OF MAGNETIC DECLINATION AT GOTTINGEN. 597 



+ 4 0"-4 cos $ + 121"-1 sin <f> + 39"-l cos 2 4> — 52"-2 sin 2 4> 

 + 7"-8 cos 3 <t)+0"-2 sin 3 c^ + 5"'0 cos 4 4) + 7"*2 sin 4 <{) 

 — 10'''-6 cos 5 <f) — 26"-yr sin 5 <Ji - 2"'4 cos 6 <^, 



where ^i denotes the number of months elapsed since the middle 

 of April multiplied by 30°. 



In eleven months we perceive a confirmation of the remark- 

 able result previously deduced from the consideration of the ob- 

 servations of the first three years, namely, that the forenoon and 

 afternoon declinations deviate from their mean values in oppo- 

 site directions. October is the only exception ; and, viewing 

 the small amount of the differences in that month, and the 

 degree of uncertainty which still remains, this exception may 

 perhaps disappear when the observations shall have been longer 

 continued. In the four winter months, November to February, 

 the forenoon declination is greater, and the afternoon declina- 

 tion less, than their respective mean values ; and both these 

 circumstances contribute, during this portion of the year, to 

 bring the whole difference below its mean value. From March 

 to September the opposite effect takes place. These opposite 

 deviations, moreover, being, on an average, nearly of equal 

 magnitude, nearly counterbalance each other in their means, 

 which are represented in the last column. The mean being 

 also very small in the exceptional month of October, the law 

 enounced in the Resultate for 1836*, appears to be confirmed, 

 namely, that the mean result of the declinations observed at 

 8 A.M. and 1 p.m. does not contain, apart from the irregular 

 anomalies and the secular decrease, any important fluctuations 

 dependent on season. 



Lastly, we have to consider the fluctuations of the declination 

 from one day to another. In the. Result ate for 1836 f the fol- 

 lowing definition was given of the term "fluctuation," namely, 

 " the difference from the declination of the preceding day at the 

 same hour;" and, by analogy with what are called mean errors 

 of observation, the 7nean fluctuation, during any given interval 

 of time, is the square root of the mean of the squares of the se- 

 veral fluctuations. It was further remarked, that when several 

 equal intei-vals, or intervals considered as equal, are united in 

 one, the arithmetical mean of the partial mean fluctuations 



• Scientific Memoirs, vol. ii. page 62. (Part V.) f Ib'ul, loc. cit. 



VOL. II. PART VIII. 2 R 



