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sophers who are best acquainted with the dipping-needle are decidedly 

 that the dipping-needle is not yet in such a condition as to induce 

 implicit confidence in its indications, and as, moreover, the influence 

 of geological and meteorological sources of disturbance are yet so far 

 unappreciated as to enable us to correct the observations for them, 

 the author hesitates to draw any positive conclusion from the results 

 he has obtained. However, the results thus obtained, being the di- 

 rect and legitimate deductive consequences of the observations, it is of 

 course impossible by any other course of investigations which proceeds 

 from the same data, to draw a conclusion more to be depended on 

 than this. The process he considers to be mathematically correct, 

 as well as complete, and practicable ; the question, as far as this test 

 is concerned, must remain open till satisfactory data can be obtained : 

 and he proposes at the earliest period to resume the numerical dis- 

 cussion of such observations as he may be able to procure. 



Mr. Davies remarks, that from the great labour of the calculations, he 

 has been led to attempt a more brief method of examination by means 

 of carefully executed geometrical constructions ; employing for that 

 purpose the descriptive geometry, which has the advantage of bring- 

 ing all the work to depend on the intersection of the hyperbola and 

 straight line, situated upon the same plane. The resulting magnetic 

 axes of the few cases he has constructed, though very far from co- 

 inciding, are yet positive in the same general region of the figure and 

 therefore the probability that their want of coincidence arises from 

 erroneous and uncorrected observation is increased, and the impor- 

 tance of a more extended and careful series of observations consider- 

 ably augmented. 



For the purpose of examining the general character of the magnetical 

 phenomena which ought to result from the hypothesis of the duality of 

 the poles, Mr. Davies proceeds to investigate the formulae which ex- 

 press those phenomena. These are, the magnetic equator, — the points 

 at which the needle should become vertical, — the lines of equal dip, — 

 the Halleyan lines, or lines of equal variation, — the isodynamic lines 

 of Hansten, — and the points at which the magnetic intensity, com- 

 pared with the points immediately contiguous in all directions, is a 

 maximum, or in other words, where the isodynamic lines are reduced 

 to points. The first two of these only, are treated in the present 

 paper ; the remaining ones will be the subject of a future memoir 

 shortly to be submitted to the Society. 



The mathematical processes themselves scarcely admit of verbal 

 description ; but the results of the investigation are briefly these. 



When the centres of force are situated within the sphere, there will 

 be one only, or some even number of continuous lines on the surface 

 of the earth, at any point of which the needle will be horizontal, ac- 

 cording as the poles be of equal or unequal intensities. Whether 

 the magnetic equator be determined with sufficient accuracy to assure 

 us that there is but one such line, is a matter of considerable doubt ; 

 but if it should be admitted that it is, it offers a strong confirmation of 

 the strict analogy between the terrestrial and all other magnets with 



