I have more 100w mercury ballasts than lamps at the moment for my display fixtures, and recently put 175w lamps in two of them. They run the 175w lamps at 100 watts and the lamps appear just as bright as 100w lamps do in the same fixtures. These are used typically no more than 3-4 hours at a time, maybe once a week at most. Ballasts are Chinese H38 HX autotransformers mounted in remote metal boxes away from the lamps, and lamps are also Chinese of dubious quality.

My thinking is as long as the lamps run up to a high pressure arc, their life won't be compromised - it will be just like "dimming" them on a dimmable ballast. As they are underdriven, I'm thinking the lamps may last longer than they would at 175w.

Is my logic correct, or would it actually shorten the lamps life? What about the ballast - will it run hotter or cooler? I can't tell a difference but I haven't taken offical voltage, current and temperature measurements.

If the arctube temperature is low enough, hte lamp may be operated with cold cathodes, what means heavy sputtering and shorter life.
Dimming with magnetic ballasts, is different than with electronic ballasts. Most HPS and pulse-start MH lamps, shouldn't be dimmed to less than 60%, because below this value, they will be operated with cold cathodes.

My thinking is as long as the lamps run up to a high pressure arc, their life won't be compromised - it will be just like "dimming" them on a dimmable ballast. As they are underdriven, I'm thinking the lamps may last longer than they would at 175w.

It is hard to say, as there are multiple phenomenons affecting lamp life, while each depend differently on the operation current:
- Lower electrode peak current load mean less sputtering, so in this way prolong the lamp life
- Lower loading run the lamps, so the electrode assembly cooler, what may lower the electron emission, so increase the cathode fall, so increase the sputtering, so shorten the lamp life.
 The cathode load wear is more related to the peak current, while the cathode heating and the lamp power to the average current (to be precise, it is avg(abs(Ilamp(time))) ). Thus for best life is beneficial to keep the peak as small as possible on the given average, so in other words keep the current crest factor low. But that is more given by the ballast concept and not the power, so I assume you have no choice there.

Both effects are there at the same time, so which one is dominant, I guess nobody know. Generally it is assumed the life of dimmed lamps is either the same or shorter than when operated at rated power.
But the MV's tend to only loose lumen output, the complete failures are very rare. As your application is only the lamp display, the real lumen output is not important, so I wouldn't wonder as much about the lamp life.

Is my logic correct, or would it actually shorten the lamps life? What about the ballast - will it run hotter or cooler? I can't tell a difference but I haven't taken offical voltage, current and temperature measurements.

This depend on whether the actual lamp arc voltage is higher or lower than the rated 100W lamp. But when the MV lamp run in an unsaturated vapor mode, it's voltage does not depend on the real power anymore, so it would be nearly the same as on the 175W. And the MV's are all designed to arc voltages around 120V, I would guess there would be no significant difference from the ballast perspective when settled at full power.
The difference would be on the startup: When the lamp is not yet warmed up, it's arc voltage is lower. This causes slight increase in the ballast cuirrent, so in the ballast losses. As the bulkier lamp would take longer time to warm up, the ballast would be exposed for longer time to these higher dissipation conditions and may eventually reach higher temperatures during lamp warmup. But usually the ballast mass is so huge, it's thermal inertia is way slower than the lamp's, so this higher power losses would be present when the ballast would be still cold. But as the temperature is the only effect affecting the life of the magnetic component life, I do not expect any adverse effects of running the 175W lamp, unless it take longer than 20 minutes to for the lamp warm up to the unsaturated vapor state...

But the 175W MV is compatible (regarding ballast parameters) with 150W pulse start MH and/or 150W 70V HPS, so you may use one of these ballasts, only remove or deactivate the ignitor (disconnect the Neutral wire,...). That would yield nearly perfect 175W drive...

Thanks for the input. I think ultimately I should buy some more good-quality NOS or Iwasaki 100w lamps and old stock USA-made ballasts. But right now I'm "using up" what I have already.

The Chinese 100w ballasts seem to slightly overdrive a 100w mercury lamp, whereas the Chinese 175w ballast considerably underpower a 175w lamp. I have noticed I get only about 1500 hours maximum life out of the 100w lamps on China ballasts; likewise, running a Chinese 175w mercury lamp on an older, full-power 175w ballast leads to short lamp life. Maybe the lamps are just REALLY bad quality, but I was hoping I could prolong their pathetic lives by underdriving them.

BTW, what does "unsaturated vapor mode" refer to - and how do I know a lamp is in this condition?

Unless most other discharge lamps, the MV's are designed to evaporate the complete arctube fill material, so all the mercury.
What happen with nearly all of the materials: The heat in them is in fact random vibration of their atoms. This vibration mean they are moving with rather a random speed, while when you average the squares of the speed of each atom, you in fact get the thermodynamic (absolute) temperature.
Now as the actual speed of each particle is random, some are faster and some slower and vibrate in any direction. What keep them from going out of the surface, are the bonds between those particles. Now when some particle just get enough momentum, so the bond does not have sufficient strength to keep it in place, such particle get released, so it become a vapor. As more of these particles get released, their concentration above, what mean the vapor partial pressure rises. But at he same time the particles in the vapor phase are moving too. And sometimes it happen, than some of them reach the surface, so get captured back, so it is not part of the vapor anymore. And this recapture happen more frequently, when there are more vapor particles above the surface, so higher partial pressure.
Now these two mechanisms run at the same time, so some particles get released and some get captured. Now as more and more of them are in the vapor phase, the faster is the rate of the recapture, so eventually at some vapor pressure both effect happen at the same rate, so an equilibrium state is reached. This is then called "saturated vapor". The dependency of the saturated vapor pressure on the temperature is given for the given vapor composition. Generally increasing the temperature mean steep increase of the pressure. And note, the pressure does not depend on the amount of liquid (or solid), just on the temperature.
This is used in many lamps to regulate the amount of the gaseous material of each gas components, so allow an excess to be stored in the arctube to cover up it's losses during lamp life (when it react with other components inside the arctube). But that mean the pressure depend on the temperature of the coldest spot (there would form the liquid reservoir). Now as the arc parameters (voltage, color,...) depend on the concentration of the active material (mercury, sodium,...), it is beneficial to keep the cold spot temperature on the designed level. But as all the temperatures depend on the thermal balance, it is the task for the ballast to feed it so, it stay there.

When the vapor pressure is higher, than correspond to the saturated vapor pressure at given temperature, it start to condense.
Now when you take some of the vapor and heat it up, more of the material would evaporate. But when there is no liquid or solid source of that material anymore, so the vapor pressure become below the saturated vapor temperature and so it become unsaturated (it could absorb more material, if there would be any source of it, but it isn't). For the discharge lamp it mean, than the concentration, so the arc parameters, can not change anymore, regardless what the temperature is doing, so the arc parameters become quite thermally independent.

Now the MV is the only the metal vapor lamp style, what is designed to operate in this unsaturated vapor state.
But when the lamp is cold, the saturated vapor pressure is so low, the mercury condense there.
Now with the low vapor pressure, the arc voltage drop is low as well, but that mean the power dissipated in the lamp is low too, as ballasts fed the lamp with current more-less independent on the arc voltage. But when the dissipated power is too low, it may not be enough to warm up the lamp to higher temperature, so the lamp may "lock in" the low temperature state, where only some mercury is evaporated, so the vapor is still saturated.
For the MV operation is critical, than the ballasr current is able to heat up the lamp all the way up to the point, when all of the mercury dose become evaporated. At this point the mercury become unsaturated vapor and the arc voltage would reach the designed ~120V (depend on actual wattage rating).

Wow...thanks for the explanation! I had forgotten that unlike HPS lamps, or low pressure mercury (fluorescent) sources, all the mercury is vaporized. So a mercury lamp that fails to reach its proper arc tube temperature may not vaporize all the mercury, causing problems.

What about underpowering an standard HPS or MH lamp? Would it increase lamp life in those cases (i.e. running a 100w lamp at 70w?

And with fluorescents, what about running a high output lamp on a standard-output ballast (i.e. F54T5HO on a F28T5 ballast, or 1600mA T12 VHO on an 800mA ballast)? I am also guilty of these mismatches...again because of a lack of owning enough of the proper ballasts, but also thinking it may increase lamp life. I am not sure my incandescent mentality (i.e. running 240v filament lamps on 120v) applies

 

What about underpowering an standard HPS or MH lamp? Would it increase lamp life in those cases (i.e. running a 100w lamp at 70w?

HPS is officially allowed to be dimmed down to 30% power, most MH to 50% power by altering the ballast impedance. But they have to start at full power and run there for at least 15 minutes, only then is allowed to dim them down.
The HPS is not as critical (unless you care about the nasty monochromatic color), but in the MH it is important to let all the arctube cleaning processes to take place to clean it up after the ignition sputtering. And these really require the heat from the full power operation for the 10..15 minutes.

So run at lower power ballast: No, you degrade your lamp.
Reduce the lamp power on a dimmable ballast: Yes, but you would need the dimmable ballast (and it won't be designed to run on the triac dimmer, but use special signal to "tell him" the required power level)... But the lamp life would be at the best case the same as when running at full power.

And with fluorescents, what about running a high output lamp on a standard-output ballast (i.e. F54T5HO on a F28T5 ballast, or 1600mA T12 VHO on an 800mA ballast)? I am also guilty of these mismatches...again because of a lack of owning enough of the proper ballasts, but also thinking it may increase lamp life.

If you provide an auxiliary heating for the electrodes, it could work on whatever reduced power you want, without the expense of the shorter life. But the key is to maintain the cathode temperature on the sufficient level. The fluorescent handle the dimming the best, as you can provide the missing heating power for the electrodes externally.

The problem with all discharge lamps is, their electrodes need o be heated to some temperature (800..1500degC, depend on the actual emission system) in order to have sufficient electron emission. If the emission is insufficient, the voltage drop on the electrode/plasma border increase, what accelerate the ions on higher speeds and these then "sand off" the electrode surface, so damage them. It is this, what make most discharge lamps to suffer by each start: (except of fluoresacents) The discharge start with cold electrodes and only heat them afterwards (about 1..5 seconds). But during this 1..5seconds the electrodes are "sandblasted" by the accelerated ions, what sputter their material on the arctube and/or wear off the emission coat (again, depend on the exact lamp design). So to prevent this to happen on fluorescents, the most modern ballasts first only apply power to the filaments, so they heat up to the sufficient temperature, and only then they strike the discharge. With that the starting wear is eliminated, as the discharge never run on cold electrodes.

I am not sure my incandescent mentality (i.e. running 240v filament lamps on 120v) applies

It does not at all. In incandescents is only one degrading mechanism: Filament evaporation. And this is accelerated at higher temperatures and slowed down at lower ones.
But the discharge lamps have many mechanisms, each behaving in different direction, so there is always some compromise power, where the lamp have the longest life.
And for obvious reasons, this compromise is designed to be the nominal operating power.