Page:Scientific Memoirs, Vol. 2 (1841).djvu/235

Rh of the accidental anomalies of the magnetic force itself, and that they do not correspond to the same year ; and, on the other hand, that our formulæ do not include members beyond the fourth order, whereas those of the following order may still be very sensible. When due weight is allowed to these circumstances, the agreement between calculation and experiment appears to be as satisfactory as we are entitled to expect from a first attempt.

As our expression for $$\frac$$ may therefore be safely regarded as coming near the truth, at least in its more important members, it has appeared worth while to form a graphical representation of the course of the numerical values of this function. This has been done in a map drawn by Dr. Goldschmidt, in three parts, the first on Mercator's projection, passing round the globe, and including all the parallels between 70° north, and 70° south lat.; the other two being polar projections, extending to lat. 65°. The corrections and additions which will arise from a fresh calculation resting on more perfect data, may, doubtless, cause material alterations of position in these lines, particularly in the high southern latitudes; but no important change in the whole form of the system of lines can be supposed without such alterations in the expression for $$\frac$$ as would destroy the agreement with existing observations. We are thus led to the important result, that the system of lines of equal values of $$V$$, on the surface of the earth, is actually comprehended by the simplest type described in Art. 13, and that consequently there are on the earth only two magnetic poles, apart from the possible case of local exception spoken of in Art. 13.