Influence of Masses of Iron on the Mariners' Compass. oA9 



within the sphere, as the radius of the sphere is to the distance 

 of the latter point from the centre ; putting which equal to c', 



this attraction may he expressed by -7^. A similar mode of 



reasoning will also hold for the attraction of a point in the interior 

 of the second sphere ; and, consequently, the forte which acts in 

 the direction of the dip, upon a point within both spheres, will 

 be equal to 7?. But this force is ecjual to the intensity of the 

 terrestrial magnetism at tlie place ; wherefore the constant co- 

 efficient 77 must be equal to the same intensity. 



From what has been demonstrated above, it appears that no- 

 thing more is necessary to convert the formulae, before given, for 

 the laws of magnetic attraction to a sphere of iron, into equa- 

 tions, than to multiply them by ^'- ; care being taken, if the di- 

 rective power of the needle is concerned, to reduce it to the ho- 

 rizontal plane. 



Applying these observations to the expression (7), and putting 

 the dip =c/, it may be readily converted into 



^ .S/3 sin i. ro-s k- ms (p 



tan = • — :; ; 7^: ; : — ', 



(^^3 — ,3j 00s d + iii- COS k cos J cos <f 



0,3 



which i)uttinc; -^ — = m becomes 



;- in. sin 2 COS Jr. cos ip , ■ ■ ■.■ r 



tan ?= ; or, wJnch will 01- 



cos (/ + m. cos k. coj i cos ip 



ten be found a convenient transformation, 



ro»('c ^A- cosec 2/ 



cot i= cot ^ + : — . 



in. (tan d. S'.'C i + cot k) 



The utilitv of these formulae is manifest: they enable us to find 

 the deflexion occasioned by the attractions of splicres, or of 

 masses of iron which can be assimilated to them, without having 

 recourse to anv previous observations; provided only that the 

 dip is known ; and when this element is not given, they enable 

 us to find it, with very considerable accuracy, from the data fur- 

 nished by a single exi)eriment ; which latter point will not be 

 esteemed of trivial importance when it is considered that the 

 high price of dip])ing needles prechid^s their being brought into 

 very general use ; whilst their delicacy, and the circumstance of 

 their motion being in a vertical })lane, renders it impossii)le to 

 em|)lov them at sea. 



As the determining the dip with precision is an object of much 

 moment, it will be necessary, in making experiments with tiiis 

 view, to place the ball at a considerable distance from the hori- 

 zontal plane, within which the deviation is totally independent 



of 



