174 DYNAMICAL GEOLOGY. 



2. The amount of work which a body of water, as that of a lake, can theo- 

 retically do, on its descent to the level of the sea, is equal to the product of 

 the height of the lake (h) into the weight (W) of the water; and hence Wh 

 is an expression in foot-pounds for the energy or working-power potentially 

 present in the lake. The amount of energy in a lake a fourth of a square 

 mile in surface, 10 feet in average depth, and 400 feet above the sea level, is 

 1,742,400,000,000 foot-pounds ; — a power sufficient, could it be expended 

 without loss, to raise a mass of stone weighing about 87,000 tons to the top 

 of a mountain 10,000 feet high. If now the water were allowed to flow by a 

 continuous slope to the sea level, without loss from evaporation, or from 

 resistance of any kind (such as friction, etc.), its velocity Avould increase 

 regularly according to the well-known law of falling bodies ; and, in this 

 increase of rate, it would be constantly accumulating energy of motion^ which 

 would be the exact equivalent of the energy of position it was losing ; and 

 when it reached the lower level its velocity would be 160 feet per second 

 (about 109 miles an hour). In the case of falling bodies the relation 

 between the vertical distance fallen through (h) and the acquired velocity 

 (v) is expressed by the formula v = V2 gh, g being the force of gravity, 

 usually taken at 32-2 (it is 32-165 at New York City) ; or, approximately 

 (since 2g = 64-3), by the formula v = 8 VA, or h = gL v^. In actual experi- 

 ence the theoretical result cannot be realized. On the contrary, the velocity 

 of a stream does not increase uniformly as it descends, and when it reaches 

 the sea, whatever the elevation at first, its velocity is in most cases nearly 

 zero. This is owing to the fact that its energy, instead of being stored up, 

 is being expended against the various resistances encountered, that is : — 



(1) In overcoming friction between (a) the molecules of the water 

 itself; (6) the water and the bed of the stream; (c) the surface of the water 

 and the atmosphere. 



(2) In impact, or blows against the rocks or earthy material of the bed 

 and banks of the stream ; and in pushing sand or gravel along the bed. 



(3) In transporting earth, sand, or stones, held in suspension in the 

 water. 



(4) In overcoming the friction between the transported particles and 

 the bed of the stream, and the frictioii between the particles themselves ; 

 and also the loss from eddies made by the character or form of the bed 

 or otherwise. 



By these means the energy is so far expended that no accumulation can 

 take place except on portions of a stream where the pitch is uniform and 

 considerable, and the bed is hard and smooth. In a waterfall, accumulation 

 goes on during the descent ; but the whole energy of the stream is lost in 

 the stroke of the water at the bottom of the fall, where it is converted 

 into heat, — a fall of 772 feet producing heat enough to raise the tempera- 

 ture of the water 1° F. 



Owing to the rapid increase of velocity in the descending water of a 

 waterfall, the stream in a high fall of small volume becomes divided up, the 



