Tdonaly wrote:
"He doesn`t say a single thing about a "cosine law" for a real
antenna...."

Like Cecil, I didn`t either, but I am surprised a challenge exists to
sine or cosine current distribution which most serious antenna authors
assume and illustrate.

If the projected height of of a sine wave is cast upon a circle, its
amplitude is completely described by the projection of the radius on the
diameter of the circle.

A sine wave amplitude is the vertical or "y" value of the (x,y)
coordinates of the tip of a radius vector rotating counter-clockwise in
a circle of unit value.

The angle considered is that made by the radius vector with the "x"
axis.

Antenna discussions often use cosine waves. These are identical to sine
waves except that they are displaced by 90-degrees, or 1/4-cycle, or pi
radians (all different names for the same thing). When sine equals +1,
the cosine equals 0-degrees, and it is about to go negative. This is
because the sine starts at a value of zero at zero degrees. At the same
0-degree start, cosine is +1.

There is no difference between a sine and a cosine wave except for
90-degrees phase lead of the cosine wave. The sine of an angle is the
same as the cosine of (that angle minus 90-degrees). Example: sine of
90-degrees = 1.
Cosine of 0-degrees = 1 also, etc. etc. etc.

Ed Laport in "Radio Antenna Engineering" says on page 19:

"The principles of the electrically short antenna are better understood
from Fig.1.1, in which the natural sinusoidal current distribution along
a straight uniform section quarter-wavelength vertical is used for
reference. A straight uniform vertical antenna with a height of 20
degrees would have the relative current distribution shown for the sine
curve above the 20-degree level A."

And in John Devoldere, ON4UN`s now famous Fig 9-22:

"Short loaded verticals with their current distribution." Note the
cosines given for each antenna height demarcation.

Best regards, Richard Harrison, KB5WZI