# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Newbie - Variation Question**

**From:**Trevor Kenchington

**Date:**2002 Feb 16, 18:16 -0400

Brian Whatcott wrote: > >At 02:42 PM 2/16/02, Trevor Kenchington responded: > >... it is easy to see that if > >magnetic north lies to the east of true north, the magnetic bearing MUST > >be numerically smaller than the true one (unless it is smaller than the > >true bearing plus 360 degrees.... > >Trevor Kenchington > > Hmmm....let's see: Trevor wants us to check that the magnetic bearing > (in the range 0 - 359 degrees) is smaller than the true bearing (0-359 deg) > plus 360 degrees (i.e 360-719 degrees). > If I understand his recipe correctly (probably not!) that means magnetic > is always numerically larger than the true. > > Now that's a novel assertion! Evidently I have made the major error of assuming that the members of Navigation-L all have at least a modicum of intelligence coupled to a basic understanding of the topic at hand. If I really have to spell it all out in detail: Bearings expressed in 360-degree notation are, by definition, constrained to be positive numbers in the range of zero to 360. When calculations produce bearings outside that range, integer multiples of 360 are added or subtracted as necessary to yield answers that fall within the defined range. In the case of comparisons between true and magnetic bearings when variation is easterly (as in my example quoted above), the magnetic bearing will be numerically smaller than the true, _except_ when the numerical value of the true bearing is less than that of the variation, in which case the (numerical value of the) magnetic bearing will necessarily be less than the sum of the (numerical value of the) true bearing plus 360. To put that another way: subtracting the easterly variation from such a true bearing would produce a negative value, which requires the addition of 360 degrees to yield a magnetic bearing within the defined range of 000 to 360. The "magnetic less" rule then relates the magnetic bearing to the true bearing plus that same 360 degrees. As to the checking which Brian seems to think that I had suggested to Andrew: I did not address anything as puerile as comparing a range (e.g. 000 to "359" -- actually 360) to another range covering larger numbers. Rather, I recommended considering, with the aid of a graphical sketch, one specific bearing expressed relative to magnetic north with the same bearing expressed relative to the true meridian. That, hopefully, was clear to most readers without the pedantic explanation. Trevor Kenchington -- Trevor J. Kenchington PhD Gadus{at}iStar.ca Gadus Associates, Office(902) 889-9250 R.R.#1, Musquodoboit Harbour, Fax (902) 889-9251 Nova Scotia B0J 2L0, CANADA Home (902) 889-3555 Science Serving the Fisheries http://home.istar.ca/~gadus