196 



KNOTT AND TANAKADAÏE 



comparing the observed and calculated values of the elements contain 

 ulso these 31. 



Each of the charts representing the various systems of lines (see 

 Plates VI 11 — XI) shows two sets of lines. The full lines are the 

 graphic representation of the Mean Formula for the whole country 

 worked out in the usual way by the method of Least Squares. The 

 dotted lines give a better idea of things as thcij are, being drawn by 

 free-hand inter[)olation amono'st the neiofhbourina" stations. The eve 

 can thus tell almost at a glance, not only to what degree of approxi- 

 mation the full lines agfree with the true state of thino's, but also in 

 what parts of the country magnetic disturbances are most pnjnounced. 



In combining the combinations, I assumed linear expressions in 

 longitude and latitude for the Dip, the Horizontal Force, and the 

 Total Force. It is quite clear, however, that any attempt to 

 represent the Declination by a simple linear function would end in 

 utter confusion. On the Declination Chart (Plate XI) it will be seen 

 that, roughly speaking, the dotted lines run parallel to the general 

 trend of the country itself and have a somewhat parabolic or hyper- 

 bolic form. To add (jther two terms involving the squares of both 

 the loni^itude and latitude would have increased the labours of cal- 

 culation enorniously. I therefore contented myself with adding a 

 term involving the square of the longitude, assuming, so to speak, a 

 parabolic curve with its axis parallel to a meridian line. The result 

 was uuicli more satisfactory than I had expected it to be. 



In the working out of the calculations, the stations were all of 

 course referred to the mean station ( 36° 30' X. Lat., 137° 9' E. Long.), 

 and the co-<jrdinates were expressed in angular units. From the 

 Formuhe so obtained, the lines shown on the charts were constructed. 

 The kilometre was then taken as the unit in which the co-ordinates- 

 were t(3 be expressed, the particular change-ratios being those which 



