Omitting correction terms depending on the temperature and on the inductive effect of the earth's magnetism on the moment of the deflecting magnet, if 0 is the angle which the axis of the deflected magnet makes with the meridian when the centre of the deflecting magnet is at a distance r, then zM sin B=I+P+y2 &c., in which P and Q are constants depending on the dimensions and magnetic states of the two magnets.
For a curve of the order the expression Zm(m - I) - 6 - K is termed the " deficiency " (as to this more hereafter); the equation (to) expresses therefore that the curve and its reciprocal have each of them the same deficiency.
The number of coefficients is 2(m+ r) (m+2); but there is no loss of generality if the equation be divided by one coefficient so as to reduce the coefficient of the corresponding term to unity, hence the number of coefficients may be reckoned as 1(m-1-- 1) (m+2) - r, that is, Zm(m+3); and a curve of the order in may be made to satisfy this number of conditions; for example, to pass through Zrn(m+3) points.