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Bill and Sam,

This is a bad habit. May I suggest: don't refer to these simple scaled plotting sheets as "Mercator". That's a long-standing abuse of the term in navigation lingo, apparently originating in USN post-war practice. These charts are simply "conformal" or if you want something more obvious, more descriptive, call them "longitude-scaled plotting sheets". Conformal is the proper cartographic term for a map which locally preserves shapes and angles, and in small scale plotting sheets, this property is nothing more than scaling the spacing between longitude lines by a factor of cos(Lat). Conformal plotting sheets are required for any plotting that depends on compass bearing. If you plot LOPs by alternative methods, like a "Sumner" approach, for example, where you caclculate and plot lat/lon pairs with no bearings involved, then you can use commmon graph paper and don't even need a conformal or "longitude-scaled" plot.

Sam, you asked what to do when your LOPs cross near the far edge of a plotting sheet that is several degrees across. Simple: do it over with a different AP. This is actually an important rule. Your intercepts should never be longer than about 30 nautical miles and ideally much shorter. If they are longer, you can't fix it with any easy tricks. Plotting on a sheet of paper is equivalent to pretending that the Earth is flat over a small area. That approximation becomes rapidly worse for longer distances from the center of the plotting sheet.

Frank Reed
Head cartographer, Centennia Historical Atlas, HistoricalAtlas.com
...among other things.