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    Re: Doniol for time sight reduction?
    From: David Fleming
    Date: 2015 May 15, 17:27 -0700

    Solution by slide rule requires the equations used, to depend primarily on multiplication ( or division ) for their solution.

    eg. Bygrave uses 1) tan(x)=tan(D)/cos(t) ; 2) y=90-x ; 3) tan(Z)=tan(t)cos(x)/cos(y)  & 4) tan(Hc) = cos(Z)tan(y) 

    Only second step is non multiplication and can be done in your head.

     

    For a time sight should use hav(t) = sec(L) csc(p) cos(S) sin(s-h) which Bowditch 1984 pg 586 says is the most common formula for time sight.

    p=90-D  or 90+D LD same/contrary respectively.  S=1/2(h+L+p)

    You would need a slide rule with log sin, log cos, and log haversine scales to implement. Either the sin or cosine scale could be eliminated by using identity cos(x)=sin(90-x) and some additional rules to take care of negative values for those functions.  Two scales could then be accomodated with a double sided circular slide rule that has a cursor locked together on both sides.

    Dave

       
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