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One point of clarification right up front: For those of you who bought a Mallory Dual Points distributor to have longer dwell for a hotter spark, you have been bamboozled, or are misinformed. The Lucas 4-cylinder distributor has dwell of 60 degrees. Mallory Dual Points distributor has total dwell of 40 or 41 degrees (depending on which spec sheet). Mallory single points distributor has dwell of 35 degrees. Yes, dwell is the rotation angle when the points are closed (connection to ground). So if you want longer dwell, stick with the original Lucas distributor. This is NOT the reason why Mallory uses dual points (but I will get to that later).
This large difference in dwell angle between Lucas and Mallory is obvious to the eye if you look inside. The Lucas 4-cylinder distributor cam is almost square with rounded corners. As the cam rotates the rubbing foot on the points spends a lot of time in open air not touching the cam. When it does touch the cam the points open momentarily to hop over the lobe and then close quickly. By simple observation it is obvious that the points are closed about twice as long as they are open, so you have 60 degrees dwell and only 30 degrees open.
The cam in the Mallory distributor is much different, and also obvious to observe. That one looks more like a cylinder with four flat sides. Here the rubbing foot on the points spends the larger part of the time riding along on the cylindrical surface of the cam holding the points open, and then takes a short dip into the flat area to allow the points to close momentarily. This is where you get the 32 degrees dwell (and 58 degrees open time) for one contact set. With two contact sets mechanically offset by 9 degrees, the closed period for the two sets overlaps by 23 degrees but extends the total dwell angle from 32 degrees to 41 degrees.
Looking at an 8-cylinder single points distributor, the dwell may be 30 degrees with an open time of 15 degrees. Here an increased dwell runs into decreased open time. When the 8-cylinder Mallory Dual Points makes 33 degrees dwell it is down to only 12 degrees open. You might see where this trend is going. This is why 12-cylinder engines commonly use two 6-cylinder distributors. For various distributors dwell can be anything from 30 degrees down to 60 degrees, and open circuit can be anything from 60 to 12. A V8 engine might run 6000 rpm with a single distributor making 400 sparks per second, and you still get a hot spark, so it's no big deal for a 4-cylinder to do 200 sparks per second (or more if you have a heavy foot).
So if neither dwell nor open time is particularly important, you might ask why dual points may have any advantage. The answer is stability, durability, accuracy, and a certain ease or convenience of adjustment.
Contact points "wear" with use in various ways. The rubbing foot may wear down a bit, which brings the points closer together and increases dwell. The contacts may wear or burn away, which would make the points gap larger and decrease dwell. If the condenser is going bad or is the wrong capacitance value, points may transfer material from one to the other, leaving a pit in one side and a peak on the other side. This may increase or decrease dwell depending on the pattern of erosion and deposition. As dwell is increased the points open later and close earlier, and vice versa for less dwell. The closing time is not very important, but the opening time is, as this directly affects spark timing. In the interest of maintaining accurate spark timing, there is a vested interest to minimize changes of dwell, which leads to an interest in decreasing wear on the contact points.
With the dual points distributor, the first points set to close "makes" the circuit and will incur any ravages caused by a small amount of arcing when closing. The last points set to open "breaks" the circuit and will incur any ravages caused by a small amount of arcing when opening. Since the make and break functions are done by different contact sets, the two sets of points share the wear and each will therefore wear less with time, causing less variation of dwell and timing, and it can run longer between required adjustment or points replacement. Also the two contact sets can share the electrical current load most of the time, so there can be less heating of the contacts and/or rubbing foot. This reduction of running heat leads to less wear on the rubbing foot as well as the contacts. This may be even more important if you also install a high output ignition coil which draws more current, which may noticeably shorten the life of single points. If the points may last roughly twice as long in service (and they do), it may not be such an increased expense to replace two sets of points instead of one. The reduced labor or inconvenience may save considerably on cost and/or tinkering time.
There is another effect which makes adjustment easier. A change of points gap induces a change in spark timing along with change of dwell. With single points you set the contact gap first, then run the engine (or spin the distributor) to check dwell, then re-adjust the points (if necessary) to get the correct dwell. Then you may need to go back and check/reset the timing again, as the dwell adjustment could have changed the spark timing. With dual points you set the gap on both sets of points, then set the timing, which is controlled solely by the secondary points (which open last). Then if necessary you can change the dwell by adjusting the primary contact set, which will have no effect whatsoever on spark timing, so you don't have to reset timing after adjusting dwell.
The real reason for using dual points is for improved life, long term stability and reduction of service calls, but has naught to do with increasing dwell. For what it's worth, I commonly run more than 20,000 miles on the Mallory Dual Points distributor without touching the points. This is one robust distributor, and I am one happy customer (except for the prices on Mallory tune up parts).
There is one more notable feature of the Mallory Dual Points distributor. It has an adjustment for mechanical advance upper limit (maximum advance stop). If you set idle timing to 10 degrees BTDC, and there is no vacuum unit, and you want 36 degrees total spark timing at road speed, you can set the mechanical advance limit to 26 degrees. If you have a vacuum unit that can produce 7 degrees advance, and you want to set idle timing at 15 degrees BTDC and limit maximum total advance to 36 degrees at speed, you can set the Mallory max mechanical advance to 14 degrees. This is a handy feature if you do any special tuning (and don't we all?) so you don't have to buy new or modify the mechanical limit stops or advance weights.