in differenl Latliudes. 25.5 



interest the series oF observations made by M. Humboldt 

 in regard tu the inclination ; and it appears to us iliat they 

 may be represented very exactly by a uialhematical hypo- 

 thesis ; to which we are far from attaching any reality in 

 itself, but which we offer merely as a commodious and sure 

 mode of connecting the results. 



To discover this law, we must first exactly determine the 

 position of the magnetic equator, which is as an interme- 

 diate line between the northern and the southern inclina- 

 tions. For this purpose we have the advantage of being 

 able to compare two direct observations ; one of Lapey- 

 rouse, and the other of M. Humboldt. The fcjrmer iound 

 the magnetic equator on the coasts of Brasil at 12-1660'* 

 (10° 57') of south latitude, and 28-2107° (25° 25') of west 

 longitude, counted from the meridian of Paris. The latter 

 found the same equator in Peru at 7-7963" (7° l') of south 

 latitude, and 89-6481° (SO" 4l') of west longitude, also 

 reckoned from the same meridian. These data are suffi- 

 cient to calculate the position of the magnetic equator, sup- 

 posing it to be a great circle of the terrestrial sphere; an 

 hypothesis which appears to be conforniable to observa- 

 tions. The inclination of this plane to the terrestrial equator 

 is thus found to be equal to 11-0247° (10^ 58' 56"), and 

 its occidental node on that equator is at 133-37U)" (120'' 

 2' 5") west from Paris, which places it a little beyond the 

 continent of America, near the Gallipagos, in the South 

 Sea; the other node is at 66-6281° (59" 57' 55") to the 

 east of Paris, which places it iii the Indian Seas*. 



W© 



• To calculate this position let NEE' (Plate V. fitj. 2.) be the terrestrial 

 •quator ; NHL the magnetic equator, supposed also to be a great circle; 

 and HL the two points of that euuator, observed by Mtssrs. Humboldt and 

 Lapeyrouse. The latitudes HE, LE', and the arc £ E', which is the diffe- 

 rence of longitude of these two points, is known: consequently, if we sup- 

 pose HE =' <\ 1,E' =- h', EE' = r, EN -- r, and the angle ENH =y, we 

 shall have two spherical triangles N E H, N E'L, which will g'xc the twa 

 following equations: 



tan"-. /■ cot v . tan?-. // cot. v 

 Sin. x — — ■ — ^ sin. [x + i) = : — 



from which we deduce 



•Sin. 

 and developing 



{x + v) _ tang. L' 

 sju. X tang, b 



tanr. V cos. i; 



tang, i sin. v sm. u 



L«t us now take an auxiliary angle f, so tliat wc may ha\'« 

 tang. /• sin. v 



and 



