/ 



> V 



Bowditch on computing the Dip of the Magnetic Needle. 61 



(1 4-cos. 6 I ) .tan 31^ 

 2.(sm.2l+siu.4l)» 



which may be reduced to the form 



1 



8. co$. 3 1. COS. P 



by putting i + cos. 6 1 = g. cos. 8 P ; sin. S I+sin. 4)1 = S. cos. I. sin. 8 Tj 



Sin S I ' 



tan. 81= — -rri, and reducing the expression which arises from tliis 



COS* o X 



substitution. By this means the two complicated factors spoken of 

 in Pas;, 90 of the same work, namely -^7^ — r- ,^"'^' . ' , ■,■ 



* ' <•> 2(sin.£I -f sin. 41) 



and tan. 3 P, 



are replaced by the more simple ones 



1 



COS. i^ 



and 



1 



COS. 3 r 



9 



\ » 



y 





\ 



