This should be used more for ascertaining relatively large differences in altitudes than for purposes where any great nicety is required.  For hills under 2000 ft., the following rule will give a very close approximation, and is easily remembered, because 55 degrees, the assumed temperature, agrees with 55 degrees, the significant figures in the 55,000 factor, while the fractional correction contains two fours.

Observe the altitudes and also the temperatures on the Fahrenheit thermometer at top and bottom respectively, of the hill, and take the mean between them.  Let B represent the mean altitude and b the mean temperature.  Then 55000 X B — b/B + b = height of the hill in feet for the temperature of 55 degrees.  Add 1/440 of this result for every degree the mean temperature exceeds 55 degrees; or subtract as much for every degree below 55 degrees.

TO DETERMINE HEIGHTS OF OBJECTS

By Shadows

Set up vertically a stick of known length, and measure the length of its shadow upon a horizontal or other plane; measure also the length of the shadow thrown by the object whose height is required.  Then it will be:—­As the length of the stick’s shadow is to the length of the stick itself, so is the length of the shadow of the object to the object’s height.

By Reflection

Place a vessel of water upon the ground and recede from it until you see the top of the object reflected from the surface of the water.  Then it will be:—­As your horizontal distance from the point of reflection is to the height of your eye above the reflecting surface, so is the horizontal distance of the foot of the object from the vessel to its altitude above the said surface.

Instrumentally

Read the vertical angle, and multiply its natural tangent by the distance between instrument and foot of object; the result is the height.

When much accuracy is not required vertical angles can be measured by means of a quadrant of simple construction.  The arc AB is a quadrant, graduated in degrees from B to A; C, the point from which the plummet P is suspended, being the centre of the quadrant.

When the sights AC are directed towards any object, S, the degrees in the arc, BP, are the measure of the angle of elevation, SAD, of the object.

TO FIND THE DEPTH OF A SHAFT

Rule:—­Square the number of seconds a stone takes to reach the bottom and multiply by 16.

Thus, if a stone takes 5 seconds to fall to the bottom of a shaft—­

5 squared = 25; and 25 X 16 = 400 feet, the required depth of shaft.

DESCRIPTION OF PLAN FOR RE-USING WATER

Where water is scarce it may be necessary to use it repeatedly.  In a case of this kind in Egypt, the Arab miners have adopted an ingenious method which may be adapted to almost any set of conditions.  At a is a sump or water-pit; b is an inclined plane on which the mineral is washed and whence the water escapes into a tank c; d is a conduit for taking the water back to a; e is a conduit or lever pump for raising the water.  A certain amount of filtration could easily be managed during the passage from c to a.