on the Mariner'' s Compass. 453 



vtrlical pliuie are much less than those in the horizontal; a 

 circumstance that was noted by Mr. Barlow, although that gen- 

 tleman has not given the law by which the former of tliese ac- 

 tions is regulated*. 



Many curious corollaries may he deduced from the formula 

 given in the preceding pages. Thus from our expressions (S) 

 and (9) it may be shown that there are tliree planes of no at~ 

 traction in every sphere; one of which has reference to the dip- 

 ping needle ; one to the horizontal compass; and one is corti- 

 nion to both : these planes are manifestly determined by making 

 cos I = o; sin I ~ o; and sin 2(p = o ; and are therefore re- 

 spectively parallel to the meridian ; at right angles to the meri- 

 dian ; and at right angles to the dip. 



Were the needle acted on by no other attraction than that of 

 the sphere, its position would be such that 



tan 8'= 2 cos 9; 

 where 5' in this case represents the dip. This formula follows 

 immediately from the equations (1) and (2; ; for from them we 

 have 2. cos ^ : sin (^ : : I : cos S . 



cos &'= i tan cp. 

 tan I'— 2 cot 9. 



The law here given is that which Dr. Young has assumed, as 

 regulating the position of the needle on the earth's surface : it 

 was first deduced by a foreign mathematician, from a much more 

 complicated expression of Biot's : and it is not a little singular 

 that that philosopher should have missed it, considering how very 

 readily it follows from the principles he has employed. 



I shall conclude this part of the subject with a deduction that 

 follows from onr })receding investigations; which serves stroa^ly 

 to mark the analogy between the natures of magnetism and elec- 

 tricity ; and is at the same time attended with rather a para- 

 doxical circumstance. I allude to the fact, that the quavMxj of 

 magnetic fluid developed in a sphere or spheroid, is as the sur- 

 face ; and is therefore the same ivilldn certain limits, for sphe- 

 roidal or spherical shells, as for the ivhole solids ; Imt thai 

 nevertheless the attraction to tlio^e solids vciries as the cubes oj 

 (heir diameters -f. 



• The relations here deduced between A and A', J and V, must be con*- 

 jidered as relating only to tlie approxiinati<e expressions 8 and 10 5 and 

 not to the n;;orous formula; 7 and '.K 



t A view of the subject something similar to vvhatjl have here g'''r.n, 

 conf.' lied by some crtperiinent'* on the attractions of iron i»kte?, had led 

 inc to pe-.-coi'vc the first part of thi:i law, about t!io same time that Mr. Bar- 

 low discovered the second. The two facts appeared so completely opj)Oseil, 

 that I found it dilFiL-ult to persuade that gentleman (unable as I then was to 

 ^cf^ojnt for ths anomaly) of tbc truth of my deduction: an accidental ex- 

 ueilftictt h%» sia",R ho'.TCvar c>iuvtiib<<4 hiaiJbf tb': fat.1. 



The 



