NavList:

David McN, you asked "given dLat and dep, what is the course and distance?"

As the traverse tables are not designed for reverse use, you need a certain amount of luck to find a pair of dLat and dep that is reasonable close to your figures. As you didn't gave your observed position in your later example, I've assumed you were then at 39°34'S 143°37'E and want to know course and distance to Portland, at 38°21'S 141°37'E. So dLat=73N and dLong=138W. Mean latitude is close to 39° so enter your traverse table on course 39° and read off the value in the dLat-column for distance one mile. The answer is 0.78, which is indeed cos 39°. Multiplying, by hand, this value with dLong gives dep=108W. 

To find the course, use tan C = dep / dLat = 108/73 = (73+35)/73 = 1+35/73 = 1.5. Now look up 1.5 in a table of natural tangents (included in all good nautical tables) and you find the course 56°, i.e. N56°W or 304°. Enter again the traverse tables with course 56° and look for either your dLat or dep value in the appropriate column, and you find that both values match for a distance of 130 miles.

This was the usual noon practice for working up the general course and general distance by account from the previous day's noon position. You summed all the dLat-values for the various courses and distances sailed during the last day, likewise with the dep-values. I have never understood the benefit of knowing the general course and distance, but in most logbook I've seen there is a box where these numbers are to be entered.
Lars