Magnetic Declination. 345 



Considering first the differences of the hourly means for the entire year, as obtained from a comparison of 

 the whole with the 60-day series, we obtain the following result : — 



The mean effect of disturbance is a maximum twice in the 24 hours ; it is a negative maximum between 

 8'' and 11'' p.m., and it is a positive maximum between 9*' and 10'' a.m. The mean effect of disturbance is also 

 a minimum twice in the day ; it is a minimum between 4'" and S*" a.m., and between 4'" and 5'' p.m. This re- 

 sult may be stated more generally thus : — In the afternoon at Makerstoun, when the sun is on the magnetic prime 

 vertical, the mean disturbance of magnetic declination is zero ; it increases till the sun makes its inferior transit 

 of the magnetic meridian, when it is a maximum, and diminishes fi'om thence till the sun is again on the mag- 

 netic prime vertical to the east ; during this period the disturbance has been wholly towards the east (or nega- 

 tive when westerly declination is considered). After this, the mean effect of disturbance again increases, but 

 in the opposite direction, being wholly to the west ; it becomes a maximum when the sun transits the magnetic 

 meridian, after which it diminishes to zero at the transit of the magnetic prime vertical. 



This law will be found to hold with more or less regularity, depending on the nature of the disturbance in 

 each month of the year. 



The approximate value of the positive maximum of the mean effect of disturbance = 1 '-2 

 negative = 1''6 



The results now given are deduced from the comparison of the whole series with the 60-day series ; the 

 comparison of the former with the 120-day series gives precisely the same law, but, as might be expected, not 

 exactly the same values. As has been already stated, the 60-day series is nearly free from even the smallest 

 irregularities; but this is not the case with the remaining 60 days which complete the 120-day series ; these 

 are affected by some small disturbances. It is quite possible that the smaller irregularities may obey some 

 other law than that of the larger ; if so, it should be exhibited by the differences of the means for the 120-day 

 series (which is affected by the smaller irregularities), and for the 60-day series (which is nearly free of them). 

 These differences are as follow : — Means for 120 days, minus means for 60 days. 



121 i3h i4h i5h ifih i7h 18b i9h ^;oh 21'' 2-><' 23'' 



-0'-25 -0'-24 -0'-21 +0'-09 -|-0'-02 -|-0'-10 -i-0'-06 -i-O'-Ol +0'-08 -h0-20 +0'-21 + 0'-26 



Oh 11. 2'' a^ 41. 51. S' T* SI' 9'' Ifli' 111. 



+ 0'-33 -h0'-28 +0'-27 -l-0'-14 -O'Ol -0'-04 -0'-09 -0'-12 -0'-26 -0'-26 -0'-20 -0'-29 



The law, it will be observed, is still nearly the same, the difference in the epochs being altogether trifiino', 

 when the smallness of the quantities is considered. From this, then, it appears extremely probable that the smallest 

 irregularities obey the same diurnal law as the larger, if not the largest. Few, if any, of the largest disturb- 

 ances occurred in 1844 ; it is probably on this account that the general laws of disturbances are shewn with so 

 much regularity in that year; a regularity which one or two of the largest disturbances would have destroyed, 

 and which could only be obtained again by grouping several years' observation. It is e.xtremely probable, how- 

 ever, since the smallest and the larger disturbances obey the same law, that the largest will not be found an ex- 

 ception when a sufficient number of them are included in the discussion. 



It is obvious, that by selecting the five days of next greatest regularity in each month and the next five, series 

 of means would be obtained representing the diurnal variation, for all the days in each month, for 20, 15, 10, 

 and 5 days, in each of which series the effect of disturbance would become less and less ; in this way, by a method 

 of limits, we might approximate to the normal form of the diurnal variation. 



In the previous investigation, only the mean effect of disturbance on the normal position has been con- 

 sidered, we are therefore still ignorant of the law of the mean disturbance, for it is evident that the effect of 

 disturbance on the true position may be zero when the mean disturbance is a maximum, the value of the former 

 depending principally on the positive and negative distribution of the individual disturbances with respect to 

 the mean position. 



At first, in order to obtain the mean disturbances, the difference was taken of each observation from the 

 monthly mean of all the observations at the corresponding hours : as it has been shewn that the arithmetical mean 

 of all the observations is not the normal mean, or mean independent of disturbance, tliis process is somewhat in- 

 accurate ; it has, however, been employed at first, as the investigation of the differences of the individual obser- 

 vations from their arithmetical mean is important in other respects ; when greater accuracy is possible, allow- 

 ance should be made for the variation of the daily means due to regular and continuous laws, such as annual 

 and secular variations. 



The following Table contains the hourly means of the differences for each day in 1844 : — 



MAG AND MET OBS. 1844. 4 S 



