FRESH-WATER STREAMS. 639 



formity. Narrows between rocky bluffs act like a dam, and diminish 

 the pitch above them, often spreading the waters into lakes, while they 

 increase the pitch below. At such narrows, floating ice often makes 

 obstructions in the spring, which increase greatly the height of the 

 waters. A dam higher up the stream, that obstructs or holds back the 

 ice during its break-up, may save large areas from the flooding effect 

 of the narrows. Narrows are sometimes created along streams by 

 encroaching human " improvements ; " but such a narrowing of a 

 river's natural flood-grounds may be easily carried so far as to be a 

 sure source of disasters. 



3. Energy or working-power of Rivers. — The energy or working- 

 power of any body of water — say a lake — equals the product of the 

 weight of the water in pounds ( W) into its height (h) above the sea- 

 level, that is, into the vertical distance which it would have to descend 

 to reach the level of the sea. The expression for its value in foot- 

 pounds is Wh. This energy exists in the water solely in virtue of its 

 position, just as potential energy, or power of doing mechanical work, 

 exists in the weights of a clock when raised to their highest point. The 

 energy potentially present in a lake a fourth of a square mile in sur- 

 face, 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 ex- 

 pended 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 of this lake were allowed to flow by a continuous 

 gradual slope down to the sea, and if it met with no loss from evapor- 

 ation, or from resistance of any kind (such as friction, etc.), its velocity 

 would increase regularly according to the well-known law of falling 

 bodies ; and, in this increase of rate, it would be constantly accumulat- 

 ing energy of motion, which would be the exact equivalent of the en- 

 ergy 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). 

 Its energy would have thus been entirely transformed from energy of 

 position into energy of motion, and into an amount capable of doing 

 work equal to that above stated. In the case of falling bodies the 

 relation between the vertical distance fallen through (h) and the ac- 



v 2 

 quired velocity (v) is expressed by the formula h= --■-, g being the 



* 9 



force of gravity, usually taken at 32.2 (it is 32.165 at New York city) ; 

 so, the energy of the moving body of water may be obtained from the 



Wv* 



formula ~ 7 — . 



In actual experience, the theoretical result can not be realized ; on 



