MAGNETIC SUKVEY OF JAPAN FOR THE EPOCH 1895.0. 131 



OY 



expre;:;sing vertical v;iriutioDS of rectangular cuuipoiients in terms 

 of their liorizontal variations.* It appears at first sight that the 

 curvature of the earth surface may he neglected for the extent 

 of the country covering only a few degrees of longitude and 

 latitude ; calculation shows, however, that it plays an important 

 part ; transforming, therefore these equations into polar co- 

 ordinates, we have 



OX J r d'A ^ 



OS K V dip 



J Y _ 1 / 1 '''>^ _y 

 dz ~ K V cos (f d'A 



dZ 1 / OX 1 OY ^. , ,„\ 



dz Vi\ df ^ coi^(p dk » ^ J 



V\. being the mean radius of the earth, I <p longitude and latitude 

 measured positive toward zenith, west and north respectively. If 

 the horizontal force, declination and dip are, as usual, expanded 

 in terms of the co-ordinates, we have to put 



X = H cos o 

 Y = II bin o 



z = \ibid 



* After tlie volume was put into i)riiit, Prof. II. Na^.'inka lias di'awn the writer's a1- 

 tentiou to the Sixth ("lKi]>ter of V. Neuinanu's " Theoi'ie des Potentials" where the saiijc 

 problem is dibcusrinl, though apiiruaelied iu diilereut way. 



