MAG^JETiC OBSERVATIONS 287 



Unfortunately the observations at Teplitz Bay cover only nine months of the year. In 

 order to arrive at an approximation of the diurnal variation in magnetic declination for the 

 missing months, values have been interpolated, by formulae based on Bessel's periodic function, 

 dependent upon all of the observations made. The hourly means of all the mean observed 

 hourly values hav6 been obtained for all of the observations in each calendar month and these 

 considered as representing the mean course of the declination for that month. This disregards 

 the fact that the mean hourly declinations are not always evenly distributed during the month ; 

 the errors, however, arising from such an assumption are certainly less than those to be expected 

 in the resulting interpolations. 



The interpolation formulae used have been developed by A. Bravais in his memoir " Sur la 

 mani^re de representer les variations diurues ou annuelles des Elements mdt^orologiques par 

 des series trigonometriques ".* In the case in hand three values, t,, t„ and t„ are missing in 



each of the cycles of twelve equidistant ordinates, t„ /„ t„ t„ /„. For this case using 



the auxiliary values 



Bravais deduces 



x=6.<)2g {^^~^\ + 3-694^1. 

 y= 1.75 ^0 ~ -g'A , and 



^. = 3.694 (f^—^) + 2-970^1. 



In these equations the values of ^„, g^, and^j are as follows : 



go = 0.533 /„ + 0.0383 (4 + ^,) + i ( _ ^, _ t,+ 4 - 4 _ 4 + /, J, . 



7 



g, = 0.0383 {t, + t,)+'- ih -h — t, + t,-i,- Ao + ^n) , and 

 7 



g. = 0.533 ^3 + 0.0383 {t,+ Q-\-\ (J,— t, - /e + 4 - tn-tn)- 



7 



By the aid of these formulae and the known hourly values of the magnetic declination for 

 the nine months from October, 1903, to June, 1904, both monthly hourly and mean monthly 

 values have been interpolated for the months of July, August, and September, 1903. 



Inasmuch as these interpolations were to be carried out directly from the observed quan- 

 tities and not from the hourly variations on the mean monthly values, all of the observed hourly 

 declinations have been reduced to one epoch, namely, 1904.0, by means of the annual change 

 in declination as determined on page 305. Thus the interpolated values all apply to the epoch 

 1904.0. The reduced observed monthly hourly and mean monthly declinations, as also the 

 interpolated values obtained for the three missing months, are contained in the following tabu- 

 lation. The interpolated quantities for the three months of July, August, and September are 

 shown graphically in figures 16 to 18 in which the interpolations are indicated by circles 

 connected by broken lines ; the smooth curves show the computed values of the diurnal varia- 

 tion resulting from the discussion of the same by means of Bessel's periodic function. 



* Voyages de la Commission Scientifique du Nord en Scandinavie, en Laponie, au Spitzberg et aux Feroe, 

 pendent les anndes 1838, 1839 et 1840, published by the French Government under direction of M. Paul Gaimard, 

 President of the Commission. The memoir comprises chapter V of volume II on meteorology, pages 291 to 332. 



