Surveying and LeveJUng. 165 



2. To latitude 50'' 50' (Table IV.) log. P is 7.992938 



Proportional part S'f^ = 0^ X — 0.4 = — 3 



Log. P to latitude 60° 58'.3 is 7.992935 



3. To latitude 66° and « = 70° log. is 7.992919 



Proportional part for lat. 4'i =: 4^ X — 0.5 = — 2 



Proportional part for a 3° J = 3i x — 7.9 = — 26 



Log. for lat. 6Q° 4'4 and azimuth 73° 13' = 7.992891 



Table II. contains numbers to reduce a base measured at the level of 

 the sea to any height above it ; and conversely, to reduce a base mea- 

 sured at any height above the sea to that level, by changing the signs of 

 of m h and p a'\ 



By shifting the decimal point, m h in the table may be readll}' got for 

 any number of feet in h ; but this method cannot be applied to p a*, 

 where the proportional parts to the first difference ^, must be taken, and 

 then corrected by subtracting the equation of second difference, or the 

 equation to a^ in the last column. 



Ex. Required the log. K when a = 1G4046 feet and h =: G562 feet ? 



Log. a -f-5.2149630 



For h = 6000 feet, mhis + 0.0001246 



500 -f 104 



62 + 13 



For a = 100000 feet, /) aMs — 4 



64000 .. AjXO.64— Eq. A, =—13X0.64— 1 = — 7 



Log. K 5.2150982 



Hence the whole correction of the log. a amounts to 0.0001352, or the 

 fourth place of decimals is increased by unit, and, therefore, in great 

 heights this correction cannot, consistently with accuracy, be omitted. 



The log. S contains the log. secant of ^ v, half the angle of the verticals, 

 and — pa^ combined to facilitate the computation of heights. 



Table III. The title of this table, and note under it, sufficiently explain 

 its use, taking care to apply the numbers according to their signs, and 

 it will be found useful when the computer has not very large and exten- 

 sive tables of sines and tangents, by enabling him to use the smaller 

 classes of tables readily, while the requisite accuracy for the nicest pur- 

 poses will still be preserved. 



Example 1. Benlomond bears from Edinburgh Observatory N. 73° 12' 

 40" W. distant 308304 feet, on an arc on the earth's surface at the level 

 of the sea. The place of the Observer on the Calton Hill was elevated 

 340.7 feet above the mean level of the sea at Leith, and its geographica 



