Heightsof the principal Hills of We7isleydale, Yorkshire. 355 



Case 1. — D and A being acute. 



X = a + 2d. 

 Case 2. — When either D or A is obtuse. 



X = 2 d—a, when d exceeds a ; 

 A- = a, when a exceeds d. 



Class IV. — Given the observed angles D and E only. 



Case 1. — D and A being acute. 

 X = 2 a-\-d. 



Case 2. — When either D or A is obtuse. 

 X = 2 a — d, when a exceeds d ; 

 X = </, when d exceeds a. 



It is almost superfluous to remark, that the logarithmic dif- 

 ferences are treated in the notation as common numbers. 



The following list contains for every triangle of which all 

 the angles have been observed, the difference of their sum and 

 180°. 



Mean error 45", or 15" per angle. 

 Registers of the Measurement of the Horizontal Angles. 



