Magnetic Declination. 



351 



The average value of the excursions, therefore, varies considerably : the positive excursions from the nor- 

 mal mean have their greatest average value about 9 h a.m., and their least average value about 10 h p.m., the 

 least value being less than half the largest. The average negative excursion is least about 10 h a.m., and greatest 

 about 9 p.m (using the interpolated epoch), the least average being less than a third of the greatest. The least 

 positive and negative averages have the same value, but the greatest negative average is fully a third greater 

 than the greatest positive average. The average value of all the excursions from the normal mean is a maxi- 

 mum (using interpolated epochs) between 9 h and 10 h p.m. ; the time of minimum is not well marked ; minima 

 occur about 7 h a.m. and 5 h p.m., and there is the appearance of a secondary maximum about 9 h a.m. The 

 greatest average is to the least in the ratio of about 3 to 2. 



Probable Disturbance of Magnetic Declination. — In order to determine the probable disturbance for each 

 hour of the day, Dr Lloyd has proposed to use the differences from the arithmetical means as errors in the ob- 

 servations of a constant quantity, and to consider the square root of the mean of the squares of these differences, 

 as the mean disturbance, corresponding to the mean error in the calculus of probabilities. It is obvious that 

 the ordinary methods of the calculus of probabilities could not be employed if the probable error were con- 

 sidered with reference to the normal mean, which is not the arithmetical mean ; considering the probable error, 

 however, with reference to the arithmetical mean, it is certain from the foregoing conclusions that the distribu- 

 tion of the individual differences or errors is not such as will satisfy the hypothesis of the observations of a con- 

 stant quantity. The differences are not distributed equally, positively and negatively ; nor is the difference 

 from such a distribution constant : a new hypothesis for the mode of distribution would be requisite for each 

 hour. Independently of this consideration, it will be found from the following results that the number of 

 errors occurring within certain limits is not satisfied by the usual function of the errors obtained from the cal- 

 culus of probabilities. 



The following Tables may be considered a contribution to the theory of the distribution of disturbances of 

 the magnetic declination, with respect to the arithmetical means of all the observations. 



TABLE XVIII. — Number of Positive and Negative Differences which occur between the limits of 

 successive Minutes for each Month, and for the year 1844. 





0' 



1' 



2' 



3' 



4' 



5' 



6' 



V 



8' 



9' 



10' 



15' 



20' 



25' 



30' 



Month. 



to 



to 



to 



to 



to 



to 



to 



to 



to 



to 



to 



to 



to 



to 



to 





1'. 



2'. 



3'. 



4'. 



5'. 



6/ 



7'. 



8'. 



9'. 



10'. 



15'. 



20'. 



25'. 



30'. 



40'. 



Jan. \ 



184 



103 



22 



13 



5 



6 



5 



1 



2 















154 



85 



38 



11 



9 



4 



3 





1 



1 





1 









Feb. i + 



157 



92 



38 



13 



5 



1 



2 



1 



1 





2 











158 



76 



22 



12 



4 



3 



4 



2 





2 



3 



1 









March j + 



102 



105 



55 



22 



9 



8 



6 



4 



1 



3 



5 



1 









142 



73 



29 



17 



6 



6 



8 



2 



3 



1 



10 



2 



2 



1 





April { + 



135 



80 



38 



14 



12 



6 



4 



1 



2 



1 



7 



2 









135 



85 



49 



22 



9 



4 



5 



3 



3 





3 







1 





May { + 



136 



85 



65 



22 



4 



5 





1 





1 



3 











156 



82 



48 



20 



4 



4 



4 



2 







4 



1 





... 





June i 



199 



81 



19 



7 



6 



3 







1 



1 













161 



63 



38 



11 



6 



2 



1 







1 













July { + 



167 



88 



29 



17 



12 



7 



3 







1 













148 



90 



54 



14 



9 



2 



4 



1 

















Aug. { + 



132 



105 



34 



21 



13 



10 



2 



1 



2 



1 



1 











147 



71 



54 



28 



11 



5 



2 



6 





1 













Sept. j + 



117 



95 



60 



21 



9 



7 



2 



3 



1 





2 



1 









111 



83 



40 



13 



10 



5 



6 



2 



2 



1 



5 



2 









Oct. 1 + 



108 



63 



50 



35 



14 



1 



9 



2 



5 



4 



3 



2 



1 



1 





116 



103 



74 



22 



12 



4 



6 



4 



1 





4 



2 





1 





Nov. | + 



87 



71 



66 



40 



18 



7 



4 



6 





1 



4 



1 









124 



108 



34 



18 



5 



8 



3 



3 



4 



1 



4 



1 



1 



2 



2 



Dec. I + 



178 



110 



32 



10 



5 



5 



1 



3 



1 















162 



70 



14 



10 



4 



4 



3 





2 



4 



1 





2 



1 





Year | + 



1702 



1078 



508 



235 



112 



66 



38 



23 



16 



13 



27 



7 



1 



1 





1714 



989 



494 



198 



89 



51 



49 



25 



16 



12 



34 



10 



5 



6 



2 



