On 1973 Ford LTD the battery runs down while

No it dosn't sound like its the ALT.
You need to check the output alt .Take a volt meter with the vehicle running and the meter set to 20 volts DC black to black red to red on the battery you should 14 to 16 volts 12 or under is no good.
If your ok with voltage shut off vehicle disconnect the NEG terimanl from the battery . Meter on same scale check the battery voltage its a 12 volt battery so it should 12 volts but you say its new .
The problem you may be haveing is a short someware in the vehicle.
You can test for this with the meter on same scale by leaving the NEG cable off the battery vehicle not running red to red black to ground on engine or know good ground under the hood . If you read voltage you have a short some ware in the vehicle and it depends how much voltage you read 1 volt its something small like a switch or something that dosn't draw a lot of AMPS .If its like 5 volts or more then its like a motor something that needs a lot of juice to opperate starting motor window motor seat motor check the connectors to them first its the easyest thing to look at also check the fuse box I have mis labeled fuses that should be 10amp but dont burn out and the wires start to melt .
These are not easy problems to figure and tend to be expensive to have someone else fix so the more you can figure out the more money you will save
Good luck

there is a drain on your batt check light switch and interior lights.

You need a better battery. When you hook the amp meter and read 0.3 the ECM needs to sleep

if you have access to a digital multimeter, connect the meter (set to volts) across positive and neg. terminal of the battery, should read roughly 12.6 volts, close to 10 volts, battery may be going out, also test the alt output, disconnect neg term and place negative lead to battery neg post and positive lead to neg battery cable (make sure meter is set to amps) should read near the rating, if both those, then you'd want to do a resistance test, (set meter to Ohms) disconnect battery and connect meter neg to either pos cable terminal or where the pos cable connects to the alt and connect positive lead to opposite of neg, should read next to 0, the check resistance of the ground by connecting meter between batt neg cable and body of alt.

- Spenser

yes look at the wireing

pos to pos and neg to neg for 12 volt but if your system is 24 volt thats a different story it will be pos to neg.and pos to neg

could be your starter solenoid. check that.

you will need a volt meter for this!
first remove the neg. clamp of your battery..
connect the pos.[red]of your volt meter to
the neg.camble and the [black] neg wire of the
volt meter to the neg. post of the battery.
if there is a draw it will show on your meter.
if thats the case start pulling your fuses one at the time until you find the circuit thats killing your battery

bad alternator possible or bad battery..even though its new that battery can be bad. I would take a volt meter and with the engine running check the volts of the battery..If the volts are 12 you need to replace alternator, if volts are 14 you need to check the battery. to check the battery hold the volt meter to the battery and have someone start the car..while the starter is cranking battery volts should not drop below 10volts.if they do your battery is bad.