I assume that "appropriate(d) order" means "deepest dive first."
For those who do not know the history, about 20 years ago a conference on what are called reverse profiles (doing deeper dives after shallower dives) was held, trying to figure out where the "deepest dive first" rule came from. They could find no research indicating a reason for the rule. The earliest mention they could find of it was a suggestion (not a rule) in the 1972 PADI OW manual. In subsequent editions, the language of that suggestion evolved into a rule. PADI representation at the conference had no idea who had come up with the original suggestion, why it was suggested, or why it became a rule. The conference (almost) concluded that there was no reason for the rule, but one participant argued strenuously for it, especially on deeper and technical dives, so they left it as a recommendation for technical diving. Even though that was 20 years ago, dive operations around the world routinely follow the "deepest dive first" rule to this day.
Although the conference did not find a reason for the suggestion/rule, the exercise in this thread can provide an example of the most likely reason. If you do the dives in a different order, you will get a very different answer. Very different. In 1972, pretty much everyone, including PADI, was using the US Navy tables, which did surface intervals based on the 120 minute compartment, leading to very long surface intervals between dives. When you plan dives using any tables, you get the shortest surface intervals if you do the deepest dive first, and with the US Navy tables, that difference could be huge. Even with the PADI tables using the 60 minute compartment, the difference can be significant.
So, there is probably no physiological reason preventing you from doing a deeper dive after a shallower dive, as long as you have the required surface interval for that second dive. If the reverse profile conference were held again, that conclusion might be unanimous, because the lone person claiming there was a physiological reason, Bruce Wienke, died earlier this year. Wienke created the RGBM algorithm used in many dive computers. That algorithm is proprietary, so I don't know if he included a penalty for a reverse profile, but it would not surprise me if people using RGBM computers will suddenly find their NDLs shortened if the second dive goes deeper than the first.
For those who do not know the history, about 20 years ago a conference on what are called reverse profiles (doing deeper dives after shallower dives) was held, trying to figure out where the "deepest dive first" rule came from. They could find no research indicating a reason for the rule. The earliest mention they could find of it was a suggestion (not a rule) in the 1972 PADI OW manual. In subsequent editions, the language of that suggestion evolved into a rule. PADI representation at the conference had no idea who had come up with the original suggestion, why it was suggested, or why it became a rule. The conference (almost) concluded that there was no reason for the rule, but one participant argued strenuously for it, especially on deeper and technical dives, so they left it as a recommendation for technical diving. Even though that was 20 years ago, dive operations around the world routinely follow the "deepest dive first" rule to this day.
Although the conference did not find a reason for the suggestion/rule, the exercise in this thread can provide an example of the most likely reason. If you do the dives in a different order, you will get a very different answer. Very different. In 1972, pretty much everyone, including PADI, was using the US Navy tables, which did surface intervals based on the 120 minute compartment, leading to very long surface intervals between dives. When you plan dives using any tables, you get the shortest surface intervals if you do the deepest dive first, and with the US Navy tables, that difference could be huge. Even with the PADI tables using the 60 minute compartment, the difference can be significant.
So, there is probably no physiological reason preventing you from doing a deeper dive after a shallower dive, as long as you have the required surface interval for that second dive. If the reverse profile conference were held again, that conclusion might be unanimous, because the lone person claiming there was a physiological reason, Bruce Wienke, died earlier this year. Wienke created the RGBM algorithm used in many dive computers. That algorithm is proprietary, so I don't know if he included a penalty for a reverse profile, but it would not surprise me if people using RGBM computers will suddenly find their NDLs shortened if the second dive goes deeper than the first.
