MAGNETISM. 



to the law already stated, $ 78. Taking 

 XV as radius, the lines VF, VG, and 



v - e sin. 



VD are the tangents of the angles 

 VXF, VXG, and VXD, respectively; 



and in the right-angled triangle VDF, 

 VD^VF'-fFD 8 ; 



that is (FD being = VG) 



VD 2 =VF 2 -f-VG 2 : 



or tang. Z VXD = tang. B VXF -f- tang. 

 S VXG; which is the formula above 

 given. 



(331.) On the other hand, the deter- 

 minations of the relative intensities of 

 the magnetic forces in different planes 

 furnish data for the computation of the 

 angles which those planes make with 

 the line of the dip, or the direction of 

 terrestrial magnetism. Thus the amount 

 of the dip may be determined by com- 

 paring the number of oscillations in a 

 given time made by the same needle, 

 when vibrating in the plane of the mag- 

 netic meridian, and also in a vertical 

 plane at right angles to it. For the 

 squares of these numbers being as the 

 intensities of the forces which respec- 

 tively act in these planes, and the force 

 in the former case being to that in the 

 latter as the radius to the cosine of the 

 angle d, which the line of dip makes 

 with a vertical line, we obtain the latter 

 by a simple proportion when the former 

 are given. Resuming the notation be- 

 fore employed, let e be the total terres- 

 trial force acting in the plane of the 

 magnetic meridian, and v that part of 

 it which acts in a vertical plane at right 

 angles to the magnetic meridian; and 

 let N and n express the number of os- 

 cillations, in a given time, which the 

 dipping-needle performs in these two 

 planes respectively : v = e cos. c^or,~d 

 being the complement of ; 



sn. = 



e 



But v : e :: w 2 : N 2 ; 



therefore 



e N 2 



and sin. = ^-_ 



N 2 



(332.) We shall give the following 

 example of the application of these for- 

 mulae to the observations of magnetic 

 intensity, made by Humboldt, near 

 Quito, exactly at the terrestrial Equa- 

 tor, and at longitude 81 2' west from 

 Paris. The number of oscillations made 

 by the dipping-needle vibrating in the 

 magnetic meridian, during ten minutes, 

 was 220 ; the number of oscillations, 

 made in the same time, when it vibrated 

 in a plane perpendicular to it, was 109. 

 Substituting these numbers in the for- 

 mula for N and n respectively, we ob- 

 tain 



220 2 48400 



From log. 11881=4.0748530 

 Subtract log. 48400 = 4.6848454 



there remains log. sin. = 9.3900076 



whence we get $ = 14 12' 35". 

 The direct observation of the dip, by 

 the dipping needle, was 



5 - 14 25' 5", 



the difference between the two methods 

 being only 12' 30". 



(333.) The angle of the dip with the 

 horizon may, in like manner, be job- 

 tained by comparing the relative inten- 

 sities of the forces, as determined by the 

 squares of the number of oscillations in 

 a given time, executed in the plane of the 

 magnetic meridian, and also in a hori- 

 zontal plane : for they are in the pro- 

 portion of the radius to the cosine of 

 the dip ; or, if we call the number of 

 oscillations made by the horizontal nee- 

 dle v, while N is that made by the same 

 needle, suspended as a dipping-needle, 

 and -placed in the plane of the magnetic 

 meridian ; then 



(334.) Methods have been devised 

 for determining the dip, from the result 

 of observations made with the horizon- 

 tal needle alone, by comparing its num- 

 ber of oscillations with the weight of 

 the counterpoise necessary for maintain- 

 ing it in the horizontal position when 

 magnetized. But the formula and mode 



