Magnetical Dip iti the United States. 17 



in the two groups, have bearings differing 19^ 53' from each 

 other. What will be the bearings of those lines in the interme- 

 diate region ? Ought the two lines to be produced, the one from 

 Iowa, and the other from Ohio, until they meet ? The two 

 would not certainly form one " straight line,^^ which is called for 

 by the hypothesis. Or, ought there to be an intermediate " cen- 

 tral position adopted," and a new bearing of the isoclinal line de- 

 termined ? This would likely give us a polygon. Now " adopt," 

 or assume an infinite number of " central positions," and calcu- 

 late as many bearings of the isoclinal or equal dip lines, and the 

 result will be curves, precisely what I contend for. But this is 

 contrary to the " hypothesis," which calls for "straight lines." 

 Here might be a very great modification of the " computed errors 

 of observation." My own opinion, founded on observations of 

 considerable extent, is that the lines do proceed in curves which, 

 in the present state of our knowledge, can be traced only by ob- 

 servation. The hypothesis that the magnetical forces proceed in 

 lines, less tortuous in their course than observations would seem 

 to indicate, is one by no means of recent date ; for it is found in 

 the philosophical writings of the Baron Swedenborg, together 

 with a very specific account of the sources of error, in making 

 observations. The appearance of mathematical calculation, espe- 

 cially under the symbols of modern analysis, is very imposing to 

 many a popular reader, who may not reflect that all mathematical 

 results are dependent on the data, the assumptions, the hypothe- 

 ses ; if these be false or erroneous, the superstructure is but a 

 wreath of mist. Grant the data, and the calculations in these 

 times, are but a schoolboy's task.* 



On page 87, Prof. Loomis observes in reference to my obser- 

 vations, as treated in his previous paper, " at Prairie du Chien, the 

 discordance is more considerable. The difference [from the hy- 

 pothesis] I now find is — 7^3 ; in my former paper —20'. The 

 discordance is owing in part to the curvature I ascribed to the 

 isoclinal lines, by which most of the observations seemed best 

 represented, though the apparent error of this observation was 

 increased." All this is perfectly candid. He admits a curvature 

 in the " straight lines," and that the lines are those of his own 

 creation, subject to be changed at pleasure ; not the isoclinal 



* It is evident from the manner in which Prof. L. uses the hypothetical straight lines, 

 that they were not really the lines of equal dip, but that they were tangents to those lines. 

 Vol. xLi, No. 1.— April-June, 1841. 3 



