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The liquid in a compass will vary depending on manufacturer, intended use and quality of the compass. The viscosity of the liquid is used to curtail the compass 'spinning', but replacing the liquid in a compass with the wrong type or especially viscosity can damage the compass seals or usablility (it might strip the markings). If the liquid has drained out, you have a bigger problem - the seals are damaged and need to be replaced before a liquid is introduced.
There are two basic types of fluid used: alcohol and mineral oil. The "Varse Oil" you suggest may or may not be a fictional product, or the trademarked name of something much more common - e.g. lamp oil. Esso used to produce a product called Bayol, for example.
Ships tend to change direction slowly and usually when they want to. Small boats are affected by every wave that crashes into them. Therefore, on a boat, you would want the compass to settle quickly, yet avoid being spun like a top. The viscosity is very important to the use the compass is designed for. Similar problems occur with light aircraft.
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I hope this helps.