Page:Scientific Memoirs, Vol. 2 (1841).djvu/225

Rh

After these components have been calculated for a given place, we obtain in the following manner the several parts of the determination of the magnetic force, according to the customary form.

Let $$\delta$$ be the declination, $$i$$ the inclination, $$\psi$$ the total, and $$\omega$$ the horizontal intensity. Determine first $$\delta$$ and $$\omega$$ by means of the formulæ and then $$i$$ and $$\psi$$ by means of the following formulæ:

As the formulæ for $$X$$, $$Y$$, $$Z$$, contain 71 members, their immediate calculation is a considerable labour. Its repetition for a great number of places appears the more alarming, considering that we could hardly hope to be secure from the possibility of mistake without going twice over the whole. But little would be gained by suppressing all those members of which the co-efficients are less than an integer, or even less than 10 integers, for the remaining members would still amount to 65. But as the whole value of the work would remain uncertain if not tested by a considerable number of actual observations, I have encountered the labour of calculating a table, by the assistance of which the work will be in the highest degree