8e Mr. Lax's Method of finding the Latitude of a Place y 
mining the log. cosine of the angle at the pole. From the log. 
sine of the altitude increased by three times the log. radius, 
subtract the sum of the log. sines of the latit. and declination ; 
take half of the remainder, and, considering it as the log. secant 
of an arc, find the log. tangent corresponding; multiply this 
by 2, and add the log. tangents of the latit. and declin. and 
reject thrice the log. radius ; the sum will be the log. cosine of 
the angle required. But, when the declin. and latit. are of a 
different denomination, it is evident that our expression be- 
comes rrd d — ^r~ • r> which is equal to d-L x 9 . into the 
square of the secant of the arc whose tangent is \ In this 
case, therefore, having found the log. value of ddL f and divided 
it by 2, we must consider the quotient as the log. tangent of 
an arc, whose log. secant being taken, we are to proceed as in 
the former case. 
The advantages of this rule are obvious. We obtain the 
angle in terms of the log. cosine; and, consequently, when we 
have calculated the second time with the new latit. we have 
only to subtract one result from the other, and we imme- 
diately determine the area corresponding to the difference of 
the times. Besides, in the second computation, fewer of the 
elements are changed by this rule, than by any of those which 
are usually employed ; and this is a consideration of much im- 
portance. But, if we are disposed to adopt the following 
method of ascertaining the incremental area gc , this advantage 
will be found still greater. Let us resume the expression 
a ~ d - , and we shall have y — ~ x ~ dU ~ (\ J be- 
9 Q A A ' 
y = 
