100 Prof. A. W. Riicker on Vertical Earth-Air 



The test to be applied is, whether the line-integral of the 

 magnetic force taken round a re-entrant circuit on the 

 surface of the earth is or is not a vanishing quantity. 



The irregular form of the United Kingdom makes the appli- 

 cation of this test more difficult than it would otherwise be ; 

 but as two detailed Surveys of Great Britain and Ireland have 

 been carried out by Dr. Thorpe and myself for the epochs 

 1886 and 1891 respectively, the data at our disposal are so 

 numerous that I thought it worth while to undertake the 

 inquiry. 



The actual work of calculation has been carried out almost 

 entirely by two of my students, Messrs. Kay and Whalley. 

 My best thanks are due to them for the care and skill they 

 have displayed. 



The facts on which the investigation is based are as follows. 



The first survey (1886) included 205 stations, at all of 

 which observations were made by Dr. Thorpe or myself. 



The true, and therefore irregular, isomagnetic curves were 

 drawn for the epoch January 1, 1886, and the terrestrial 

 curves, from which the local disturbances were eliminated, 

 were also calculated for the same date (Phil. Trans, vol. 

 clxxxi. A, 1890). 



The second survey included observations at 677 stations. 

 These were made by ourselves, or, under our superintendence, 

 by Messrs. Briscoe, Gray, and Watson. The results are 

 about to be published by the Royal Society. The terrestrial 

 isomagnetic curves were drawn for the epoch Jan. 1, 1891. 

 The secular change having been carefully determined by 

 special observations and methods, the values of the elements 

 and the terrestrial curves obtained for the earlier date were 

 reduced to Jan. 1, 1891. Thus the whole of the 882 stations 

 were available for drawing the true isomagnetics for the 

 latter date. The two sets of terrestrial curves obtained from 

 the second survey and from the first survey reduced to the 

 second epoch did not agree exactly, and the lines bisecting 

 the intervals between them were taken as our final result for 

 the terrestrial curves in 1891. 



The following sets of curves will be considered in this 

 paper : — 



(1) The terrestrial isomagnetics obtained in the first sur- 

 vey for Jan. 1, 1886. These will be referred to as the 1886 

 curves. 



(2) The same curves reduced by the secular change to 

 Jan. 1, 1891. These will be called the first survey 1891 curves. 



(3) The terrestrial curves for 1891 deduced from the second 

 survey. These will be called the second survey 1891 curves. 



