304 Hoyal Society. 



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 5 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 coin- 

 ciding, are yet positive in the same general region of the figure j 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. 



Forthe purpose of examining the general character of the magnetical 

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

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

 press those phsenomena. 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 Hansteen, — 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 oflVrs a strong confirmation of 

 the strict analogy between the terrestrial and all other magnets with 

 two poles, and thence an increasing confidence in all the other ana- 

 logies conceived to exist between them. 



The points at which the needle is vertical are given by means of two 

 equations, one of the fifth and the other of the second degree, and 

 hence altogether there are ten such points theoretically possible. How 

 many of these may be simultaneously real the equations do not, in 

 their literal form, seem capable of determining ; but at all events they 

 will, in all cases, bean even number, either 0, 2, 4, 6, 8, or 10. One 

 having been determined, one other at least must exist in the actual 

 circumstances of the terrestrial two-poled magnet. How many so 



