XIV 



Geneeal Results or the Makerstoun Observations. 



also be stated as very probable, that the errors in the corrections employed (to reduce the means obtained to 

 those derivable from complete series) are insufficient to account for the differences of these variations from those 

 for the preceding years ; as is evident for the year 1847, corrected by two very different methods. The only 

 evident explanation remaining is to be found in the varying secular change for these years ; and it does not 

 appear at all improbable that the difference is connected with this variation. It has been shewn that the annual 

 period has appeared inverted when the sign of the secular motion was opposite ; it is the most remarkable fact 

 in connection with the differences of the results for the two periods 1843-6 and 1847-9 that they are exactly 

 the inverse of each other (see columns 8 and 13 of Table 3) : the completeness of the opposition in the double 

 maxima and minima appears too curious to be accidental. If the latter result be a true exposition of the annual 

 law for these 3 years, it will follow that the inversal of the law observed at the same time with an opposite 

 secular motion is not necessarily a consequence of that opposition.* 



Differences of the Daily Means of Declination from the Means for the corresponding Months. — The discus- 

 sion for 1844 will be found in the volume for that year, page 332, the results for 1845 and 1846 are obtained 

 from Tables I. and LI. of this volume. 



Table 4. — Means of the Westerly and Easterly Departures of the Daily Mean Magnetic Declination 



from the Monthly Means, with their Differences. 



Month. 



Mear 



1 Westerly Departures. 



Mean Easterly Depart 



ures. 



Diff. of 

 Mean 



Jlean 



Departures, without reference to 

 Direction. 































1844. 



1845. 



1846. 



Mean. 



1844. 



1845. 



1846. 



Mean. 



Depart. 



1844. 



1845. 



1846. 



Means of each 





























Month. 



3 Months. 



Jan. 



0-48 



0-59 



0-51 



0-53 



0-69 



100 



0-48 



0-72 



-0-29 



0-56 



0-74 



0-49 



0-60 



0-64 



Feb. 



0-70 



0-64 



0-92 



0-75 



0-75 



0-54 



0-92 



0-74 



+ 0-01 



0-72 



0-59 



0-92 



0-74 



0-63 



Mar. 



0-35 



0-43 



0-80 



0-53 



0-41 



0-80 



0-59 



0-60 



-007 



0-38 



0-56 



0-68 



0-54 



0-64 



April 



0-77 



0-53 



0-80 



0-70 



0-41 



100 



0-59 



0-67 



+ 003 



0-53 



0-70 



0-68 



0-64 



0-59 



May 



0-44 



0-58 



0-83 



0-62 



0-65 



0-54 



0-61 



0-60 



+ 002 



0-53 



0.56 



0-70 



0-60 



0-59 



June 



0-40 



0-34 



0-88 



0-54 



0-37 



0-37 



0-88 



0-54 



000 



0-38 



0-35 



0-88 



0-54 



0-58 



July 



0-61 



0-45 



0-94 



0-67 



0-49 



0-31 



0-87 



0-56 



+ 0-11 



0-54 



0-37 



0-90 



0-60 



0-64 



Aug. 



0-70 



0-76 



134 



0-93 



0-41 



0-65 



0-98 



0-68 



+ 0-25 



0-52 



0-70 



1-13 



0-78 



0-75 



Sept. 



0-87 



0-56 



1-35 



0-93 



0-58 



0-48 



1-35 



0-80 



+ 013 



0-70 



0-52 



1-35 



0-86 



0-80 



Oct. 



1-31 



0-55 



M9 



1-02 



0-66 



0-60 



0-60 



0-62 



+ 0-40 



0-87 



0-58 



0-79 



0-75 



0-80 



Nov. 



0-40 



105 



0-91 



0-79 



0-63 



M4 



0-71 



0-83 



-0-04 



0-49 



1-09 



0-80 



0-79 



0-70 



Dec. 



0-38 



0-64 



0-52 



0-51 



0-72 



0-60 



0-65 



0-66 



-015 



0-50 



0-62 



0-58 



0-57 



060 



1 1 . The conclusions from this Table are :— 



\st, The daily mean declination departs farthest to the west of the monthly mean in August, September, 

 and October, on the average about 0'-96 : the average departure for each three of the remaining nine months 

 is nearly constant ; about 0'*60. 



* I have pointed out in a paper on the magnetic declination read before the Royal Society of Edinburgh, May 3, 1847, that the 

 annual variation is inverted vrhen the secular motion has an opposite sign. M. Aeago made an indistinct approximation to this fact 

 in comparing the observations of Cassini with those of Bowditch (1810), AnnaUs de Chimie, svi., p. 66. M. Kaemtz also allades 

 to the fact in comparing Cassini's observations with observations by M. Ktjpffek and M. Gauss (Kiimtz Lehrbuck, iii., 426). In 

 both cases the fewness of the latest observations are considered to render the conclusion doubtful. Dr Lloyd has recently distinctly 

 stated the fact from the comparison of Cassini's observations with his own {Trans. Roy. Ir. Ac. xxii., May 1846). The following is 

 from the abstract of my paper : — " The annual period of magnetic declination consists of a double oscillation, having nearly the fol- 

 " lowing epochs of maxima and minima : — 



" A max. Jan. 30. The min. April 30. The max. Sept. 10. A min. Dec. 10. 



" The author examines Cassini's observations (1783-7). Although they confirm this law to some extent, it is not conceived that 

 " they can be trusted for such a determination. The author also verifies his result by grouping a large mass of modern observations. 

 " The observations at Washington [1840-42], and Toronto [1841-42], [discussed in the paper] with other facts, prove that theoscilla- 

 " tion is inverted, when the secular motion of the needle has an opposite sign ; and Colonel Beaufoy's observations [1817-20] seem to 

 " prove, that when the secular motion is zero, the annual period is a combination of the oscillations for a positive and negative secular 

 " motion." {Proceedings Roy. Soc. Edin. May 1847.) 



