Gas and Oil Home Heating Furnaces - Hot water radiators

I recently purchased a home (built in 1940) with hot water radiator heat. After bleeding all the radiators I notice that several do not come up to temperature. During a normal heating cycle these radiators are 15 to 20 degrees cooler than the others.

Could be several things. The easiest would be if you have zone valves and they are not open all the way. You could try closing some partially in the rooms that get plenty of heat.

The heating boiler has probably been changed sometime in the life of the house and upgraded to forced circulation. That can cause some odd conditions for heating. You should probably try partially closing the radiator valves on the radiators nearer to the boiler and give some of that extra flow to the cold radiators. You will probably have to close the valves almost all the way to reduce the flow in the hot radiators. Eentually, you will get it balanced. There are ways to avoid this problem but they require different piping around the boiler and most contractors in my area do not go to that extent on an installation. They take the quick way out and just cut the supply and return pipes and drop in a new unit.

many homes have a single loop system...there may be too few BTU's left in the loop. If it's a single loop system, reducing the flow will make it worse. If it indeed is a single loop you may have to swap radiators around for smaller ones in the begining and the larger for the end, or repipe for two pipe reverse return...compare the water outlet temp at the pump to the return temp on the pump....it should be no more than 20 degrees different

Series connection of radiators is almost never done because of the reason hvac states. Reduced water content of a replacement boiler makes the problem seem even worse. The ultimate solution is to move water through the radiators but not make all that water go through the boiler. Keep the water moving during the entire heat call and add heated water from the boiler to the circulating mass. All the radiators get warm gradually and at just about the same rate. It adds comfort and only requires one additional pump and a few fittings. If you get to the point where you decide to make any changes to piping, I can explain what to change in near-boiler piping.

We are assuming you are talking about steam style radiators and not baseboard??? This would require only a small diameter pipe going in, like say, 3/4". It would also have same size outlet, and would have no trap type fitting on the outlet... This too, is most likely copper.
I'm saying this because some people say radiators when baseboard is the case...
You should also have a circulator for each heating zone, and maybe one for hot water. How many thermostats are there in the house?