There's really no telling how the author got his numbers. Using Hassler's tables from 1830, Logarithmic and Trigonometric Tables - Google Books
I get:
log cos 8-19-34 = 9.9953982, which agrees with the author,
log sin 8-19-34 = 9.1607900, which agrees with you,
log tan 8-19-24 = 9.1563379, which agrees with you.
All of my answers agree with my TI89.
Hassler's tables are 30-second intervals with proportional parts for 10 seconds. It's been a long time since I interpolated using proportional parts, but it jogged my memory and reinforced the fact that cosine is a decreasing function.
Checking with the TI89 reinforces how linear a log-trig function becomes as successive points get closer. Great calculus concept.
The spreadsheet for Vincenty's calculation is coming. I haven't decided whether to use his approach to solve the 3-equation system with one a quadratic by his method or by deriving another. One interesting note on that little project is the meaning of FORWARD's "longitudes are all considered to be west" when one needs and East longitude. NGS may force us to use "all East longitudes" so playing with FORWARD and east longitudes may be informative.
Old stuff is fun; thanks for sharing.