106 Transactwiis. — Miscellaneous. 



Let h = height of the station A above the surface of the lake. 



Then K = h sin. (N-mC) sec. {N-mC+^C). 

 = h sin. (N—mC) ,^. 



cos. {N-mC-\-iC) ■ ^ ^ 



li Z = the observed zenith distance, then the following will be the 

 formula : — 



E = h sin. (Z+?wC*) /pv 



COS. {Z+ni C-^C) ^ ^ 



li D = the observed angle of depression ; then 

 K = h COS. {D-]-7nC) cosec. (B-j-mC — ^C) 

 = h COS. (D-{-mC) /q% 



sin. (D+mO-iC) ^ ^ 



These 3 formulas require the angle C (or contained arc) to be known, but 

 as this is measured by the distance HB, some method of approximation 

 must be employed in order to get this distance. This may be done gra- 

 phically by making AH = the height in links, then draw HE perpendicular 

 thereto, and draw AF making the angle HAF = N, then Hi^ will be the 

 distance required in links nearly, but always less than the true distance. 

 The same thing may be done by calculation, by multiplying AH by tan N. 



A. more accurate method may be investigated as follows : — 



To investigate a method of finding the distance HB approximately. 



Draw HE perpendicular to AH, then the distance HE (to a point ver- 

 tically over B) will not differ much from the distance HB. Draw the line 

 AE, then the angle BAE will be nearly = the angle BHE, which is = -J C 



Assuming the angle BAE = i C and the angle BAD = yL c, then the 

 angle DAE = ^ ^—jt ^ — f^'» therefore 



Multiply AH by tan [N + f C) and the result will be HE nearly (4) 



Or if I) be the observed angle of depression, then 

 ^Hcot {D-^C) = HE nearly (5) 



Or if Z be the observed zenith distance, then 

 .4i? tan (Z-fC) = £f£' nearly (6). 



Aet. X. — Notes on the Height of Mount Cook. By C. W. Adams. 



[Read before the Philosophical Institute of Canterbury, 1st September, 1881.] 



The height of Mount Cook has been calculated in August, 1881, by Mr. 



George John Eoberts, assistant geodesical surveyor of the Westland Survey 



Department, as 12,349 feet above the mean level of the sea. 



This altitude is a mean result deduced from observations at twenty-two 

 stations, and may be considered as final. .> 



