SUBROUTINE GAUSS8 (nracp, RACP, PG, SIA, RAD, PGGSIN2,
        SINM1, SINM2, SIN2)

ARGUMENTS

OUT

RACP(NRACP)     Legendre polynomial roots
                =sin(Gaus. lat.)
                =cos(Gaus. colat.)                 real*8
PG(NRACP)       corresponding Gaussian weights     real*8
SIA(NRACP)      sin(Gaus. colat.)=cos(Gaus. lat.)  real*8
RAD(NRACP)      Gaus. colat. in radians            real*8
PGSSIN2(NRACP)  PG/(sin(Gaus. colat.))**2          real*8
SINM1(NRACP)    (sin(Gaus. colat.))**-1            real*8
SINM2(NRACP)    (sin(Gaus. colat.))**-2            real*8
SIN2(NRACP)     (sin(Gaus. colat.))**2             real*8

IN

NRACP           number of positive roots of the 
                Legendre polynomial                integer

DESCRIPTION

EXAMPLE

NOTES

All the NRACP roots are anti-symmetric relative to 
equator(pi/2), being positive between colatitude 0 and pi/2.
After using an asymptotic formula to obtain an approximation
of the gaussian colatitudes, a Newton's method is employed to 
gain precision, then Gauss weights and other functions 
are calculated.
Notice that sin(lat.)=cos(colat.) where colat.=90-lat.