864 



MR HENRY BRIGGS ON 



By the theory of errors- 



= ± \/|(sr5- c ') 



. 8a X' ., /8a\ 2 



• ( sa)"' + ( 8 o 



)',} 



cV cos 2 A cV sirr A cos 2 C 

 + — ■ ., n + 



I s c 



sin 4 C 



= ± * / \ ■ o ^ ■ c i + «'«'- cot- A + d 2 v" cot 2 C > . 

 V ( siir C j 



Therefore the average fractional error in a is determined by — 



^± v /{^(cot2A + cot 2 C) + (^) 2 } . 



jr-i 



(24) 



It is evident then, that the fractional error in a can be made to alter by varying the 

 shape of the triangle, keeping the length of the base, c, and the fractional error in the 



base, — , constant. Substituting from (22) we obtain, for an isosceles triangle- 



■f = ± -y/ { " 2 (cot 2 A + cot 2 2A) + (-*\ } . 



(25) 



and this is a minimum when (cot 2 A + cot 2 2A) is a minimum. By differentiating the 

 latter expression with respect to A and equating the result to zero, it is found that 

 A = 56 15' gives (25) a minimum value. 





