Deviation of the Compass by the Length of its Needle. 151 

 of a diameter, the deviation is 



M 1 f A . 3a 2 \ . y , . 15 a 2 cos 3 a . Q r ,l 



So that if a =30°, or if the two needles be each 30° on each side of the 

 diameter which is parallel to them, the sextantal term disappears. 



If we have four needles the ends of each pair a° and a'° from the 

 ends of a diameter, the sextantal term has a factor, 



cos 3 — ! 



2 



Showing that if, as in the Admiralty compass, the needles of each 

 pair are placed at equal distances on each side of the lines of 30°, 

 the sextantal deviation will he reduced to zero. 



A similar investigation shows that the same arrangement of 

 needles reduces to zero the octantal error introduced by the too 

 great proximity of the soft iron ; and further, the error introduced by 

 the magnetism of the needle inducing magnetism in the soft iron in 

 its vicinity. 



The conclusion of the authors is that by the use of the Admiralty 

 standard compass, or of a compass with two needles each 30° from 

 the diameter parallel to them, the correcting magnets and soft iron 

 correctors may be placed much nearer the compass than can safely be 

 done with a single needle compass card, and the large deviations 

 ound in iron ships far more accurately corrected. 



Correction of the Quadrantal Deviation. — It has long been known 

 that two compasses placed as in the common double binnacle, produce 

 in each other a negative quadrantal deviation. The discussion by 

 Mr. Evans of the deviations of all the iron-built ships in the Koyal 

 Navy (Phil. Trans. 1860, p. 337), showed that the quadrantal devia- 

 tion in such ships is always positive ; and as there is great difficulty 

 and inconvenience in the usual mode of correcting large quadrantal 

 deviation by soft iron, it occurred to Mr. Evans that the correction 

 might be made by the reciprocal action of two compasses placed at 

 the distance of 18 to 24 inches from each other, as in the common 

 double binnacle. The precautions to be used are that the two com- 

 passes must be of equal power, and as the correction is inversely as the 

 earth's horizontal force at the place, if great accuracy is required there 

 ought to be the means of adjusting the distance of the two com- 

 passes, and the method will probably be found inapplicable in very 

 high magnetic latitudes. 



The deflection so produced by one compound compass on a like 

 compass is 



3M1 

 b 



1 f/. . 5 a* 2 \ - n yf 35 a 2 cos 3 a . .oil 



- a cos a ^ [ 1 +- - 72 cos 2 a sin 2 £'— — sin 4 £' y , 



H L\ 3 b 2 J b b~ cos a J 



In this arrangement therefore an octantal error is introduced which 

 may be avoided by the use of two Admiralty standard cards, or cards 

 with two needles each 30° from the diameter which is parallel to them. 



