This is an operation i do quite a bit, homebrewing regenerative
Here is my method:
to find the tuning range for a 30-365 picofarad capacitor and a 240
Let me do it two ways, one for use on a slide rule with a mannheim
layout, one for a Doric arrangement. (on the mannheim, i often make a
gauge mark at 2Pi on the CI scale... then it all works out like the
Lets find the low frequency range on the mannheim.
Set left A index to 240, set cursor at 365 on B. Because this is 3+3
digits (even) use the leftmost pair. (roughly 8.78) (See note).
Line up the 2 on the CI scale on the cursor, and then move the cursor
to the PI on the C scale. (*2 *pi) (Roughly 1.86)
Index on C, read resonant frequency on C opposite index on D. Answer
is 537 KHz.
Note: This is easier if you have a gauge mark at 2PI on CI or have a
CIF scale. Simply line up the 2PI (2 on CIF) with the answer from
step 1, and read the resonant frequency off at the D index.
High resonant frequency:
Left A index at 240, set cursor at 50. (this is 3+2 digits, so use
right hand pair)set cursor there (roughly 8.5 on D).
Line up the 2PI gauge mark or the 2 on CIF at the cursor, read 1.873
MHz on C above D index.
This does not work nearly as well on my N4 with no A-B scales, i wind
up having to read the root and placing it on the C-D scales.