TERRESTRIAL MAGNETISM. 213 



+ (64-437 - 79"518e + 122-936 e- - 152-589 e^) sinX 



+ (90-184 + 45-532 e — 185-46 e") /cos 2 X 



+ (14-070 - 146-386 e - 91-582 e^) /sin 2\ 



+ (56-250 + 0-534 e)/2 cos 3 \ 



+ (4-188 + 59-322 e) /^ sin 3 \ 

 - 12-701 /3cos 4X 



+ 16-508/3 sin4\ 



Z= — 24-593 + 1896.847 e + 400-343 c^ _ 75-471 e^ 



- 544-275 e^ 



+ (79-700 - 107-763 e + 491-744 e^ - 762-946 e^)/ cos \ 



+ ( - 395-724 - 155-473 e + 191-176 e^ + 320-560 e^) / sin \ 



+ (34-187 - 292-772 e - 228-955 e^) /* cos 2 \ 



+ ( - 147-439 - 91-064 e + 212-865 e^) /^ sin 2\ 



+ (5-584 + 98-870 e) /3 cos 3 X 



+ ( - 75-000 - 0-890 e) f^ sin 3 X 



+ 20-635 /4 cos 4 \ 



+ 15-876 /4 sin 4 X. 



After these components have been calculated for a given place, 

 we obtain in the following manner the several parts of the de- 

 termination of the magnetic force, according to the customary 

 form. 



Let S be the declination, i the inclination, -^^ the total, and &> 

 the horizontal intensity. Determine first S and a> by means of 

 the formulae 



X ■= (I) cos S, F = ft) sin 8, 

 and then i and 1^ by means of the following formulae : 



(o = yfr cos i, Z =■ "^ sin i. 



28. 



As the formulae for X, Y, Z, contain 7l members, their 

 immediate calculation is a considerable labour. Its repetition 

 for a great number of places appears the more alarming, con- 

 sidering that we could hardly hope to be secure from the pos- 

 sibiUty of mistake without going twice over the whole. But 

 little would be gained by suppressing all those members of 

 which the co-efficients are less than an integer, or even less than 

 10 integers, for the remaining members would still amount to 

 65. But as the whole value of the work would remain uncer- 

 tain if not tested by a considerable number of actual observations, 

 I have encountered the labour of calculating a table, by the 

 assistance of which the work will be in the highest degree 



