PHILOSOPHICAL SOCIETY OF WASHINGTON. 



49 



observation is deduced from the differences A of the n observed 

 and computed declinations, and is expressed by e^= /0- 455 SA ^ 



where ?i = the number of unknown quantities in the equation 

 which were found from the observations themselves. The 

 principal uncertainty in the investigation arises from compara- 

 tively large observing errors in the older observations and from 

 the fact that the observations are made at different places in the 

 same general locality, thus introducing possibly local deflections. 

 For Philadelphia the deflecting force, when greatest, is estimated 

 at about j\ of the horizontal force. 



To illustrate the above formula we have the expression for the 

 secular change for New York 



I)=+Q°A'6 + 2°.29 sin (1.6 m — 5\5) + 0°.14 sin (6.3 m + 

 64°) with the following table of observed and computed values, 

 where + indicates tcest deflection. 



jSTumber of observations 19 ; apparent probable error of an 

 observation rt 15'; time of last stationary epoch, easterly di- 

 gression, 1797 ; amount at easterly digression -}- 4°. 0; annual 

 change (increase) in 1870 + 2'.4, and in 1880 -\- 2'. 5. 



For San Francisco, California, W'e have the expression D = 

 — 13°. 34 + 3°.23 sin (1.00 m— 130°.3) and the corresponding 

 values: number of observations 15, probable error of an observa- 

 tion ±8', time expected for next stationary epoch, easterly digres- 



