120 HANDBOOK OF MAGNETIC COMPASS 



form of equipment, hence the force instrument method is discussed 

 below. 



The horizontal force instrument is simply a magnetized needle 

 pivoted in a horizontal plane, much the same as a compass. It will 

 settle in some position which will indicate the direction of the resultant 

 magnetic field. The method used to determine the strength of this 

 resultant field is by comparing it with a known field. If the force 

 needle is started swinging, it will be damped down with a certain 

 period of oscillation dependent upon the strength of the magnetic field. 

 The stronger the magnetic field, the shorter the period of time for each 

 cycle of swing; in fact, the ratio is such that the squares of the periods 

 of vibration are inversely proportional to the strengths of the magnetic 

 fields, as : 



In the above formula, let H represent the strength of the earth's hori- 

 zontal field in gauss and T represent the time in seconds for ten cycles 

 of needle vibration in that earth's field. Should it be desired to find 

 the strength of an unknown magnetic field, fl"', a comparative meas- 

 urement of time in seconds, T'^ for 10 cycles of vibration of the same 

 needle in the unknown field will enable calculation of H' . 



Since A is the ratio of two magnetic field strengths, it may be found 

 directly by the inverse ratio of the squares of the periods of vibration 

 for the same horizontal force instrument in the two different magnetic 

 fields by the same formula, without bothering about the values of H 

 and 5^'. 



The above may be used on one heading of the ship if the compass de- 

 viations are less than 4°. 



To obtain the value of lambda. A, more precisely, and where devia- 

 tions of the compass exceeds 4°, the following equation should be used : 



y^Fcos dy, j_cos dg.cos d^.cos dyT] 



where : 



T is the time period for the field H. 



Tn is the time period for the resultant field with ship 

 on a north heading, etc. 



cos d„ is the cos of the deviation on the north head- 

 ing, etc. 



