m= 4nx,/gl - nT, the upper limit of integration in the second 
term of (5.16) and the first term of (5.17) is zero. The upper 
limits of integration of the other two terms is given by (g/anx, )V? 
2nT and its value is greater than 10 for all values of Xy less 
than ten thousand kilometers. Note also that a wave train with 
3600 waves of 10 second period in it would be about 600 km long. 
For a fixed point, Xy> then, if xy is less than approximately 
ten thousand kilometers, the transformation of variable given by 
equation (5.24) can be applied where the time of passage of the 
forward part of the wave train occurs near t' equal to zero. 
Equation (5.15) then simplifies to equation (5.25). The first 
integral in equation (5.16) is practically a constant; the second 
integral in equation (5.17) is practically zero; and some alge- 
braic manipulations then yield equation (5.25) where G* and H* are 
defined in (5.26) and (5.27). The value of x, is fixed; equation 
(525) does not imply that the waves are traveling in the negative 
x direction. 
G* and H* are functions of the variable upper limit of inte- 
gration. For Xy small, the upper limit of integration is greater 
than ten or less than minus ten after t' has varied through a small 
range of values. For Xy large, t' must vary through a much larger 
range of values. G* and H* are graphed in figure 7 for A =1 as 
a function of (g/arx,)/7t", 
The appearance of the solution as a function of t' fora 
fixed Xj depends upon the choice of Xy° For small values of xy» 
the effect of G* and H* is to put ripples on the first two or 
three waves in the wave train and to leave the remaining waves 
o> onl & 
7 
