106 Transactions. —Miscellaneous. 
Let h = height of the station A above the surface of the lake. 
Then K = h sin. (V—mC) sec. (N—mC+}4C). 
= fA sin. (V—mC) . 
cos. (VN—mC+4C) 
If Z = the observed zenith distance, then the following will be the 
K = hsin. (Z7+mC) (2) 
cos. (Z-+-m C—4C) 
If D = the observed angle of depression ; then 
K = hcos. (D+mC) cosec. (D+mC—4C) 
= hos. (D+mC) (3) 
sin. (D+mC—3C) 
These 8 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 4H = the height in links, then draw HF perpendicular 
thereto, and draw 4F making the angle HAF = N, then HF 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 4H, then the distance HE (to a point ver- - 
tically over 6) will not differ much from the distance HB. Draw the line 
AF, then the angle BAF will be nearly = the angle BHE, which is = } C. 
Assuming the = 38 BAE = } C and the angle BAD = {, C, then the 
angle DAK = 4 C—7, C = 30, therefore 
Multiply 4H by o (NV + 2 C) and the result will be HE neatly (4) 
Or if D be the observed co of depression, then 
AH cot (D—3C) = HE nearly (5) 
Or if 7 be the observed zenith distance, then 
AH tan (7—3C) = HE nearly (6). 
Arr. X.—Notes on the Height of Mount Cook. By C. W. Apams. 
(Read before the Philosophical Institute of Canterbury, 1st September, 1881.} 
Tue height of Mount Cook has been calculated in August, 1881, by Mr. 
George John Roberts, 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. 
