XVlll 



General Results of the Makerstoun Observations. 



17. From the first series, the number of observations to the west of the monthly means for the correspond- 

 ing hours was greatest in the 4 months December to March, there being on an average 6 more to the west than 

 to the east in 100 : the number was least in the months of October and November, there being on an average 

 7 less to the west than to the east in 100. July is the only other month, in the mean of the two years, for 

 which the number of observations to the west of the mean was greater, than the number to the east. The num- 

 ber for each of the months from April till September varies little. 



18. From the second series, for which the mean hourly position is deduced from days selected as nearly free 

 from disturbance, the number of observations to the west of the hourly means was greatest in the 6 months 

 from November to April, there being an average of 12 observations in 100 more to the west than to the east ; 

 in the remaining 6 months. May to October, there is an average of about 2 less to the west than to the east. 



The number of observations to the west of the hourly means (whether these are obtained from all the ob- 

 servations, or from the undisturbed observations only) is greatest about the months December to March. 



19. By both series, each year shews more observations to the west than to the east of the hourly mean posi- 

 tions, however obtained ; so that the greatest departures from the mean position are to the east, the direction 

 of the secular motion : the 2d series shews this fact most distinctly, as might be expected, since the mean posi- 

 tions are nearly unaffected by distui'bance. 



20. Annual Variation of the Probable Error of an Observation of Magnetic Declination from the Monthly 

 Mean for the corresponding Hour. — It has been already shewn in the volume for 1844, p. 351, that the probable 

 error cannot be deduced on the assumption that the differences from the mean position are analogous to the 

 errors in the observation of a constant quantity, since that assumption is inaccurate ; the diflFerences do not 

 occur equally to the east and west of the mean, as is shewn in the following discussion ; nor is the number 

 occurring within certain limits satisfied by the usual function of the eiTors obtained from the calculus of proba- 

 bilities, as will be found from Table XIX., p. 352, 1844, and Table XVI., p. 10 of this volume. In conse- 

 quence, a graphic interpolation has been employed to determine the probable error, that is to say, the depart- 

 ure from the hourly mean position, for which there were as many observations with a greater, as there were with 

 a less departure ; these, deduced from the two tables last referred to, for each month are : — 





Jan. 



Feb. 



March. 



April. 



May. 



June. 



Jul J'. 



Aug. 



Sept. 



Oct. 



Nov. 



Dec. 



Mean. 



1844, 



0'-93 



0'-94 



r-35 



l'-20 



l'-16 



0'-78 



r-04 



l'-20 



r-36 



l'-58 



r-51 



0'-90 



r-16 



1845, 



l'-38 



l'-25 



l'-24 



l'-08 



l'-08 



0'-91 



l'-05 



l'-35 



l'-56 



l'-14 



l'-27 



l'-09 



l'-20 



Mean, 



l'-15 



r-09 



r-29 



l'-14 



r-12 



0'-84 



l'-04 



l'-27 



l'-46 



l'-36 



l'-39 



0'-99 



ri8 



These numbers on the whole follow the same law as the mean difference : The probable error of an obser- 

 vation of magnetic declination from the monthly mean of the corresponding hour (without reference to which 

 hour) is least in June ( = 0'-84) and in December ( = 0'-99), and it is greatest in September ( = l'-46) of the 

 autumn months, and in March ( = l'-24) of the spring months. The remarks already made in the case of the 

 annual variation of the mean disturbance apply equally here, see No. 16. 



Monthly Variations for the Magnetic Declination. 



Table 9. — Mean Variations of Westei'ly Declination free from Regular Secular Change, with 



reference to the Moon's Age and Declination. 















After 













Moon's 













Moon 













Age. 



1843. 



1844. 



1845. 



1846. 



Mean. 



farthest 

 North. 



1843. 



1844. 



1845. 



1846. 



Mean. 



rt. d. 



' 



■ 



/ 



' 



/ 



d. d. 



- 



- 



/ 



/ 



• 



14—16 



+ 0-24 



-004 



+ 006 



+ 0-32 



+ 0-15 



27— 1 



+ 0-25 



+ 019 



+ 007 



+ 0-35 



+ 0-22 



17—20 



+ 0-42 



+ 0-24 



-008 



+ 0-09 



+ 0-17 



2— 5 



+ 015 



-005 



-012 



-0-04 



-001 



21—24 



-0-34 



+ 0-15 



-0-12 



+ 0-03 



-0-07 



6— 8 



+ 003 



-018 



-0-14 



+ 0-11 



-004 



25—28 



-0-14 



+ 0-01 



-0-08 



+ 004 



-004 



9—12 



+ 0-08 



-0-24 



+ 001 



+ 00] 



-003 



29— 1 



-0-33 



000 



+ 0-04 



+ 0-22 



-001 



13—15 



+ 0-20 



+ 0-02 



+ 0-06 



-0-35 



-0-05 



2— 5 



-0-08 



+ 0-03 



+ 009 



-0-36 



-0-07 



16—19 



-015 



+ 013 



+ 0-02 



-019 



-005 



6— 9 



+ 001 



-0-16 



+ 0-08 



-0-05 



-002 



20—22 



-0-60 



+ 001 



+ 0-01 



+ 0-01 



-014 



10—13 



+ 0-21 



-0-23 



+ 0-01 



-032 



-0-08 



23—26 



+ 0-06 



+ 012 



+ 0-18 



+ 007 



+ 0-11 



