I have two Luxo incandescent/fluorescent drafting lamps.  One has a defective swing arm assembly and one has issues in the lamp head.  So I clipped the power cord between the transformer and the lamp head and put the good head on the good swing arm.  Problem; the 3 wires in the power cord of one are black, white and green and the other are black, white and red.  I connected white & white, black & black and red & green.  Power on blew the incandescent bulb.  What should I do next please?
Tony

Are they both the same configuration of fluorescent and incandescent lamps ? If so, they should wire up in a similar fashion. I'm guessing 120V 60Hz mains here by the colour of the wires. White is neutral, so they could all be wired together. Green is ground and should all be wired together and to the ground pin in the plug. Black and red are hot, and sometimes the different colours indicate different switching/other functions, but both are hot.

Now, I'm guessing here. Black could be to the incandescent lamp, and red could be to fluorescent ballast. You mention that there is a "transformer" in the plug (I imagine a "wall wart" type of plug), which in this case houses a ballast. If there are no provisions in said "wall wart" ballast for a hot bypass, you cannot use it for the incandescent lamp. If you want both light sources with this, you will need 2 mains plugs, one being this ballast plug and one standard plug.

All this is guessing from your description. Photos would help clear up the confusion and will make it easier for us to troubleshoot.

Here is the lamp and the connection that didn’t work

Are the two lamp heads identical, with one circline and one incandescent ? Maybe someone rewired it (black cord) and bypassed one or the other.

Yes, both lamps seem identical except for the wiring color.  Should I just randomly reconnect the wires until something works or could that be dangerous because of the fluorescent?

No. First of all, if you mistakenly connect the fluorescent lamp directly to the mains, it will destroy it. I gather it is a 22W circline and it will strike on 120V.

From what I can see in the wires you showed, it looks like it is not grounded. In that case, you should "officially" either change the cord for the appropriate colours, or  at least mark them with coloured electrical tape. It would make it easier to troubleshoot in the future, especially if it is not you. I used quotation marks because that is the best thing to do for the confusion in the colours. It will work fine once you sort it out without the proper colours so it is up to you...

Regarding the three wires, you have a neutral which would be common to both lamps (so connected together). Then you have one hot that is connected directly to the mains and goes to the incandescent socket (there is no ballast needed for incandescent lamps). Then you have a second "hot" that goes through the choke ballast in the base and to the fluorescent lamp. Then you have a starter loop that is completely contained in the lamp head and connects to the start button that you hold for several seconds to preheat the lamp.

Regarding mistakes in the wiring, if you wire up the fluorescent directly to the mains, you destroy it (mentioned above). If you connect the incandescent through the ballast, it will light up dimmer than normal but not be destroyed.

Two questions : does the fluorescent lamp work the way you have it wired ? Did you try another incandescent lamp in case the one that blew was bad and the socket was wired correctly ?

Having never operated one of these specific lamps, I gather the black button in the centre is press on/press off for the incandescent. The white button is off for the fluorescent and the red button is on/preheat for the fluorescent (you  hold it down for a few seconds when the ends of the lamp only will light and the tube fires up when you release it).

Then again, maybe you have a bad switch, in which case you might be able to find one on eBay, otherwise I do not know of a source for these switches.

First, thanks so much for the feedback.  I originally thought this would be a simple response but not so.  Sorry to be a pain in the butt. 
You were correct that the black cord is a rewire.  In fact they cut the green wire before the transformer and then used it between the transformer and the lamp for Some function of the fluorescent.. 
I use this fixture as a work table lamp because the extending arm allows me to move the light to where I need it.  The fluorescent feature isn’t really necessary so I’ve just wired the switch for the incandescent lamp and that will be just fine.  Again, thanks so much for your time.
Tony