Hi Roger - Sorry if my posted design was  misleading; 163.5 mm diameter = 210 cm^2(Pi*r^2) is the formula for the area of a  circle I chose 210cm^2 because that is the Sd for the  Lowthers. The indicated dimensions are the outside dimension  for each square (with all corners radiused @  81.75mm). A 163.5 mm square with all 4 corners radiused to  81.75 mm is a 163.5 mm diameter circle. This is an easy  method to convert a circular throat to an almost square  mouth. It would be more complex to reduce the radius at each step  to get to a completely square mouth. I added 57.3225 cm^2 to  the area at each cm spacing: (16.35 cm)^2 - Pi*(8.175  cm)^2.The square root of this increased area gives the  basic size of each step shown, subtracting the areas outside  the radii gets back down to the correct area at each  step. I like the rounded corners is why I did not change  the corner's radius at each step. Check out my midrange horn v.1  for a transition from round to elliptical to rectangular,  the math was more difficult for that. http://www.geocities.com/loudspeakerguru/Jeff_Midrange.gif The equation to continuously reduce the corner  radius for eachspacing step is: r=(8.175cm*(43cm-x)/43cm); where x  is the distance in  centimeters from the throat, then the variation in area has to  be calculated for each step instead of adding a  constant amount  to the area for each step. I guess studying symmetry in microwave antenna  design helped me to see these simple geometrical  procedures. Ciao... Jeff 
	----- Original Message ----- To:Jeff RobinsonSent: Saturday, February 10, 2001 12:02    PMSubject: Round throat? Hi Mr.RobinsonWow!  Great design..You are the    best! So..It is a round throat. May I ask? Is    throat size=163.5mm^2 on the    drawing34 or is 210 cm^2 on    webpage? Best regards Roger C...