subroutine lr_tilt (tilt,hapog,h,tilth)
c
c	s/r to calculate the tilt to apply to a Dudeney profile along
c	a long, but one-hop circuit. The full tilt TILT is assumed to
c	apply at the height HAPOG, and to tail off to zero at the base
c	of the layer corresponding to HAPOG. TILTH is the reduced tilt
c	at the height H. In practice, HAPOG would be the apogee of the 
c	ray for the no-tilt case, and TILT would be a guess at the tilt
c	(ALONG THE CIRCUIT ONLY) required to make the rays land on a 
c	check target. This procedure ensures that only the reflecting
c	layer is tilted, and not the whole ionosphere
c
c	written by leo mcnamara 9-jul-97
c-----	last modified 9-jul-87
c
	common / iondat / fof2,fof1,foe,hff2,m3000,hme,yme,hmf2,
     a                    ymf2,h0,xd,dv
	common / parms / beta,ht,ft,a,hf,ad,tau,hd
	data pi2 / 1.570796327 /
c
c	for short ranges, we would set hapog = 0, and require the full tilt
	tilth = tilt
	if(hapog.le.1.0) return
c
c	base of layer in which apogee occurred for no tilt
	base = hd
	if(hapog.gt.hme) base = hme
	if(hapog.gt.ht)  base = ht
c
	tilth = 0.
c	no tilt below base of layer 
	if(h.le.base) return

c
	tilth =  (h - base)/(hapog - base) * tilt
ccc	type*,' base,h,tilt,tilth', base,h,tilt,tilth
ccc	type*,' hd,hme,ht ',hd,hme,ht
c
	return
	end