212 C. F. GAUSS ON THE GENERAL THEORY OF 



the theory of terrestrial magnetism, are used both here and m 

 the formation of the table to be described in the sequel, just as 

 they were given by calculation, without omitting decimals. To 

 any one conversant with calculation it is superfluous to remark, 

 that these fractional parts have in themselves no value, as we 

 are still far from being able to ehminate with certainty even the 

 integers. But it is important that the observations should be 

 closely compared Avith one and the same definite system of ele- 

 ments ; and, as by leaving out decimals nothing would be gained 

 in point of convenience in computing, there was no reason for 

 altering in any respect the elements given by calculation. 



27. 



The expression for V, developed according to the above num- 

 bers, is as follows : for the sake of brevity e stands for cos u, and 

 f for sin u. 



^= - 1-977 + 937-103 e +71*245 e' - 18-868 e^ 



- 108-855 e* 

 + (64-437 - 79-518 e + 122-936 e^ + 152-589 e^)/ cos \ 

 + (- 188-303 -33-507e + 47-794 6^ + 64-112 e^)/ sin X 

 + (7-035 - 73-193 e - 45-791 e'^) f^ cos 2\ 

 + (-45-092 — 22-766 e — 42-573 e")/^ sin 2 X 

 + (1-396 + 19-774 e) P cos 3 X 

 + (- 18-750 - 0-178 e)/^ sin 3 \ 

 + 4-127/'* cos 4\ 

 + 3-175 Z'* sin 4X. 



We may here add the completely developed expressions for 

 the three components of the magnetic force. 

 X - (937-103 -I- 142-490 e - 56-603 e^ - 435-420 ^) f 

 + ( _ 79-518 + 181-435 e - 298-732 e^ - 368-808 ^ 



-I- 6IO-357 e"*) cosX 

 4- (- 33-507 + 283-892 e + 259-349 e^ — 143-383 ^ 



-256-448 e^) sin\ 

 + (-73-193 ^ 105-652 e + 219-579 e-+ 183-164 e^) /cos 2 \ 

 + ( — 22-766 + 175-330 e + 68-098 e-- 170-292 e^)/ sin 2X 

 + (19-774 - 4-188 e — 79-096 e^) /^ cos 3 X 

 + ( - 0-178 + 56-250 e + 0-716 6^) p sin 3X 



— 16-508 ep cos 4 X 



— 12-701 ef^ sin 4 X 



y= (188-303 + 33-507 e — 47-794 e^ - 64-112 e^) cos X 



