You said it gains about a minute every 24 hours, I see the beat adjustment lever (the one that is bent downward over the back plate) is pushed to one side, this lever will advance or retract the beat therefore speeding the clock up or slowing it down. Also check to see if the balance spring is free in the slot of this lever if not it may be putting too much tension on the spring. Just so you know, the closer the slot end of the lever is to the end of the spring (where the taper pin holds it) the slower the clock will run.
It's very difficult to provide help without pictures. From the information you've provided, I can tell you that Omega pocket watch with movement number 5,694,216 would have been made between 1916 and 1923. The 15 jewels and 2 adjustments would align with these dates as well. I do not know what "Fortune" or the other number mean. Here is a picture of a watch made in the same time period...does your movement look like this?
Hi Andy, The link introduces/defines Thermodynamic which is the study of heat energy conversion to work and vice versa. It is about transformation of energy. One form of energy (heat) transforming into another form ( work) and not concerned with transfer of heat, from hot to cold.
Understanding the nature of heat and the mechanism heat transfers from hot source to cold, is a key len33 is prepared to use. His question shows him ready to absorb the concept.