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"^ a.m., and their least average value about lO*" p.m., the 

 least value being less than half the largest. The average negative excursion is least about 10'' 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'' and 10'' p.m. ; the time of minimum is not well marked ; minima 

 occur about 1^ a.m. and S^ p.m., and there is the appearance of a secondary maximum about Q"^ 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 fi-om the arithmetical means as errors in the ob- 

 servations of a constant quantity, and to consider the square I'oot of the mean of the squares of these differences, 

 as the mean disturbance, corresponding to the mean en-or 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 wei'e 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 hj-pothesis 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. 



