Tom,

I found the procedure in the Antenna Manual for what you want to do. In the
19 th edition, it is listed in the index under "Series Section
Transformers", and is on page 26-5. Lot of terms in the formula, but nothing
fancier than an arctangent.

For a 70 Ohm load, you calculate the SWR for a 50 Ohm system as 1.4. The
MINIMUM impedance for the second coax is
50*SQRT(1.4)=59.16. So, 75 Ohm coax will work. The formulas will give you
the lengths for L1 and L2, where L1 is 50 Ohm and L2 is 75 Ohm coax.

Have fun when you get the book!

If you can't wait for the book, here are the formulas

n=Z1/Z0, where Z1 would be 75.

r=RL/Z0

x=XL/Z0

num= (r-1)^2 +x^2

den=r(n-(1/n))^2 -(r-1)^2 -x^2

B=SQRT(num/den)
L2=ARCTAN(B)

A={B(n-(r/n))+x}/{r + xnB -1}
L1=ARCTAN(A)

I don't guarantee error free typing.

Tam/WB2TT