64 INTRODUCTION. 



+ B + b ; but if they differ considerably, we must 

 seek the true dip by the follov/ing formula.* 



Let cotg. A + cotg. a = M J cotg. A — cotg. a 

 = m 



Then let cotg. B + cotg. b = N; cotg. B — 

 cotg. b =: n ; then 



2 cotg. 1 = M. n N. m. 

 m + n ' m + n 



It is taken for granted that, by the dip of the 

 needle is understood its distance from the nearest 

 horizontal point, so that the dip is = 0° when the 

 needle lies horizontally, and, on the other hand, 

 has attained the maximum, or 90°, when it stands 

 vertically. 



EXAMPLE. 



In the harbour of St. Peter and St. Paul, in 

 Kamtschatka, the following observations were 

 made with a dipping-needle, from which the 

 balance balls, (applied on the plan of Cavendish,) 

 were taken off. 



The division turned towards the east = 46° 20' 

 = A. 



The division turned towards the west — 82° 30' 

 = a. 



After the poles of the magnetic needle were 

 turned, it gave 



The division turned towards the east = 66° 28' 

 = B. 



* By Professor Tobias Mayer, in the Comment. Societatis 

 Reg. Scient. Goett. Math. torn. iii. 



