119

Since

t=

_ y _

jbcos. $log.tang.(4 5°+t<p),

t a minimum , and y constant, we

1

---- = a minimum.

m:os.ipiog.tang.(45°+$<?>)

have

Hence its reciprocal, mcos.plog.taxig.(45°+^) = cos.«phyp.log.tang.(45°-4'i < P)

must be a maximum.

Whence coS.fhyp.log.tang. (45°-|- ih 5 ) -f-cos. p,F.hy p .log.tang. (45°-f-|f)=0.

Butcos.<pF.hyp.log.tan.(45°-f|?>)= »consequently, cos. fhyp.log. tang.(45°-}-£<p)

_ cos. _ q

sin. p ~~~

Or hyp.log.tang. (45°-}-^)=^^-=: cosec. pOr mlog.tang. (45°-f-y ‘P) — cosec. p

Whence,

cosec. p

log.tang.(45°4-5ip)

= m. from which

P may be found by approximation.

In order to determine p from this expres-sion, we shall use Mr. Bonnycastle’s rule ofDouble Position, after first finding, by trial,that the value of p lies between 50° and 60°.

i 4