34S On Mr. Boiwycasllcs DUsotation on the 



the expression been correct, I think there would have been little 

 embarrassment in derivii^g it thus : 



When a magnetic needle is governed oiilv by the attractio)i of 

 a sphere, it has been demonstrated, in what precedes, that it is 

 acted on bv two forces ; one of wiiich tends to the centre of the 

 sphere, and the otlier arges it from the centre, in a line drawn in 

 the magnetic meridian, at right angles to the direction of the first 

 force. Hence, joining the centres of the needle and sphere, and 

 from the latter drawing a line as above; asd further making 

 these lines bear to each other the ratio of 2 cos (f: sin f, which 

 has been shown (page 450) to be the ratio of the forces in those 

 directions, they will represent those forces ; and hence the di- 

 rect'on of the needle will be that of the hvpothenuse of the tri- 

 angle of which these lines are the sides. 



But it is manifest that the angle included between the hvpo- 

 thenuse and the second of the above lines is e(jual to the dip of 

 the needle, or to its deviation from a tangent to the sphere ; 

 therefore putting this angle equal I', the first lina will be to the 

 second as 1 tf) cot I' ; combining which ratio with that of the 

 lines tl?emsclves there arises the required proportion 



2 cos (^ : sin <^ : : 1 : cot S'. 



Having now, I trujt, sufficiently explained those jioints which 

 have been objected to as obscure, I will take the op])ortunity ot 

 mentioning an improveme}it which has occurred to me since my 

 paper was inserted ; the nature of which will be best seen by 

 referring to our former expression 8 ; where it will be observed 

 that, since the constant quantity A is not given, the quantity of 

 the deviation cannot be determined without having recourse 

 either to experiment, or to a further application of the theory 

 than has yet been made; in which last manner the value of A 

 may be found as follows : 



Since it has been shown (page 450) that the force in the di- 

 rection CO varies as 



^ I (I + r. COS I ^ 



l~(J ~ (:■> + iJf (Flo? ip ) ' 

 and that, ctrfcris parilius, the attraction is as the cube of the 

 diameter; it follows that this force may be represented by 



fir' ^1 i! + I' cos ip ) 



c ( ri'' (.3 + ;j, ij-i COS if S 



Which formula expresses the diftcrence of the attractions of the 

 two spheres AN BS and A N'B 6' ; the attraction exerted by the 

 first of these will therefore be equal to 



Kilt the atti action of a point o*i the surface is to that of a jtoint 



within 



