42 



REPORT — 1861. 



thirty years, Professor Hansteen has inferred that its progressive change from year 

 to year sometimes increases, and at other times diminishes, retm-ning to its former 

 value in a limited time ; and that, to represent it algebraically, it was necessary 

 to add to its expression a term proportional to sin mt, t being the time reckoned 

 from a particular epoch. In other words, the mean yearly value of the inclination 

 is subject, according to Professor Hansteen, to s, periodical fluctuation, whose length 

 is 11| years, and which accordingly resembles the periods which have been ascer- 

 tained to exist in the magnetical changes. Correctmg for the progressive change, 

 the inclination was foimd to be a maximum in 1828, 1840, and 1851, and a mini- 

 mum in 1823, 1834, 1845, and 1856. 



From a comparison of the Makerstoun observations with those made at other 

 places, ]Mr. Broim has arrived at a similar conclusion with respect to all the mag- 

 netic elements ; and he has pointed out the fact that the periodical changes of their 

 mean yearly values arc connected with the decennial period in the magnetic dis- 

 turbances. 



These important conclusions are fully confirmed by the Dublin observations^ 

 Assuming that the inclination decreases proportionally to the time, and comparing 

 the results calciilated according to this hypothesis -with those actually observed, I 

 have found that the differences clearly indicate a cyclical or periodic change. 

 Applying the method of least squares to the observed results, the inclination at 

 Dublin will be given, on the former supposition, by the formula 



61=70° 2r-95-2'-76x«, 



n being the number of the year reckoned from 1850. The values of the inclination 

 calculated by this formula, as well as the differences between them and the observed 

 ■results, ai-e given in the following Table : — 



There is therefore a residual phenomenon, plainly indicating a cycle or period, 

 the minimum occumng in the beginning of theye;xi- 1845, as observed by Professor 

 Hansteen at Christiania. I may add tliat the amount of the change at this epoch 

 is such as to musk altogether the regular yearly decrease ; in fact it led me at first 

 to the supposition that the progression had been reversed, and changed from a 

 decreasing to an increasing one. 



The horizontal component of the magnetic force is a function of the force itself 

 and of the inclination. It was therefore to be expected that it shoidd manifest a 

 .corresponding fluctuation. This anticipation is fully proved upon an examination 

 of the observations made with the bifilar magnetometer of the Dublin Observatoi-y. 

 The indications of this instrimaent at Dublin have been confii-med, in a remarkable 

 manner, by the observations of intensity in absolute measm-e ; and they are such as 

 to afford most satisfactory conclusions with regard to the secular changes of that 

 element. The mean yearly increase of the horizontal intensity at Dublin is 1322 

 miUionths of the whole. It is, however, very far from rmifoi-m ; on, the contrary, 

 it varies in magnitude from 641 to 1743 millionths, or nearly in the ratio of 1 to 3. 

 - The annexed Table gives the absolute values of the horizontal intensity at Dublin, 

 a,s deduced from the bifilar magnetometer and fi-om the absolute observations. The 

 first column contains the results of observation ; the second the results calculated 

 according to the hypothesis of a vmiforiu progi'essive change j and the thiz-d the 



