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Dave,

Mark the D scale at 1.96 with a 0.5mm pencil and set slide to S scale index 90° (1) on the mark to start the calculation of value a. Pencil in cos degrees on rule every 10° if not marked. You will need to flip rule over to do the second formula. The a value is saved under the index mark. No intermediate values need to be recorded. Pencil mark the C scale of the slide at 2.67 which makes for quicker sets on follow-up ex-meridian calculations. 

The Frederick Post 1460 10" rule has cos marked and doesn't need flipping to complete calculation making it ideal for ex-meridian calculations. These are very good value Japanese slide rules made of bamboo. The pocket 6" version may not have the cos marked. I'll have to check on that.

Greg Rudzinski

P.S. Just did the example ex-meridian calculation in 52 seconds time using the marked 1460 rule which equals the pocket calculator.

From: David Pike
Date: 2016 Jan 1, 13:21 -0800

Having not used a slide rule in earnest since my last BSc exam in June 1966, I thought it was about time I got into practise again using the various bits of slide rule I’ve rescued from the bottom drawers of desks I’ve inherited over the years.  Having revised multiplication and division, I looked for trig functions.  First problem, there’re no cosines.  Presumably this is got around from cosine angle = sine 90- angle.  Next problem, the trig functions are on the stock, not the slider.  Is there a way to multiply more than one sine at a time without having a good memory for numbers (like more than two seconds) or writing the value down?

One rather upmarket Government 10” slide rule, with a spare cursor and a tightening key, that I’ve rescued appears to have a way around this.  The trig functions are on the rear of the slider.  If you’ve got more trig functions than numbers, you can turn the slide upside down and use that side. The only problem is working out where left-hand one is.  Right hand one’s OK; its sine 90.

Using Greg’s example, I was getting answers in the region of 1.7-1.8, but by golly you need good eyesight.  I wouldn’t like to try it in a bumpy boat or aeroplane on a dark night.  Using a x10 magnifier, I managed to get 1.775. 
I didn't pursue the calculator solution, but presumably you need to spend time converting from degrees and minutes to decimals of a degree. DaveP

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