448 On a new Method of determining the Latitude 
By reducing the sine and cosine of (z+), and putting 
2 tan—- I— tan2 gs 
2 
5 and cos « = : 
1+ tan? — 1 2 — 
4 3 + tan 3 
sina = 
we shall, by neglecting the fourth and fifth powers (which we 
may safely do) have 
nie 
v . 
tan > = 7 sin p. cost 
— j sin’ p. sin’ ¢. cot z 
+ isin} p. cos ¢. (1+ sin? ¢) 
whence, by a very simple transformation, we have the correction, 
x= p.cost — 3 p*. sin® é, cot z + 4p}. sin* ¢. cos ¢ 
which is the expression required: and which, for all observa- 
tions of the pole-star, is correct as far as p4, This formula is very , 
easy to calculate: and still more easy to reduce into tables.” 
M. Littrow then goes on to state that, fora fixed observatory, 
we may put into one table the last two terms of this expression, 
for all the values of ¢; viz. by making A = sin* ¢. cot % — 
ca sin? £. cos £. Whence we shall have ) = x + p. cost—A. 
But, he seems to have forgotten that z also is variable; which 
would render a table of this kind (even for a fixed observatory) 
more extensive than is necessary. The most convenient mode 
of arranging such tables appears to be as follows : 
3 
B= + sin’ ¢ 
1 nelle 
C= - sint ¢ 
whence we shall have 
b= 2+(p +C) cost — B cot z. 
In order to render this method more conveuient in practice, 
I have computed the values of B and C for every ten minutes ; 
which are inserted in the two small tables annexed: and which 
will be found to be somewhat different from those given by 
M. Littrow. I have assumed the north polar distance of the 
star to be 1° 38’: but, as the mean north polar distance of this 
star is constantly decreasing, 1 have subjoined the decimal, by 
which the quantities in the tables must be multiplied, when the 
star’s apparent north polar distance is at any of the points there 
stated. The observer will adopt or reject these corrections ac- 
cording to the degree of accuracy required, , 
For 
a 
