Formula and Determination of Constants 27 



As the first values of P and Q must be determined by an approximate value of 

 Hjm, a second approximation is sometimes necessar>\ The coefiicients, P and Q, 

 are also determined from observations made occasionally in the field, particularly 

 so at stations where comparisons of instruments with standards have been made. 

 In such cases, the observer carries out the usual field program of intercomparison 

 by using different pairs of deflection distances on different days, the various dis- 

 tances being ri, r-i, and rz, etc., used in pairs 1 and 3, 2 and 4, 3 and 5, etc. Equa- 

 tions of the form: 





are established for each pair. From the various pairs normal equations may be 

 formed and solved by the method of least squares. 



For obtaining the temperature coefficient, g, observations made for determining 

 the distribution coefficients are used, as this work extends over three or four days, 

 and generally sufficient range of temperature is had to secure fairly accurate values 

 of q by grouping the results for the magnetic moment, m, according to high and 

 low temperatures. This method has been adopted in preference to the ice-and- 

 boiling-water-bath method as approximating more nearly to natural conditions. 

 Furthermore the compilation of values of the magnetic moment of long magnet, 

 reduced to the standard temperature of 20 C, as resulting from the field work, 

 serves to improve the value of the temperature coefficient first used. 



It has not been possible to set forth more fully in this publication the methods 

 of observation and reduction in use by the Department. They are substantially 

 the same as those adopted by the writer when in charge of the magnetic work of 

 the United States Coast and Geodetic Survey. The reader desiring further 

 information may therefore be referred to the following publications issued by the 

 Coast and Geodetic Survey: Principal Facts of the Earth's Magnetism, by L. A. 

 Bauer, Washington, first published in 1902 and reprinted in 1909; Directions for 

 Magnetic Measurements, by D. L. Hazard, Washington, 1911.^ 



' For more extensive reference to the theory and methods of magnetic measurements the following publications, 

 among others, may be given: Handbuch des Erdmagnetismus, by Lament, Berlin, 1849; A treatise on magnetism, 

 by G. B. Airy, London, 1870; A treatise on magnetism, by Humphrey Lloyd, London, 1874; Directions for magnetic 

 observations with portable instruments, by C. A. Schott, U. S. Coast and Geodetic Survey, Washington, 1881; Theory 

 of magnetic measurements, by F. E. Nipher, New York, 1886; Traite de Magnetisme Terrestre, by E. Mascart, Paris, 

 1900; Erdmagnetismus, Erdstrom und Polarlicht, by A. Nippoldt, Jr., Leipzig, 1903; The law of action between 

 magnets, by Charles Chree, Philosophical Magazine, August, 1904; Ableitung des Ausdrucks flir die Ablenkung eines 

 Magnetnadel durch einen Magnet, by C. Borgen, Hamburg, 1891; see also Terrestrial Magtietism and Almospheric 

 Electricity, vol. I, 1896, p. 176. Reference might also be made to the various volumes of this journal for later develop- 

 ments in theory and practice of magnetic measurements. 



