NavList:

Having spotted a few more typos and a couple of ‘howlers’ I’ve rewritten the complete explanation together into one script.

Jim S you asked about the Weems Plath Celestial Computer.  It’s simply a device to allow you to add or subtract one value in degrees between 0 and 360 to another value in degrees between 0 and 360 without thinking.  As Frank says, by the time you understand it, you realise you no longer need it.  It probably remains useful only to those people who complete celestial so rarely that they can never remember whether to add or subtract their own longitude during the calculation. 

To complete celestial calculations you need to know the difference in longitude on the celestial sphere between your own position on Earth and that of your chosen Sun, Moon, planet, or star on the celestial sphere at the time of your observation, except we don’t say ‘longitude difference’; we say ‘local hour angle’   You get this from the Nautical Almanac and use it in nautical tables.  Unfortunately, the observer could be at any one of 360 longitudes.  This would need you carrying around 360 different Nautical Almanacs.  We get round this by printing only one almanac for an observer sitting on the Greenwich Meridian.  For Sun, Moon and planet observations the navigator must then convert the Greenwich value to the value for their own longitude.  For stars it’s slightly more difficult but the roughly same principle. 

Please note that for any simple analogue tool there are invariably two or three equally correct ways of using it to come up with the same result.  Everybody is convinced that their method is the best, but really, it’s just which works for you.

One method for calculating local hour angle (LHA) of the Sun, (Moon or a planet) is:
i.   Go to the appropriate date and time in your Nautical Almanac and note the Greenwich hour angle (GHA) of the Sun. 
ii. Move the blue (GHA) disc so that the Sun’s GHA is under the hair line of the cursor. 
iii. Move the yellow disc until your longitude is under the hairline.   
iv. Swing the cursor so that the hairline lies over zero on the yellow disc.
v.  Read LHA Sun from where the hairline crosses the blue scale.

E,g.  GHA Sun = 350, longitude is 60W, your LHA Sun is 290.  It’s just LHA Sun = GHA Sun -longitude west or + longitude east. 

When it comes to stars, there’s not room in the Nautical Almanac to list the GHAs for all 57 navigational stars, so we list the GHA for just one point on the Celestial Sphere and convert this to the GHA of the required star.  The reference point is called the First Point of Aries.  It’s represented in diagrams by a little ram’s horn.  It’s where the ecliptic crosses the celestial equator on its way north.  The difference in celestial longitude between the First Point of Aries (Aries) and the star is called the star’s sidereal hour angle (SHA).  It’s measured from Aries to the star in a westerly direction.  A list of the SHA for each of the 57 navigational stars can be found in the Nautical Almanac.  Therefore, GHA Star = GHA Aries + SHA Star, and LHA star = GHA star plus or minus longitude east or west.

One way of using the WR calculator to get LHA star might be as follows.
i.   Place the hairline over SHA star on the white scale.
ii.  Move zero on the blue scale under the hairline.
iii. Move the cursor so that the hairline lies over GHA Aries on the blue scale.
iv.  Place your longitude on the yellow scale under the hairline.
v.   Move the cursor until the hairline lies over the zero on the yellow scale.
vi. Read SHA Star off the white scale. 

E,g.  SHA star = 053, GHA Aries = 077.  So, GHA star = 053+077 = 130
but longitude = 040W, so LHA star = 130-040 = 090

So, what about ‘t’?   ‘t’ is called the meridian angle.  It’s the angle between the meridian the star lies on and the meridian of the observer.  It’s also the angle P in the PZX triangle that we use in celestial spherical geometry calculations.  I’m not familiar with using this method to get t or P.  I just draw a diagram of a sphere and draw lines on it.  However, there are two PZX triangles for any pole, star, and observer position combination.  We prefer to work with the smaller one.  So to get t or P if LHA star is less than 180, we would simply use t=LHA.  If LHA is greater than 180, we would use t = 360-LHA.  You could calculate this using the two scales on the yellow disc.  I can’t imagine anyone doing that when you can do it so easily with a diagram, and then you know in your head what’s going on. 

The scales on this slide rule are all linear.  Therefore, all it can do is add and subtract.  If you wanted multiplication and division, you'd need logarithmic scales.  Hope this helps.   DaveP