150 



SCIENCE 



[N. S. Vol. XXVIII. No. 709 



the efficiency of the cataract (in relation to 

 recession). To say that the rate of recession 

 is proportional to the energy is equivalent to 

 saying that the efficiency of the cataract ia 

 constant, that it does not change with varia- 

 tion of energy. Now the efficiencies of 

 engines of human construction have been 

 elaborately tested, and they have been found 

 to vary, and vary greatly, with the energy 

 received. Usually the efficiency increases as 

 the energy increases; and an engin with con- 

 stant efficiency would he a striking exception. 

 Not merely does Spencer's supposed law fail 

 to find support in engineering experience; it 

 is contradicted by it. If the Niagara engin 

 corresponds in this respect to the great ma- 

 jority of man-made engines, the error intro- 

 duced in the computations by the use of a 

 false law is one tending toward undervalua- 

 tion of the age of the cataract. 



It would perhaps be more pertinent to com- 

 pare the Niagara engin with other physio- 

 graphic engines, but in general the efficiencies 

 of such engines have not been investigated. 

 The solitary exception is that of running 

 water regarded as a carrier of detritus, and it 

 happens that the unpublisht results of a study 

 of this engin (Science, XXVU., 469) are in 

 my possession. Drawing upon them, I am 

 able to say that the efficiency of a stream in 

 the work of transportation rises and falls as 

 its total energy rises and falls, and not only 

 that, but it rises and falls with each of the 

 two factors of energy specified by Spencer, 

 the head and the discharge. If the efficiency 

 of Niagara in producing recession varies ac- 

 cording to the same law as the efficiency of a 

 river in transportation, Spencer's estimate of 

 the age of the river should be multiplied by a 

 factor larger than four (assuming, of course, 

 that his other data are accurate). 



If the quantitativ data were adequate, the 

 question- of the law of efficiency might be 

 discust in a more satisfactory way by study- 

 ing the American fall in comparison with the 

 Canadian. The mechanical energy of the 

 American is much less than that of the Cana- 

 dian; and its rate of recession is also much 

 less. By computing an efficiency factor for 

 each fall it is evidently possible to obtain two 



points on an efficiency-energy curve and thus 

 throw light on the way in which efficiency 

 varies with energy; and the method is pecul- 

 iarly applicable because the computed energy 

 of the American fall does not differ greatly 

 from the computed energy of the main cata- 

 ract during the longest division of its history. 

 Calculated from Spencer's data, the energies 

 of the American and Canadian falls, respect- 

 ivly, are as 1 to 14, and the rates of reces- 

 sion are as 1 to 7, the efficiency of the Ameri- 

 can being twice that of the Canadian. Had 

 Spencer used this method, or had he based 

 his earlier rate of recession on the American 

 instead of the Canadian fall, his result for 

 the age of the cataract would have been nearer 

 20,000 than 39,000 years. 



But unfortunately the data needed to apply 

 this method do not really exist, the most seri- 

 ous defect being in the measure of the rate 

 of recession of the American fall. Spencer's 

 estimate is 0.6 ft. a year, but is dependent on 

 the map of 1842, which has been shown (Bull. 

 306, U. S. G. S.) to involve a serious error. 

 The records made by relativly accurate sur- 

 veys (1875 to 1905) indicate that the recession 

 is so small that its amount is maskt by errors 

 of survey ; and a study of the f otografic record 

 (1854^) yields no sure determination of 

 an actual change in the crest line of the fall. 

 It may with confidence be said that 0.06 ft. a 

 year is nearer to the truth than 0.6 ft. ; but no 

 definit estimate is warranted. In the judg- 

 ment of the reviewer, the rate of recession is 

 BO small as to indicate that the efficiency of 

 the American fall is much less than that of 

 the Canadian. 



Thus in three ways — by comparison with 

 man-made engines, by comparison with river 

 work in the carrying of detritus, and by con- 

 trasting the Canadian fall with the American 

 — it is suggested or indicated that the effi- 

 ciency of the Niagara engin, instead of being 

 constant, increases with increase of energy 

 and decreases with diminution of energy. If 

 the true law were known its application would 

 probably enlarge the time estimate. 



But while the discovery of the real law of 

 efficiency would be a notable contribution to 

 the problem, it would not remove every dif- 



