7(5 



M A G NE TI C SURVEY < » F 1' E N N S V L V A X I A 



Let X = resulting horizontal force, 



X = assumed mean horizontal force for 1842.0 at the mean latitude and 



mean longitude, x its correction. 

 dL = difference of latitude, dM= difference of longitude, 

 x, y, z, p, q, and ^ to be determined from the observations 

 X = X Q + x + xdL + yd M cos L + zdL dM cos L + pdD + qdJP cos 2 L. 

 Forming the conditional and normal equations we find the expression 

 X = 3.890—0.1787 dL + 0.0085 dMcos L + 0.0161 dL dMcos L—O.OOlldL 3 



+ 0.0027 dlP cos" L. 

 where dL = Lat.— 41°.38 

 <1M= Long.— 77.58. 

 This formula is applied for determining the relative weights of the observations 

 from vibrations and by deflections of the dipping needle ; for this purpose the hori- 

 zontal force was computed by the formula, and the results compared with observa- 

 tion. From the differences Ave find the probable error of an observation (and local 

 irregularity) = _+ 0.036 for the bar and cylinder vibrations, and Hr 0.062 for the 

 Lloyd needle deflections and dip ; the relative weights, therefore, become 754 for 

 the former, and 257 for the latter, or nearly as 3 to 1. These weights have been 

 adopted. 



Formation of nine groups of five or six observations in each, with weights. The 

 arrangement is the same as in the case of the dip. The sum of the weights for 

 each group is, as near as may be equal. 



