166 MESSES. SMITH AND EVANS ON THE EFFECT OF THE LENGTH OF 
In this case there was no sextantal deviation, but with a 7^-inch single needle there 
was a large octantal term in addition to the normal quadrantal deviation, while with an 
Admiralty Standard compass card the octantal term almost entirely disappeared^ leaving 
only a true quadrantal deviation. 
These results, as to the deviation of single needles, explained the residual error found 
in the corrected standard compass of the Great Eastern. These errors were evidently 
partly sextantal and partly octantal, and had been caused by the great length of the 
needles and by the proximity of the magnets and soft iron correctors, particularly of the 
latter. 
The remarkable features observed in the deviation of the Admiralty Standard compass 
suggested the idea that the arrangement of the needles in that compass might produce, 
in the case of deviations caused by a magnet or mass of soft iron in close proximity to 
it, a compensation of the sextantal and octantal deviations, and this, on the subject 
being investigated mathematically, proved to be the case, this particular arrangement of 
needles reducing to zero the coefficients of the terms involving the square of the ratio of 
the length of the needle to the distance: of the disturbing iron ; so that this remarkable 
result was obtained, that the arrangement of needles which produces the equality in the 
moments of inertia is by a happy coincidence the same as that which prevents the 
sextantal deviation in the case of correcting magnets, and the octantal deviation in the 
case of soft iron correctors. The consequence is that, by the employment of Admiralty 
Standard compass cards, or of cards with two needles each 30° from the central line, 
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 that the large denudations 
found in iron ships may be thus far more accurately corrected. 
The mathematical investigation further shows, what we have already adverted to, the 
advantage, when a magnet is used to correct a large deviation in a single needle, of the 
magnet being placed as nearly as possible directly above or below the centre of the 
needle. A magnet so placed has the further advantage of causing no error from 
heeling. 
The mathematical investigation led to another result, which has also been confirmed 
by experiment, viz. that the sextantal deviation of a single needle caused by a magnet 
at the same level may be prevented by using, instead of a single magnet, two equal and 
similar magnets, similarly placed with regard to the needle, but arranged so as to form 
an equilateral triangle with the centre of the compass. Such a pair of magnets pro- 
duces a semicircular deviation without any sextantal deviation. But this result, how- 
ever interesting theoretically, is probably not one which can be made practically 
useful. 
The length of the single needle may also be a cause of error in a different way. The 
magnetism of one end of the needle induces magnetism in any soft iron near it, which 
magnetism reacts on and causes a deviation of the needle. This deviation likewise is 
prevented by the arrangement of the needles in the Admiralty Standard compass. 
