NavList:

Jim Wilson wrote:

I understand that the purpose of the double altitude sight is to get time
of meridian passage. Is there another use?

To be specific, it is the method of equal altitudes that give the time of the meridian passage rather easily, from which you can derive longitude. In fact, before the advent of GPS technology, it was probably the most accurate way of deriving longitude available - giving very similar precision. This alone justifies its continued presence in the navigator's "kit of useful methods".  One great advantage of this method (if not the great advantage) is that corrections for refraction etc are not required. The so called "Equation of Equal Altitudes" can used to correct for declination changes if the sun is being used as the celestial object.

The method of double altitudes, on the other hand, does not require the body to cross the meridian, but does require accurate altitudes corrected for refraction etc.

Geoffrey Kolbe