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Art. XII.— Ori a New Method of Working Lunars. By Mr 
William Mar rat, Member of the Philosophical and Li- 
terary Society of New York, and Lecturer on Natural Phi- 
losophy and Astronomy, Liverpool. In a Letter to Dr 
Brewster. 
The new method of working lunars which I now send 
you, is superior, taking it altogether, to any that I have yet 
seen. It is as short as any, and the navigator sees clearly what 
he is doing ; whereas, by most of the other methods, he is al- 
ways in the dark, knows nothing of what he is about, and, for 
any thing that he can tell, his result may be either right or 
wrong. The peculiar excellence of this method consists in this : 
It proceeds regularly on first principles, and is extremely easy to 
commit to memory : It is as easily understood as any other method, 
and, when once known, the whole theory of the lunars is clearly 
understood. The logarithms to five places, and which are con- 
tained in the common books of navigation, are quite sufficient, 
and the result of each proportion needs only be taken out to the 
nearest minute. The whole of the work, from beginning to end, 
can be performed in ten minutes. The only additional table 
required, beside the common logarithmic tables, is one for se^ 
cond differences^ (the in the Requisite Tables), entitled, “ A 
Table for computing the final effect of Parallax on the distance 
between the Sun and Moon, or the Moon and a Fixed Star f 
and even this is only necessary when extreme accuracy is re- 
quired. 
Let MZS (Plate III. Fig. 2.) be a spherical triangie, in which 
MZ is the moon’s zenith distance, ZS the zenith distance of the 
sun, or star, and MS the observed distance. Let also m s re- 
present the true distance, and let fall the perpendiculars m tz, S o, 
and draw the perpendicular ZN. By the principles of Spherics, 
— As the tangent of half the base is to the tangent of half the sum 
of the sidea^ so is the tangent of half the difference of the sides 
to the tangent of half the difference of the segments of the base; 
which . half difference being added to half the base, gives the 
greater segment, but being subtracted from half the base, gives 
the lesser segment. Hence we have the segments MN, and NS 
