222 



Absteacts of the Makeestoun Obseevations, 1843. 



TABLE II. — Mean Variations of Westerly Declination, after Eliminating the Secular Change, with 

 Eeference to the Moon's Age, Declination, and Distance from the Earth, for 1843. 





Variations 





Variations 



After 



Variations 



After 



Variations 



Before 



Variations 



Before 



Variations 



jMoon's 



of West 



Moon's 



Of West 



Moon 



of West 



IMoon 



of West 



and 



of West 



and 



of West 



Age. 



Declina- 



Age. 



Declina- 



farthest 



Declina- 



farthest 



Declina- 



after 



Declina- 



after 



Declina- 





tion. 





tion. 



Nortli. 



tion. 



North. 



tion. 



Perigee. 



tion. 



Apogee. 



tion. 



Dav. 



' 



Day. 



' 



Day. 



' 



Day. 



' 



Day. 



' 



Day. 



. 



15 



0-85 







0-19 







1-05 



14 



1-28 



7 



0-72 



7 



0-88 



16 



0-94 



1 



0-30 



1 



0-80 



15 



0-64 



6 



0-00 



6 



0-93 



17 



1-07 



2 



0-00 



2 



1-40 



16 



0-84 



5 



1-02 



5 



0-54 



18 



1-04 



3 



0-43 



3 



0-69 



17 



116 



4 



0-40 



4 



0-18 



19 



MO 



4 



0-71 



4 



0-96 



18 



0-47 



3 



0-23 



3 



0-19 



20 



0-89 



5 



0-96 



5 



0-66 



19 



0-25 



2 



0-62 



2 



0-08 



21 



0-35 



6 



0-88 



6 



0-53 



20 



0-00 



1 



0-35 



1 



0-03 



22 



0-32 



7 



0-71 



7 



0-89 



21 



013 



P 



0-40 



A 



001 



23 



Oil 



8 



0-71 



8 



102 



22 



0-40 



1 



0-60 



1 



0-40 



24 



0-25 



9 



0-14 



9 



0-99 



23 



0-76 



2 



0-64 



2 



0-24 



25 



0-66 



10 



0-32 



10 



0-40 



24 



0-30 



3 



0-66 



3 



0-42 



26 



0-84 



11 



0-96 



11 



0-64 



25 



119 



4' 



0-85 



4 



1-23 



27 



0-06 



12 



0-92 



12 



1-42 



26 



Ml 



5 



0-82 



5 



0-89 



28 



0-30 



13 



1-04 



13 



103 



27 



1-24 



6 



0-75 



6 



0-67 



29 



0-32 



14 



0-73 











7 



0-60 



7 



0-80 



The above Table was formed from the daily means in Table I. in the following manner : — The mean westerly 

 declination on the 12 days, between January 15. 1843 and January 4. 1844, on which the moon's age was 15 days, 

 were summed together, similarly for 16 days old, 17 days old, . . . the means of these sums were then taken, and 

 the differences from the lowest mean are given in the above Table. In these summations the approximate means 

 for Sundays were used, as it was conceived that the want of any means on these days would affect the results more 

 seriously than the use of the approximations. As in some lunations the 29th day was awanting, the mean of the 

 declinations on the 28 day and the day of new moon was summed instead. 



For the variations of westerly declination with reference to the moon's meridian altitude, the day on which 

 the moon was farthest north was numbered 0, and the days after this were numbered up to 26 or 27, the day before 

 the moon again attained its greatest north declination ; if there were only 26 days the mean of the declinations on 

 the 26th and 0th day was substituted for the mean on the 27th day ; the mean westerly declination was then ob- 

 tained for all the days of the same number from January 13. 1843 till January 3. 1844, each mean being the 

 mean of the westerly declinations on 1 3 days ; the differences from the lowest were then taken, and are inserted above. 



For the variation of westerly declination with respect to the moon's distance from the earth, it will be seen in 

 the foregoing Table that the days before and after apogee and perigee are numbered from 1 up to 7 ; m some 

 instances there are only 5 days before apogee and 5 days after perigee, or before perigee and after apogee ; in these 

 cases, for example, the 5th day before apogee has been numbered also as the 6th and 7th after perigee, and the 

 5th after perigee as the 6th and 7th before apogee ; when there are 1 1 days between apogee and perigee, or perigee 

 and apogee, the 6th is counted as the 6th and 7th before and after ; when there are 1 2 days between, the 6th 

 before apogee is counted as the 7tli after perigee, and vice, versa; when there are 13 days, the 7th day is counted 

 as the 7th before and after, and when there are 15 or 16 days, the mean of the declinations for the 7th and 8th 

 days is used as the mean for the 7th. The mean westerly declinations for the days with similar numbers, between 

 Januai-y 12. 1843 and January 5. 1844, were then obtained as in the previous cases, and the differences from the 

 lowest mean are given in Table II. ; each number is the mean of 13. It would have simplified the summations, 

 and this statement of them, to have rejected the means on the 8th, 7th, and 6th days (of themselves they would 

 have been useless), but it seemed better to combine them with other means nearly similarly related to the distance 

 of the moon than to throw them away. 



After the summations for each of the above cases had been performed, and the means obtained, the secular 

 change was eliminated at the rate of O'"0165 per diem. 



The above staj;ement will apply to the similar summations for the horizontal and vertical components of mag- 

 netic force. 



