OF MAGNETIC DECLINATION AT GOTTINGEN. 



591 



years, — manifest that even six years' observations are not suffi- 

 cient to give with certainty the mean value of the difference be- 

 tween the dechnations at 8 a.m. and 1 p.m., although they leave 

 no doubt as to the general progression. 



The following periodical function, which represents the mean 

 of each month, derived from the six years' observations, is to 

 be regarded, therefore, only as an attempt to reproduce this 

 progression by a formula ; longer continued observations may 

 stiU perhaps occasion considerable alteration in the coefficients. 

 In this formula cf) denotes the number of months from the 

 middle of April multiplied by 30°. 



11' 7"-0+I24"-0 cos <p+23y"-4 sin <p+84"-8 cos 2 (p— 63"-6 sin 2 (p 

 + 20"-4 cos 3 (p+9"-5 sin 3 (p+23"-5 cos 4 (p— 6"-0 sin 4 (p 

 + 0"-8 cos 5 <p— 26"-4 sin 5 ip+2"-5 cos 6 <p. 



In the second period of three years, eight exceptional instances 

 have occurred of days on which the declination was greater at 

 8 A.M. than at 1 p.m. ; of these seven were in winter months, and 

 only one in the summer months, being almost the same propor- 

 tion as in the former three years. The following table contains 

 the days, and the amount, by which the forenoon declination 

 exceeded that of the afternoon. 



It is worthy of notice, that of the twenty-two exceptional 

 cases of this nature which have occurred since the commence- 

 ment of the observations in 1834, only two (December 15th, 

 1837, and February 14th, 1839) have been occasioned by a de- 

 rangement of the declination in the afternoon; there are two 

 others, in which the anomaly was produced by derangements 

 both in the forenoon and afternoon; whilst the remaining 

 eighteen originate in considerable irregularities in the forenoon 

 declination. We may hence conjecture that great anomalies 

 are of more frequent occurrence in the forenoon than in the 

 afternoon, which appears to be confirmed by the fluctuations 

 on successive days, which will be discussed in the sequel. 



In comparing the mean declination of each month with that 



