332 Results of Makerstoun Observations, 1844. 



Very nearly the same result as may be deJuccJ from these quantities is exhibited by the simple means for 

 fach of the succeeding years, 1845 and 18-1:6 ; it is therefore stated with considerable confidence, that the mag- 

 netic declination at Makerstoun has an annual period, consisting of a motion of the north end of the needle 

 towards the ivest from April till August or September, of an easterly/ motion from September till the end of 

 November, of a secondarji westerly motion from thence till February, and of an easterly motion from thence 

 ■igain till April. 



It should be remarked that this result differs little from what might be at once concluded from the simple 

 n\onthly means for 18-1:4, and (with the exception of the principal westerly deviation) from the simple monthly 

 means for 1843; in the consideration of the annual period from the means for 1843 (1843, p. 221), the 

 secondary maximum and minimum were overlooked as possibly accidental, which might have been done still 

 hut for the strong confirmation of each successive year's observations. 



Differences of the Daily Means from the Monthly Means. — The following are the means of these differences 

 for each month in 1844: — 



The apparent law of these values is rendered moi"e regular by taking the means for each three months, in the 

 manner already indicated for the monthly means, as the mean for the middle month ; these are : — 



The average differences are therefore a minimum about May, and a maximum about September, a secondary 

 minimum occurring about December, and a secondary maximum about January ; the latter are more distinct in 

 the simple means. It is impossible not to remark the coincidence of these epochs with those stated already for 

 tlie mean westerly declination. The result may be thus generalized : — -The average difference of the daily 

 means from the montldy means in 1844 was a minimum when the mean westerly declination was least, and a 

 maximum when it was greatest. 



The previous quantities may perhaps be considered as some measure of the amount of disturbances of the daily 

 mean positions in each month of the year, without distinguishing, however, between what we may term consecutive 

 disturbances, or those which are due to a regularly vai-ying cause (as the lunar phase or declination) and intermit- 

 tent disturbances, or those which are irregular in amount, and occur at intervals. Since the sum of the posi- 

 tive diffei'ences is necessarily equal to the sum of the negative differences, if we divide half the siun in each 

 month by the number of days for which the mean westerly declination was greater than the monthly mean, and 

 also by the number of days for which it was less, we shall have the average of the positive and of the negative 

 differences in each month. These, ivith their differences, are as follow : — 



July. Aug. Sept. Oct. Nov. Dec. 



0'-61 0'-70 0'-87 l'-31 0'-40 0'-38 



0'-49 0'-41 0'-58 0'-66 0'-63 0'-72 



+ 0'-12 -(-0'-29 -|-0'-29 -|-0'-65 -0'-23 -0'-34 



In the year 1844, the greatest departures of the daily mean positions from the monthly means were towards 

 the west in the months of August, September, and October, and towards the east in November, December, and 

 January. 



The following Table was formed from Table I. The means of westerly declination on the 12 days between 

 January 4 and December 23, 1844, on which the Moon was 1.5, 16, 17 . . . days old, having been obtained, 

 they were corrected for secular change at the rate of -|-0'-0156 per diem ; the ditferenees between the lowest 

 mean and the others are inserted in the first portion of Table II. As in some lunations the 29th day was want- 

 ing, the mean westerly declination for the 28th and 0th day was used instead. 



For the variations with reference to the moon's declination, the 13 days on which the moon was farthest 

 north between January 3 and December 23, 1844, were numbered 0, the days after these were numbered 1, 2, 

 3, . . . 26 or 27 ; in cases in which the moon was again farthest north at the 27th day, the mean westerly de- 

 clination for the 26th and 0th day was used for the 27th, the mean westerly declination for each day was then 

 obtained, and after correction for secular change as before, the differences from the lowest mean were entered in 

 the following table. 



For the variations with respect to the moon's distance fi-om the earth, the days between January 7 and 

 December 30, 1844, before and after apogee and perigee, were numbered from 1 to 7, in some instances there 



