Page:Scientific Memoirs, Vol. 2 (1841).djvu/222

 210 given in Art. 22, consists in the unknown values being broken into groups, each of which is determined by itself, whereby the calculation is greatly facilitated; whereas, in the other mode of proceeding, the intermingling of all the unknown quantities renders their separation extremely difficult. On the other hand, the disadvantage of the second method is, that, instead of being founded on direct observation, it rests on graphical representations, which, in districts where we do possess observations, represent them but rudely, and which, in districts where observations are wanting, are only conjectural, and, to a certain degree, arbitrary, and may therefore differ considerably from the truth. However, we must either postpone all attempts, till such time as we shall be provided with far more complete and trustworthy data than we now possess, or, with our present very scanty means, make a first attempt, from which we are entitled to expect little more than a rough approximation. A close comparison of the results of calculation with those of actual observation in all parts of the earth, furnishes a certain standard by which our success may be estimated. And if this test shall show that the first attempt has not entirely failed, it will powerfully assist suitable preparations for future fresh attempts by either method.

Several years ago I repeatedly began attempts of this kind, from all of which the great inadequacy of the data at my command forced me to desist. I might earlier have concluded such an essay if I had obtained the fulfilment of my often-expressed wish for a general map representing the horizontal intensity. This want could not be supplied by the combination of the imperfect general maps of dip and of total intensity, then existing.

The appearance of Sabine's Map of the Total Intensity (in the Seventh Report of the British Association for the Advancement of Science) has stimulated me to undertake and complete a new attempt, which must be regarded, however, only in the light mentioned in the foregoing article. The data employed in the calculations are for twelve points on seven parallels. They are taken for the intensity from the above-mentioned map; for the declination from Barlow's map (Phil. Trans. 1833); and for the inclination from Horner's map (Physikalisches Wörterbuch, Band vi.). Considerable portions of these maps still remain blank,