290 SCIENTIFIC RESULTS OF ZIEGLER POLAR EXPEDITION 



In the case of a cycle of twelve equidistant observations : 



^ = — (/,+^, + 4 + '4+ A,) 



12 



6«, = 0.866 (/i — 4 — ^, + ill) + o. 500 (4 — it — 4 + Ao) — 4 + 'h 

 6.5, = o. 500 (/, + 4 — A — Ai) + o. 866 (/?, + i^i — 4 — i?,o) + ^3 — ^s 

 6a, = o. 500 ( J?! — /j — i?! + ^6 + A — 4 — Ao + Ai) — A + A — A + A J 



63, = 0.866 it, + A — A — A + A + A — Ao — A.) 

 6a3 = — /, 4-/^ — 2;, + /?g — ^,„ + /„ 



63, = +A— A + A — A + A— Ai 



6*4 = 0.500 (— /f, — A — A— A — A — A — Ao— Ai) + A + A + A+ A. 



63. = 0.866 (i?. — A + A — A + A — A + A. — Ai) 



On the evaluation of these equations the coefficients B,, B,, B, B„ , and the angles 



Ci, Q, Cj C„ are found as before.* 



The results of the discussions for the various periods from the observed and interpolated 

 hourly declinations are as follows, the probable error of a single representation being indicated 

 by the ' ' plus or minus ' ' quantity at the end of each formula : 



Formula Represbnting Diurnal Variation in Magnetic Declination at 



Teplitz Bay 



October 4 to October 30, 1903 : 



Z>= 22° 36.'7 + i3.'67 sin (6 + 2° 31') + 6.'98 sin (2 (? + 282" 25') + 

 i.'33 sin (3»+ 16° 46') + i.'55 sin (4^ + 62° 47') ±o.'37 



November i to November 28, 1903 : 



B = 22" 49.'8 + i9.'74 sin (<?+ii°44') + i4.'o3 sin (2^+303° 01') + 

 3.'9i sin (3 ^ + 285° 42') + 3.'i3 sin (4 S + 145° 38') ± ©.'94 



November 29 to December 26, 1903 : 



Z>= 22° 45.'9 + i3.'i3 sin {0 + 6° 09') + 4.'97 sin (2 fl + 270° 44') + 

 4.'5o sin (36+ 103° 12') + 2.'oo sin U^ + 78° 58') ± 6.'24 



December 27, 1903, to January 23, 1904 : 



Z? = 22° 46.'7 + i3.'96 sin (5 + 9° 40') + 8.'6o sin (2 e + 295° 59') + 

 3.'97 sin (31?+ i59° 26') + 2.'oi sin (4^ + 330° 00') ± o.'35 



January 24 to February 20, 1904 : 



B = 22° 46/3 + i3.'54 sin (^ + 15° 04') + 7.'72 sin (2 (9+317° 17') + 

 2. '19 sin {3O+ 126° 14') + 2.'79 sin (■40+318° 22') zt 0.^48 



February 21 to March 19, 1904 : 



Z>= 22" 4i.'6 + 9.'47 sin (»+ 357° 48') + 3-'65 sin (2^+247° 46') + 

 2.'38 sin (3^ + 4° 04') + 2.'34 sin (4 + 346° 42') ± o.'24 



* These solutions are given by C. A. Schott in Appendix No. 8 of the Report of the Superintendent of 

 the United States Coast and Geodetic Survey for 1890. 



