150 Royal Society : — 



1? and C arc coefficients depending partly on the distribution of the 

 hard and soft iron of the ship, and partly on the magnetic dip and 

 horizontal force at the place. 



In all ships which have been examined, A and E are so small that 

 they may be neglected ; and, if the deviation be of such an amount 

 that we may take £ for sin £, 



£=B shU' + C cos £' + D sin (£ + £'). 



The first two terms represent the " Semicircular" deviation, the 

 last term the '* Quadrantal" deviation. 



The "semicircular" deviation is, on the plan proposed by the 

 Astronomer Royal, and extensively practised in the mercantile marine, 

 corrected by magnets ; the "quadrantal " by masses of soft iron placed 

 on each side and at the same level as the compass ; and when the di- 

 stance of the correction is sufficiently great, this correction may be 

 considered as perfect for the time and place at which it is made ; but 

 when this is not the case, errors are introduced, which it is the object 

 of the paper to consider. 



Mr. Evans observed that the standard compass of the 'Great 

 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 G-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 " octantal " 

 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 simpler 

 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 2a by a magnetic particle M at the same level 

 and at a distance b, is 



M 1 J A , 3a 2 \ . ., , 15« 2 . „„,"} 



giving a sextantal deviation bearing to the semicircular proportion of 

 Id a 2 # , , 3 a 2 

 8"^ : 8 b 2 ' 

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



