 



whence the Tables are computed. 



(the last factor being independent of »), and we have 



Observed Mean Time 



i ! 



.A.B. 



0+t) 



