452 
The Account of a 
s, 1" : 1 :s,d a (in parts of radius unity) : —7 x s, d a = d a in 
seconds. 
= -77 xk - 2 s*,±da.'t,a \da.’t,a = 
~7 *.* if we put » = — x/', — 5) 
— t, \ a . j*, i (H + 5 ), and d a = a number of seconds, we 
shall have 
d a — n—d a . s,\ d a .'t, a ; and, for the most part, without any 
sensible error, d a = n — n . s,\n . 't, a. 
Table I. contains -■ * ■ ’ : a , and — - x — ? a ; Table II. contains 
10000 10000 
10000 x s l , {(H + l)). Table III. contains the term — n . s> 
\n At, a. The argument on the side is a , and that on the top 
is n or the result found by the help of the t\^o first tables. If 
this correction should be considerable, with the value of d a , 
found after this correction has been applied, enter Table III. ■ 
again at the top, and with a on the side as before ; the number 
now found subtracted from n will give the correct value of d a. 
By the investigation, 
da — ^'ty^ a .vsW 2^ h — \ t, \ a . vs, H ± b — vs, d a .'t a, 
where the upper or lower signs are to be used, according as 
the objects are on the same, or on contrary sides of the great 
circle to which they are referred ; the third term will be nega- 
tive or positive, according as a is less or more than 90° .* If da 
should come out negative, A will be less than a, or a greater 
than A. In the case of reducing a spheric angle to the angle 
* Compute the two, which will give the approximate value of d a, and make use of 
them in computing the third term ; and join the three terms together according to 
their signs, which will give d a still nearer ; and, if this should prove considerable, 
compute the third term a second time with the new value of d a. 
