Discussions of Ocean Magnetic Work, 1905-16 431 



of an abnormal value can only be detected when there are a sufficient number of obser- 

 vational results to determine the normal value with fair accuracy. 



At sea, the distribution of stations around the track-crossings, or intersections, can not 

 be planned with certainty. Conditions of sea and weather, and the ship's course, combine 

 to crowd or to scatter the magnetic observations irregularly along the tracks followed. 

 Consequently, the determination of the annual change may be strong, depending on many 

 observations for both dates, or it may be weak on account of a paucity of observations at 



one or the other time. 



As new tracks are made, the crossings become more frequent, so that in a tew years 

 more the annual amount of the secular variation for a given period may be determined at 

 any desired part of the navigable oceans. For the present, however, the average annual 

 changes as deduced from Galilee-Carnegie crimes to date, must be considered as 'preliminary, 

 vending additional information and more complete investigation. 



The prehminary mean annual changes for the three magnetic elements, as detemuned 

 from the Galilee and Carnegie results for an interval of four years or more, between August 

 1905 and September 1916, are given in Tables 96-98 for the Pacific, Atlantic, and 

 Indian Oceans, with the time-intervals for which they apply. The number of observa- 

 tional results from which the annual change is deduced is given for each date and also the 

 least number that occurs in any group. These numbers together with the elapsed time- 

 intervals are some indication of the relative reUabiUty of the corresponding annual change. 

 When the least number is 3, or less, the corresponding value of the annual change must be 

 regarded as weakly determined until future results confirm the hnear distribution assumed 

 and the absence of abnormal values. 



In these prehminary computations no attempt has been made to ehmmate the ettects 

 of the diurnal variation of the magnetic elements. In general, at the tunes selected for the 

 observations, these effects are small. Furthermore, usually the local mean tunes are about 

 the same for the two dates of comparisons so that the diurnal-variation effects are practi- 

 cally eliminated in taking the differences of the values of the magnetic elements at the two 



The annual changes given in Tables 96-98, have been derived by several different 

 methods, briefly described as follows: 



a If the mean geographic positions of the two groups of observations for the two intersecting 

 tracks are practically identical, the mean values of the magnetic elements of each of the two groups 

 are taken as the values at the common point for the respective dates. The difference between the 

 two values of each element, divided by the elapsed time, is taken as the average annual change. It 

 most frequently happens, however, that the mean geographic positions for the two dates do not 



6 The method most commonly used was to arrange in groups the observations made at the 

 intersection of two or more tracks. The mean values of the dates, geographic positions, and cor- 

 responding magnetic elements for each group having been determined, the pomt of intersection of 

 lines joining the mean positions of the two groups of each intersecting crmse was found graphically. 

 By the method of simple ratios and from a comparison of the mean values of date, position, and 

 magnetic elements, as determined for each group, the magnetic element for its corresponding date 

 was deduced for this point of intersection. 



c When two groups as in a, or four groups as in h, were not available, as, for example, in 

 the case of the observations made on the tracks converging to Gardiners Bay, then a least-square 

 adjustment was made, assuming that the values of the magnetic elements depend upon their geo- 

 graphic position and that the value of an element E, at a point whose latitude and longitude are 

 * and X, respectively, may be expressed by an equation of the form 



E = E,t-'ry^4t-'rZ^\ cos <^ 



in which A,t> = <t> -<!><» AX=X-Xo, and «o, ^o are the geographic coordinates corresponding to the 

 approximate mean value £«• The terms of second degree and above have been omitted and cos 4> 



