372 Mrs. Bryant on an Example in 



So far as the first power of j3 the action upon the boundary 

 is thus purely tangential, and of magnitude given by (66). 

 The periodic part has the same sign as the constant part at 

 the places where the boundary encroaches upon the fluid. 



This result finds immediate application to the question of 

 wave-formation under the action of wind, especially if we 

 suppose that the waves move very slowly, as they would do if 

 gravity (and cohesion) were small. The maintenance or 

 augmentation of the waves requires that the forces operative 

 at the surface be of suitable phase. Thus pressures acting 

 upon the retreating shoulders are favourable, as are also tan- 

 gential forces acting forwards at the crests of the waves, 

 where the internal motion is itself in the forward direction. 

 Equation (65) shows that the pressures produce no effect, 

 and that we have only to consider the action of the tangential 

 stress. We see from (66) that when the waves move in the 

 same direction as the wind, the effect of the latter is to favour 

 the development of the former. Whether the waves will actu- 

 ally increase depends upon whether the supply of energy, 

 proportional to ft 2 , is greater or less than the loss from internal 

 dissipation, itself proportional to the same quantity. If the 

 waves are moving against the wind, the tendency is to a more 

 rapid subsidence than would occur in a calm. 



Terling Place, Witliam. 



XXXIX. An Example in " Correlation of Averages "for Four 

 Variables. By Sophie Bryant, D.Sc* 



IN Professor Edgeworth's papers t on "Correlated Averages" 

 he has shown how to obtain for any number of variables 

 the coefficients of the quantic of the second degree which, 

 taken negatively, is the exponent of e in the equation express- 

 ing frequency of correlation. Thus, w denoting frequency, 

 and #!, x 2 . . . x n the correlated variables, such as lengths of 

 limb in an n- limbed animal, the locus of w, x x , x 2 . . . x n is 

 given by the equation 



v) = Je~ R y 

 where 



B=p 1 x i 2 +p 2 x 2 2 + . . . +p n x 2 n + 2qn®i%2 + • • • + %q n -i A- A- 



And all the n-dimensional quartics with equations of the form 



B — constant 



* Communicated by the Author. 



t See Phil. Mag., Aug., Nov., Dec, 1892, and Jan. 1893. 



