The summing method means each decade can be built independently, and matching the relative contribution of each decade is done by adjusting one summing resistor for each decade.

The Hamon divider method can be used for ratios that are the square of numbers - ie 2^{2}:1, 3^{2}:1, 4^{2}:1, etc.

That means you get ratios of 4:1, 9:1. 16:1, 20:1 or voltage dividers that divide by 5, by 10, by 17, by 21.

It is hard to see how you would get a divide by 8 ratio.

A better technique that has been used in lots of older instruments is arrange for each decade to go from 0 to 10 (instead of 9).

Then calibration consists of two major steps. Step One is is you get all the resistors within each decade matched to each other.

Step 2 is you adjust each decade, starting from the second most significant so that "10" is exactly equal to "1" on the range above.

If you are using electronic switches, then to match the ranges, you can switch between the "1" on one range and the 10 on the next lower range at rate of 133Hz (or any frequency that is not a mains harmonic). You will get a square wave out when they do not match, and when you adjust the summing resistor for a match, the amplitude of the squarewave will go to zero. If you built an sensitive AC amplifier, along with a tuned 133Hz bandpass filter to eliminate everything but the 133Hz Ac, and put your multimeter on the output, then you can match the decades with extreme precision without needing anything expensive or precise.

So calibration comes down to matching resistors within a decade, and zeroing an AC value. These are two steps that can be done simply and very accurately without expensive equipment.

In practice, any time you are chasing precision, it is always the detail that you have to be obsessive about. You have to consider all the factors you normally do not have to consider in other designs. If you are using analogue switches you have to look at the switch resistance, the switch-to-switch variations of resistance, the temperature coefficient of the switch resistance, the OFF leakage current through the switch, and the leakage current from the supply rails to both sides of the switch. The currents will probably rise exponentially with temperature, so you have to think of the maximum operating temperature.

The beauty of the totally passive resistive-based dividers is that as long as you start with great resistors and great switches, there is nothing else to go wrong. After a few years, it stabilizes and remain incredibly accurate. Put it in the cupboard, drag it out in 20 years and it will still work perfectly.

Part of the genius of the Kelvin-Varley divider is that the whole divider can be build from the built from one single batch of resistors, all of the same value. If all the resistors have matching temperature coefficients, then errors due to ambient temperature changes cancel out. Hopefully, they will age the same too. In the summing method, you have a very wide range of summing resistors, all that have to stay accurate. Is the 1Mohm resistor temperature characteristics going to match the 1Kohm characteristics? Yes if you were Fluke of 50 years ago, and you make all the resistors from wire of the precisely same composition, and yes if you are HP or Fluke today, and you can make a laser trimmed thick film resistor network, where all the resistors are made from exactly the same deposited film. Probably not if you are a hobbyist getting whatever parts you can find.

Richard