" TERRESTRIAL MAGNETIC INTENSITY. 25 



the results by the method of least squares, I had little confidence in having ob- 

 tained any positive result. A careful examination of the station marked on the 

 inap, will shew that they were almost invariably chosen so that an elevated sta- 

 tion lay between two others at a lower lead, by which the effect of change in lati- 

 tude and longitude might be eliminated. When we criticise these groups of three 

 series, we find for the most part an agreement greater than I had myself antici- 

 pated that the instrument could insure ; yet the combination of all with two in- 

 dependent needles, and likewise in two series in different countries and different 

 years, unite in giving a negative coefficient to the height, which I believe to be 

 true and not accidental, though it could not safely be inferred from one or two 

 insulated observations. I should be disposed to deduce its probable value thus, 

 taking the circumstances of the observations into consideration : — 



Alps, Needle No. I, 

 Alps, Flat Needle, 

 Pyrenees, both, 



Weight. 



4 

 2 

 1 



Probable 



Coefficient of Varied Intensity 

 for 100 feet of Elevation. 



.000033 

 .000027 

 .000053 





mean, .000034 



Hence to produce a variation of .001, an elevation of 3000 feet is necessary. At 

 the height to which Gay Lussac ascended, the change of intensity would be 

 nearly .008 of the whole ; but the variation in the time of an oscillation would be 

 only half as much. 



43. The smallness of the variation fully explains the difficulty of ascertain- 

 ing its existence from a very limited number of observations. It is hoped that, 

 notwithstanding the imperfection of the instruments, the extent of the induction 

 will entitle the result to some confidence. By adding together the elevations of 

 the distinct stations contained in Table VII, it will be found that the aggregate 

 of the heights to which I have ascended amounts to above 160,000 feet, or more 

 than thirty vertical miles. 



§ 5. On the Magnetic Dip. 



44. Although the horizontal magnetic force be only a sort of mathematical 

 abstraction, and bears no direct relation to the earth's action until the effect of 

 dip is considered, we do not therefore think it improper to be made a separate 

 subject of inquiry. From the projected lines of equal horizontal intensity and of 

 equal dip, the lines of equal total intensity are deducible. The two elements may 

 therefore be made the subject of distinct inquiry ; and though these elements are 

 probably in a condition of continual change, yet, considering the present errors of 

 observation, any moderate lapse of time between the formation of these curves 

 Avill not be productive of serious anomalies. By deducing the total intensity 



VOL. XIV. PART I. D 



