NavList:

Ed J
If you have one of these, please provide a better photograph, or describe what’s written on the scales.  Also please check the instructions aren’t printed on the back. 
However, from the low-resolution picture provided. 

Weems and Plath Celestial Slide Rule – Provisional Analysis

The white scale appears to have 360 equal divisions increasing anticlockwise.  This could be used to represent GHA, SHA, or LHA

The blue scale appears to have 360 equal divisions increasing anticlockwise.  This could be used to represent GHA, SHA, or LHA

The outer amber scale appears to have 180 equally spaced divisions increasing either side of zero, one clockwise, and one anticlockwise.  Probably the writing around zero labels the anticlockwise increasing scale ‘West’ and the clockwise increasing scale ‘East’.  This is probably the longitude scale and the meridian angle scale.

The inner amber scale appears to have 360 equal divisions increasing anticlockwise.  24 hours or 360 equally spaced divisions increasing clockwise might have been more imaginative, but as it stands, it’s probably there a fast way of converting LHA to meridian angle.

To obtain meridian angle from LHA: Move the cursor over LHA on inner amber scale.  Read meridian angle from the outer amber scale.

To obtain LHA Sun (or Planet):  Align GHA Sun on the white scale with zero on the outer amber longitude scale.  Move cursor to the observer’s longitude on the outer amber scale and read off LHA Sun (or Planet).

To obtain LHA Star:  Align GHA Aries on the white scale with zero on the outer amber longitude scale.  Move cursor to the observer’s longitude on the outer amber scale and read off LHA Aries.  Being careful not to move the cursor, slide zero on the blue SHA scale under the cursor.  Move the cursor over SHA Star on the blue scale and read off LHA Star from the white scale.  With practice the user might find an easier order to do this.

The best way to use this device is probably to work out the figure you require manually on paper first and use the slide rule as a check while you build up confidence.  Then the day you forget your slide rule it won’t matter (unless you’ve forgotten your pencil as well).  DaveP