180 



Eastern/ which had been corrected on Mr. Airy's plan by Mr. Gray 

 of Liverpool, had errors of between 5 and 6 on some points. It 

 occurred to him that this error was caused by the length of the 

 needle and the proximity of the correctors, and to test this he made 

 experiments on the deviation produced on needles of different length 

 by magnets and soft iron with the following results. 



"With 3-inch single needles deflected by magnets, the deviations 

 were nearly "semicircular;" but with 6-inch needles, and still more 

 Strongly with 12-inch needles, a "sextantal" error of very consider- 

 able magnitude was introduced. 



"With soft iron correctors deflecting a 7^-inch single needle, in 

 addition to the " quadrantal" deviation, a considerable " octautal " 

 error was introduced. 



"When the same experiments were made with an Admiralty standard 

 compass card, constructed as usual with four parallel needles, the ex- 

 tremities of which are 15 and 45 on each side of the extremities of 

 the diameter to which they are parallel, there was no appreciable sex- 

 tantal or octantal deviation. And on investigating the subject mathe- 

 matically, it appeared that this arrangement of needles, or the sintpler 

 arrangement of two needles each 30 on each side of the diameter^ 

 produces a complete compensation and correction of these errors. 



The formulae are the following : The diviation produced in a 

 single needle of length 2 a by a magnetic particle M at the same level 

 and at a distance b, is 



giving a sextantal deviation bearing to the semicircular proportion of 



15 a 2 , ,3 a 2 

 ~ti& : ^~8b*' 



If the compass has two needles the ends of each a from the ends 

 of a diameter, the deviation is 



So that if u =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, 



