Logos

You could argue that the Compromise of 1850 actually relies on implied ethos, since it's coming from the government, an authority. However, the actual style of writing is designed to convey information and rules, so ultimately the main form of rhetoric is logos.

Even when dealing with the most hotly debated aspects of the Compromise, the final result doesn't try to do anything but lay out the law.

For example: "when admitted as a State, the said Territory, or any portion of the same, shall be received into the Union, with or without slavery, as their constitution may prescribe at the time of their admission." (Texas.Section 2. 4) Or, from the Fugitive Slave Act: "all good citizens are hereby commanded to aid and assist in the prompt and efficient execution of this law, whenever their services may he required, as aforesaid, for that purpose." (Fugitive Slave Act.Section 5.2)

Both of these are dealing with emotional, complicated issues—the expansion of slavery and requiring everyone to help catch runaway slaves—but the way the ideas are written take emotion out of the equation. Legislation is generally written this way, because it has a job to do and needs to not take sides.

Just lay out the rules, and let the people fight it out as they will. There will be plenty of emotion later.