THE COMPASS IX MODERN XA Via A TKiS ...7, 



found similarly disposed on the ]).)i-t side ; and the |.rc)l)leni i.s 

 simplified to pairs of parallel forces, each pair having its result- 

 ant parallel to one of the ciiordinate axes. The etl'ect of everv 

 magnetic particle, whether of permanent or induced niagiietisnl 

 may be reduced to this condition. If the sum total of all the 

 magnetic forces parallel to each ci3ordinate axis he trauslerred 

 to it, and the whole be conceived to he concentrated ui)on tlie 

 north point of the compass-needle, the entire magnetic i)ower 

 of the ship may be compared to that of three imaginary com- 

 pound-magnets—one laid horizontally in the axis of X ; the 

 second, also horizontally, in the axis of Y, and the third, verti- 

 cally, in the axis of Z. By steaming around a circle in the open 

 sea and observing the compass ])earing of the sun with theship'.s 

 head on equidistant compass courses, and also, at tlie same 

 times, the astronomical bearings of the sun, the magnetic etl'ect 

 of the ship — that is, of the three imaginary compound-magnet.s 

 in the axes of X, Y, and Z— which causes the needle to detlect 

 from the magnetic meridian by different angles at the different 

 headings, can be immediately found, if the variation of the com- 

 pass due to the geographical locality is known. As the .ship 

 makes a complete circle in azimuth, the north end of the needle 

 is drawn sometimes to the right hand of the magnetic meridian 

 and sometimes to the left hand ; in the tbruier case the detlec- 

 tion is called east deviation and in the latter west deviation. A 

 table of these deflections, serially arranged, is called a table of 

 deviations of the compass. The harmonic analysis of such a 

 table of deviations consists in representing each of the element- 

 ar}' magnets, whose effects contribute to make up the imaginary 

 compound-magnets, as a separate disturbing cause whose effect 

 upon the compass needle may be represented by a constant 

 multiplied b}' a simple harmonic function of the compass-azi- 

 muth of the ship's head. Adding together the effects of the 

 different disturbing causes, thus represented, and jilacing them 

 equal to the deviation observed on a certain heading of the ship, 

 a conditional equation may be formed for each of the headings 

 upon which the deviation was observed. 



From such a series of conditional equations normal equations 

 may be found by the method of least squares, and from them 

 the harmonic constants which rei)resent the elementary disturb- 

 ing magnets. Thus it is that from the ertect an intelligent com- 

 prehension of the cause may be gained. 



With these coefficients a navigator may comitate heforehan.l 





