834 



SCIENCE 



[N. S. Vol. XLII. No. 1093 



son's " Bright-line " (3) curve^ and has the 

 equation 



/ r \ 3.96S21 / T \ 5.17262 



Curve II. is Pearson's " Bisection " (3) 

 curve^ and has the equation 



/ 3- \ 5.41 665/ X \ 3.33995 



,=71.56246(1+^-^^3^^) (l-^^^ ■ 



Curve III. is Pearson's " Bisection " (2-3) 

 curve^ and has the equation 



(3- \9.763S85/ 3- \8.1851S0 



^+llU66r2) 0-13:55284) ' 



Curve IV. is Pearson's " Bisection " (1-2) 

 curve^ and has the equation 



/ ,■ \ 35.390655/ 3. \ 47.884605 



,=56.21.36(1+^-^;^^) (1-3^:69023) ■ 



It will be noted that these are all Type I 

 curves and represent a rather wide range of 

 values of the a's and m's. The expression for 

 2/(1 in a Type I curve is 





)?ij"'imj™2 



where 



K- 



b (m, + m.j)'"i+'"2' ■ 



r(mi+m,+ 2) 

 r(m, + l)r(mj + l) 



The table shows the change in the maximum 

 ordinate, y„, produced by altering log K to the 

 amount indicated. 



TABLE I 



Showing the Maximum Effect on an. Ordinate of 



the Curve Produced hy a Change in the 



Value of the Log Gamma Term of 



the Indicated Amount 



5 Loc. cit., p. 287. 

 eioc. cit., p. 288. 

 T Loc. cit., p. 288. 

 8 toe. cit., p. 289. 



From this table it is evident that : 



1. An alteration of as much as one in the 

 third decimal place in log K makes a change 

 in the maximum ordinate of between 1 and 2 

 in the first decimal place, an amount practi- 

 cally negligible in many curve-fitting studies. 



2. A degree of approximation to log r(n) 

 such as is obtained by interpolation from a 

 table of log \n, when only second differences 

 are used in the interpolation,^ involves errors 

 in the fourth decimal place in log Tin), or 

 the fifth for values of n > 25 circa. These 

 mean errors of the order of .02 ca. in the 

 maximvun ordinate (and, of course, smaller 

 absolute errors in all other ordinates). 



3. Interpolation from a table of log | n using 

 second differences is, as we concluded in the 

 earlier paper, quite sufficiently exact for all 

 practical curve-fitting purposes. If any one 

 desires to use ten-place logarithms or some 

 other method, and make all his computations 

 precisely exact to seven (or for the matter of 

 that to 15, 20 or 50) places of figures he may, 

 of course, do so. It is reasonably open to 

 question, however, whether the additional con- 

 tributions to knowledge which may fairly be 

 expected to accrue from such procedure are 

 likely to be of such magnitude or originality 

 as to justify the labor. 



Kaymond Pearl 



the origin op lost river and its giant 

 potholes 



Iif a short article in Science in 1913,^ Mr. 

 Robert W. Sayles, of Harvard University, de- 

 scribed and sought to explain the block-filled 

 gorge and giant potholes of Lost River, in the 

 Kinsman Notch, New Hampshire. During a 

 first visit to the place, last summer, I saw cer- 

 tain features which seem worthy of attention, 

 in formulating any working hypothesis of the 

 origin of the phenomena. 



As Mr. Sayles stated, Lost River is a small 

 stream which flows eastward from the notch 

 between Mt. Moosilauke and Mt. Kinsman, 

 eddying and cascading beneath a deep pile of 

 huge angular blocks and rifted ledges for a 



9 Cf. Table I. of the writer 's earlier paper. 

 1 Vol. XXXVII., pp. 611-613. 



