Iloyal Society. 295 



some natural philosophers with a view to apply that mode, have either 

 entirely failed, or their results can at best be considered only as im- 

 perfect approximations. 



Professor Gauss, who has made frequent trials of both those modes 

 of proceeding, is satisfied that the second is, on many accounts, far 

 preferable to the first. 



The real difficulty consists in this, that other elements depending 

 on the individual nature of the needles, enter, as well as the value 

 of the limit, into the influences observed. That effect is represented 

 by a series which proceeds by the negative powers of the distance, 

 beginning from the third; where, however, the following terms be- 

 come more considerable as the distance is smaller. Now those follow- 

 ing terms are to be eliminated by means of several observations ; but 

 a slight acquaintance with the theory of elimination easily convinces 

 us that unavoidable errors of observation will never fail to endanger 

 the exactness of the results, as the number of co-efficients to be eli- 

 minated is greater ; so that their number need not be very consider- 

 able to render the results of computation entirely useless. No pre- 

 cision, therefore, in the results can be expected, unless such consider- 

 able distances are employed as will make the series rapidly converge, 

 and a few terms of it suffice. But in this case the effects themselves 

 are too small to be determined with exactness by our present means 

 of observation ; and thus the ill success of the experiments hitherto 

 made is readily explained. 



However easy, therefore, in theory the methotrs of reducing the 

 intensity of terrestrial magnetism to absolute unities may appear, yet 

 their application will ever remain precarious until magnetic observa- 

 tions have attained to a much higher degree of precision than they 

 have hitherto possessed. It is with this view that Professor Gauss 

 has followed up several ideas long ago entertained by him relative to 

 the improvement of our means of observing; confidently expecting 

 that magnetic observations will, ere long, be carried to a degree of 

 perfection nearly, if not altogether, equal to that of the most delicate 

 astronomical observations. The expectation has been answered by 

 the result. Two apparatus fitted up in the observatory of Gb'ttingen, 

 and which have been employed for making the observations, of which 

 several are given in his memoir, leave nothing to desire but a suitable 

 locality completely secured from the influence of iron and currents 

 of air. 



The following short abstract from the detailed description of the 

 two apparatus and their effect, given in the memoir itself, will no 

 doubt be acceptable to naturalists interested in this kind of research. 



Professor Gauss has generally employed needles (if prismatic bars 

 of such strength may be designated by that name) of nearly a foot in 

 length, weighing each about one pound. They are suspended by an 

 untwisted thread of 2| feet in length, composed of thirty-two threads 

 of raw silk, and thus able to carry even double that weight without 

 breaking. The upper end of the thread is tortile, and the degree of 

 torsion is measured by means of a divided circle. To the south or the 

 north end of the needle (according as the locality renders either the 



