CONCERNING TERRESTRIAL MAGNETISM. 



233 



The equations of the magnetic needle for different places, in reference to rectangular 

 coordinates, when the geographical coordinates, dip, and variation are given. 



Let A O A' be the meridian of Greenwich, 

 E O Q the equator, C the position of a place 

 where a magnetic observation is made, A C B 

 the variation, and B C equal to twice the dip 

 of the needle. Then B is the point on the 

 surface of the earth towards which the dipping- 

 needle is directed, and that in which the straight 

 line which coincides with the needle intersects 

 the earth a second time. 



Estimating (as is done in my paper on Sphe- 

 rical Loci before referred to) the positions of 

 places on the surface of the earth by means of 

 the polar angle C A O and radius -vector C A, we 

 have the coordinates of C directly from observation ; and by means of the triangle 

 A C B, whose sides B C, C A, and included angle A C B are given, we can compute 

 the coordinates of B. Denote the polar distance and polar angle of C by a^ j3^, and 

 those of B by a^, 1^^. 



In the next place, by the employment of equations (1.), (2.) of IL, we may obtain 

 the equations of the needle, referred to three rectangular axes, the coordinate planes 

 of which are the meridian of Greenwich, the meridian of 4; 90°, and the equator. 

 The results for the six different places before mentioned are given in the last column 

 of the following Table. The construction of the Table itself is indicated at the head 

 of each column, in a way that renders further explanation unnecessary. 



Place, Date, Observer, and 

 Authority. 



Port BoAven. 1824. 

 Capt' Parrt & Foster. 

 Phil. Trans. 1826. 



Boat Island, 1821. 

 Captain Pahry. 

 Voyage, I. 



Chamisso Island. 1827. 

 Captain Beechet. 

 Voyage, A pp. p. 732. 



Paris. 1829. 

 M. Arago. 

 Annuaire, 1830. 



Valparaiso. 1821. 

 Captain Bash- Haix. 

 "Magnetism," Enc.Met 



Paramatta. 1823. 

 Sir Thomas Brisbane. 

 Phil. Trans. 1829, pt. 3. 



Geographical coordinates 

 of the place. 



Lat. 730 14' 0"N 

 Long. 88 54 W. 



Lat. 68° 59' 13" N 

 Long. 53 12 56 W 



Lat. 66° 12' 0"N, 

 Long.161 46 W. 



Lat. 48° 50' 0"N. 

 Long. 2 20 E. 



Lat. 33° 1' 0"S. 

 Long.288 29 E, 



Lat. 33° 48' 50" S. 

 Long.151 1 34 E. 



Spherical coordinates of 

 the place of observation. 



Dip. 82° 53' 40" N 

 Var. 72 2 W. 



Dip. 77° 39' 0"N. 

 Var, 32 30 W, 



Dip. 67° 41' 18" N. 

 Var. 22 12 5 W, 



Dip. 38° 46' 0"S. 

 Var. 14 43 E. 



Dip. 62° 57' 0"S. 

 Var. 8 47 41 E- 



Spherical coordinates of 

 the second intersection. 



cc„= 165° 25' 32" 

 li„ = - 256 3 55 



a, = 41° 10' 0" 



;3, = 2 20 



a, = 123° 1' 0" 



/3, = 288 29 



«, = 123° 48' 50" 

 /3, = 151 1 34 



«„= 151° 5' 36" 

 a,, = = 204 45 57 



a„= 133° 34' 36" 

 /3„ = 27 25 



Rectangular equations of the needle. 



X = _ -278746 z - -023702 r 

 y= -0346112- -027756 r 



x= - •270U7z- -034011 r 

 y= -122598 2- -122598 r 



«„= 96° 10' 34" 

 li„ = - 1C2 10 56 



156°58'2r 

 85 20 23 



«,, = 109° 46' 44" 

 li„ = - 21 23 25 



»= - -081565 2- -051635 r 

 y= - -690471 z + -248470 r 



x= -384722 2- -262819 r 

 y= 1-8645002- -745899 r 



T = - 3-159630 2 - 2-518180 r 

 y- -621395 2+ -206769 r 



= - 3-418875 2 - 1-500120 r 

 y = 7-349865 z + 3-363313 r 



MDCCCXXXV. 



2 H 



