352 



-Results of the Makerstoun Observations, 1844. 



TABLE XIX. — Number of differences in 1000 (without reference to sign), which occur between 

 the limits of successive minutes, for each Month, and for the Year 1844. 



Month. 



0' 

 to 

 1'. 



V 



to 

 2'. 



2' 

 to 

 3'. 



3' 

 to 

 4'. 



4' 

 to 

 5'. 



5' 

 to 

 6/ 



6' 

 to 

 7'. 



7' 

 to 

 8'. 



8' 

 to 

 9/ 



9' 

 to 

 10'. 



10' 

 to 

 15'. 



15' 

 to 



20'. 



20' 

 to 

 25'. 



25' 

 to 

 30'. 



30' 

 to 

 40.' 



January 



February 



March 



April 



May 



June 



July 



August 



September 



October 



November 



December 



Year 



528 

 525 

 391 

 433 

 451 

 600 

 486 

 431 

 380 

 346 

 338 

 545 

 453 



290 

 280 

 285 

 264 

 258 

 240 

 275 

 272 

 297 

 256 

 287 

 288 

 274 



93 

 100 

 135 

 140 

 174 



95 

 128 

 136 

 167 

 191 

 160 

 074 

 133 



37 

 42 

 62 

 58 

 65 

 30 

 48 

 76 

 57 

 88 

 93 

 32 

 57 



22 

 15 

 24 

 34 

 12 

 20 

 32 

 37 

 32 

 40 

 37 

 14 

 27 



15 



7 



22 



16 



14 



8 



14 



23 



20 



8 



24 



14 



16 



12 

 10 

 22 

 14 



6 



2 

 11 



6 

 13 

 23 

 11 



6 

 12 



2 

 5 

 10 

 6 

 5 



2 

 11 

 8 

 9 

 14 

 5 

 6 



5 

 2 



6 

 8 



2 



3 

 5 

 9 



6 

 5 

 4 



2 

 3 

 6 

 2 

 2 

 3 

 2 

 3 

 2 

 6 

 3 

 6 

 3 



8 

 24 

 16 

 11 



2 



12 



11 



13 



2 



8 



2 

 2 

 5 

 3 

 2 



5 

 6 

 3 



2 



3 



2 

 2 

 3 

 1 



2 

 2 



3 

 3 

 2 

 1 





3 



Annual Variation of the Probable error of an Observation of Magnetic Declination. — From Table XIX. 

 I have determined by a graphic interpolation the probable error of a single observation from the monthly mean 

 for the corresponding hour, that is to say, I have determined approximately the error for which there are as 

 many greater as there are less than itself. These are : — 



Jan. Feb. March. April. May. June. July- Aug. Sept. Oct. Nov. Dec. 



0'-93 0'-94 l'-35 l'-20 l'-16 0'-78 l'-04 l'-20 1 A 36 l'-58 l'-51 0'90 



The probable error of a single observation from the monthly mean for the corresponding hour (without 

 reference to which hour) is a minimum at the solstices, and a maximum at the equinoxes : the principal mini- 

 mum occurs at the summer solstice, when the probable error is only 0'-7%, or about half the value of the prin- 

 cipal maximum which occurs in October. In order to shew the difference of these values from those to be de- 

 duced by the aid of the calculus of probabilities, we may obtain the latter with sufficient accuracy by means of 

 the formula* 



Probable error = - 845 x mean of errors, 



which formula gives the following values : — 



.Tan. 



l'-13 



Feb. 



l'-18 



March. 



l'-88 



April. 



r-58 



May. 



l'-35 



June. 



0'-95 



July. 



l'-21 



Aug. 

 1-45 



Sept. 



l'-63 



Oct. 

 l'-91 



Nov. 



l'-95 



Dec. 

 l'-18 



values which are from a fourth to a third more than the truth. 



Mean of i 

 two. ! 



l h A.M. 2^ 3 h 4 h 5 h 6 h 7 h 8 h 9 h 10 h ll h h lh P.M. 2 h 3 h 4 1 ' 5 h 6 h 7 h 8 h 9 h 10 1 ' ll h 

 l'-12 0'-96 l'-10 0'-93 0'-95 0'95 l'-04 l'-00 l'-17 l'-10 l'-17 l'-04 l'Ol l'-24 l'-24 0"97 0'.79 l'-16 l' - 24 l'-63 l'-41 1 

 l'-04 l'-02 0'-95 l'-02 !'•]* l'-ll l'U3 l'-ll 



0'-98 



l'-44 



l'-40 



12" 

 l'-55 l'-22 

 l'-38 



Diurnal Variation of the Probable Error of an Observation of Magnetic Declination. — The following are 

 probable errors of a single observation for each hour (without reference to month) from the monthly means at 

 the corresponding hours, deduced from Table XXI. by a graphic interpolation. 



From these values it appears that the probable error of a single observation from the monthly mean, for 

 the corresponding hour (without reference to the month to which the observation belongs), is a minimum about 

 5 h a.m., and about 5 h p.m., being, in both cases, rather less than a minute; it is a principal maximum between 

 9 h and 10 h p.m., being nearly a minute and a-half (l'"5), and a secondary maximum about noon, being about 

 l'-13. 



On the whole, it appears that, if it were required to make a single observation which should be as near to 

 the monthly mean for the corresponding hour as possible, the observation should be made in June, and about 

 5 h a.m. or 5 h p.m. When a greater number of observations are obtained, more accurate values for each hour in 

 each month may be found. Upon examining the distribution of the errors in the months of May, June, and July, 

 o h or 6 h p.m. is found to be the hour of the smallest probable error in each month ; the probable error at 5 h 



* Encke on " The Method of Least Squares." Taylor's Scientific Memoirs, vol. ii., p. 355. 



