120 
Mr. de Mendoza y Rios on the principal 
l and L the apparent and true altitude of the moon, g and G 
the apparent and true distance of the moon and star. Let 
the sine and cosine of g = d. and <5“, the sine and cosine of 
l = a and «, the sine and cosine of b = b and (3 ; and the 
sine of the actual and mean horizontal parallax = p and *■ ; 
and let the sine of L — a — in -f- p e, and its cosine 
= a(i-[-^ — p e) and let the sine of H = b — n , and its 
cosine — (3 (l + »')• 
“ Then the cosine of G = J(i -}-/*— />s)(i -\-v)-\-(a—?n -f pe) 
( b — n ) — ah (l -f yu. — p e) (i + v), which equals $-{- -f — 
ip e-\-$ pv — ipev-\-ab— bm-\- bp e — a n-\-nm — np e — a b — 
ub a bp e — a bv — a b pv -|- a bvp e = $-\-£ v — S p e — b in — 
b a p-\-b p e -\-b apt — an— a b v-\-n m — np e—a b pv-{-a b vp t -|- 
i [A V $ TT £ V. 
“ To make use of this rule, it must be considered that the 
quantity <1 p v — $p e v is so small that it may safely be disre- 
garded; but n m — npe — ab pv -f ab v p e, if the altitudes are 
not more than 5 0 , may amount to about 12 ", and therefore 
ought not to be neglected. The quantity e -\ -ae also differs 
very little from one, but is not quite equal to it. Let there- 
fore a table be made under a double argument, namely, the 
altitudes of the moon and star, giving the value of ... . 
n m — nTre — abpv-\-abv7r£-]-bve-\-baTre — b «■, answering 
to different values of these altitudes, which call A. Let a 
second table be made under a double argument, namely, the 
altitude of the star and the apparent distance of the moon 
and star, giving the value of iv, which call D. Let a third 
table be made with the observed altitude for argument, giving 
the logarithm of a m -J- a z p ; and let this quantity, answering 
to the moon's altitude, be called M, and that answering to the 
