December 10, 1915] 



SCIENCE 



833 



Astronomy " has called attention to the un- 

 explained fact that the full moon tends to 

 disperse the clouds under it. This follows as 

 a necessary consequence of gravitation; but it 

 is not restricted to the full moon, but is in 

 active operation at all times by both sun and 

 moon. The fact is however most easily ob- 

 served at the time when the sun is absent. 



Incidentally we may mention that were the 

 moon's orbit in the plane of the ecliptic, the 

 eclipse conditions of the tenth of August would 

 be mostly repeated at each new moon; but the 

 tidal phenomena would be fundamentally dif- 

 ferent. In the supposed case the crossing of 

 the two tidal waves would be constantly at 

 the pole of the ecliptic during the whole luna- 

 tion, and the high tides would be confined to 

 the latitudes of the arctic and antarctic circles. 

 If, at the same time, the earth's equator were 

 shifted into the ecliptic, there would be a 

 constant elevation of water at both poles of 

 the earth, while all other places on the surface 

 of the earth would have four simple tidal waves 

 each day. The general problem of the height 

 of the tidal wave at any time and place on 

 the earth's surface can not be considered here, 

 but tables for that purpose have already been 

 computed, though still impublished. 



We see from this exposition of the subject 

 that all the infinite variety of tidal phenomena 

 are fully explained by the operation of the 

 forces of gravitation as developed under exist- 

 ing conditions in the solar system. The 

 eclipse of August 10 represents a case in which 

 the forces of the sun and moon act in perfect 

 harmony during a few minutes of time; but it 

 recurs at such infrequent and uncertain in- 

 tervals that nothing useful can be learned 

 from a single performance unless there be 

 some known theoretical connection with pre- 

 ceding and subsequent events. The problem 

 of the tides, which has been aptly called the 

 " Riddle of the Ages," and designated in de- 

 spair by an ancient philosopher as " the tomh 

 of humun curiosity," may therefore now be 

 considered as completely solved. 



John N. Stockwell 

 Cleveland, 

 November 4, 1915 



ON THE DEGREE OP EXACTNESS OF THE GAMMA 

 FUNCTION NECESSARY IN CURVE FITTING^ 



The note by Mr. P. F. Everitt in a recent 

 number of this journal- discussing an earlier 

 note by the present vsriter^ seems so likely 

 to obscure the essential point and pur- 

 pose for which the earlier note was written 

 that it appears desirable to advert to the sub- 

 ject once more. 



In practical biometric work the gamma 

 function is chiefly (though of course not en- 

 tirely) used in connection with the fitting of 

 Pearson's skew frequency curves, where such 

 function appears in the expression for y„. In 

 other words, the exactness of approximation 

 to the gamma function in these cases can af- 

 fect nothing but the calculation of the ordi- 

 nates and areas of the fitted curve. The writer 

 finds it difficult to conceive of such circum- 

 stances in the ordinary prosecution of prac- 

 tical statistical researches as would necessi- 

 tate or warrant the calculation of the ordi- 

 nates or areas of a frequency curve to more 

 than two places of decimals. This being the 

 case, it seemed desirable, in the earlier paper, 

 to call attention to the fact that a quite suffi- 

 ciently " exact " approximation to the values 

 of the gamma functions could be made by 

 simple interpolation in a table of log \ji. 



In order that the statistical worker may 

 form his own judgment as to what degree of 

 exactness in approximating the gamma func- 

 tion is necessary in calculating y„. Table I. is 

 presented. This table shows, for four differ- 

 ent skew frequency curves, the change pro- 

 duced in 2/„ by altering the logarithm of the 

 term involving gamma functions by the fol- 

 lowing amounts: .0000001, .000001, .00001, 

 .0001 and .001. The curves used for illustra- 

 tion are taken from Pearson's memoir " On 

 the Mathematical Theory of Errors of Judg- 

 ment, with Special Eeference to the Personal 

 Equation." * 



The curve marked I. in the table is Pear- 



1 Papers from the Biological Laboratory of the 

 Maine Agricultural Experiment Station, No. 90. 



2 Science, N. S., Vol. XLII., pp. 453^55, 1915. 



3 Science, N. S., Vol. XLI., pp. 506-507, 1915. 

 iFhil. Trans., Vol. 198^, pp. 235-299, 1902. 



