ANALYSIS OF DISTUKBANCES. 175 



To give greater dcfiniteness, take the most favourable case where three consecutive turning-points 

 present themselves simultaneously in the D, H, and V records. Suppose the 1st and 3rd to represent 

 minima, the 2nd a maximum, and suppose the values of the elements answering to the two minima to be 

 identical. 



Let li, 1-2, l s be the times of the three turning-points, and let AD, AH, and AV represent the excess of 

 the values of D, H, and V at time (> over the values at time (i or at time ^3. 



If we take the condition of matters existing at time t\ as fundamental, we may regard the condition 

 existing at time (3 as arising from the action of a disturbing force All, whose components AX, AY, AZ are 

 obtained from (8) by assigning to AD, AH, and AV their values with positive sign. If, however, we take 

 the condition at time t- 2 as fundamental, we regard the condition at time t z as due to a disturbing force 

 AR', whose components are obtained from (8) by assigning the same numerical values to AD, AH, and AV, 

 but giving them the negative sign. The vectors All and AR' assuming the changes AD, AH, AV to be 

 small are numerically equal, but are oppositely directed. Presumably AR and AR' really represent, the 

 one the application of a force, the other its removal. The difficulty in practice is to know which is which. 

 As a rule, when an oscillatory movement occurs, the to-and-fro movements are not equal, and there are 

 usually both preceding and succeeding movements. Even if we take the sudden movements ushering in 

 storms there is room for some doubt. At Kew, for instance, when such a movement occurs, H is usually 

 found to bo enhanced after the first rapid change has ceased, but at the very commencement of the 

 movement there is at least sometimes a slight depression in the value. If no preliminary depression is 

 seen, it is certainly the natural thing to regard the disturbance as simply an increase in H, but still there 

 is the possibility that the rise represents in reality the removal of a disturbing force which has remained 

 nearly constant for a considerable time. We are much in the same position as an observer who sees the 

 length of a bar under test, but does not know whether it is loaded or unloaded, nor whether the load is a 

 tension or a compression. 



91. An investigation was made of the disturbed curves received from the co-operating stations, and 

 when the three elements presented synchronous changes and there appeared an agreement in time between 

 the changes recorded at two or more of the different stations, measurements were made. The algebraical 

 excess of the value of an element at the end of the interval considered over the value at the commence- 

 ment was regarded as representing the action of a disturbing force. No attempt was made to determine 

 whether the change was really due to the application of a force or to its removal. From the AD and AH 

 thus found the values of AN and AE (the components to geographical north and east) were calculated, and 

 also the values of AX, AY, AZ as given by (8). 



The resultant AR of AX, AY, and AZ was then found, and finally the inclination of this resultant to 

 the Earth's axis and the easterly longitude </> of the meridian plane containing it. 



The positive direction of the Earth's axis was taken as given by the radius drawn to the North Pole. 

 and <t>, are given, of course, by 



cos 6 = AZ/AR, tan </> = AX/AY (9). 



The most uncertain measurements by far at the co-operating stations were those of AV. The changes 

 in V were usually small. For 1902 no Falmouth V curves were available, so that there was nothing to 

 check the Kew ones by, and at Colaba the sensitiveness was throughout so small that a small change was 

 hardly visible. 



92. Tables LXII to LXVI at the end of this chapter give the results obtained from the measurement 

 of corresponding movements at Kew, Colaba, Mauritius, Christchurch, and the Antarctic. The occasions 

 dealt with are taken from the storms included in the plates. The times are all G.M.T. 



Of the examples for Kew in Table LXII, p. 181, those from August 20, 1902, April 5 and August 25, 1903, 

 refer to sudden commencements of storms. The same is true of the disturbance on May 8, 1902, between 

 11.59 a.m. and 0.9 p.m. This disturbance is treated as a whole for purposes of comparison with the other 

 co-operating stations, but also as composed of two parts for comparison with the Antarctic, where the 

 commencing movement is pronouncedly double. The rapid commencements were also treated as if the 

 mean derived from them represented a disturbance. 



