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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.


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