ASTRONOMY. 59 



contiguous degrees ought to be proportional to the 

 sines of twice the middle latitude, ( 59. c.), and 

 therefore ought to follow a very regular progres- 

 sion. This, however, has not been found to take 

 place in any instance of actual measurement. In 

 the great arch measured in France, in those of the 

 Peninsula of India, and in the south of England, 

 the contiguous degrees have differed very irregu- 

 larly, and by such considerable quantities, as could 

 not be explained by any probable error of obser- 

 vation. Local irregularities in the figure of the 

 earth, manifesting themselves by the deflection of 

 the plumb-line, seem to give rise to these anoma- 

 lies. The deflections are but small, and disappear 

 altogether when arches of great extent, and differ- 

 ing by large quantities, are compared with one 

 another. 



This subject will be more fully considered under the 

 head of Physical Astronomy. 



SECT. IV. 



GEOGRAPHICAL PROBLEMS. 



64f. THE situation of a point in a given superfi- 

 cies is determined, when its distances are known 



from 



