Dependency of a dependency in make?

[Peter Sherwood]

I have a problem in using GNU make, probably because I don't understand how
to use it.

I have a C source file which includes a header file, which in turn includes
another,like this:

source.c                   header1.h
...                        ...
#include "header1.h"       #include "header2.h"

The relevant parts of my makefile looks like this:

OBJECTS = source.o 
LIBRARIES = /usr/X11R6/lib/libX11.a ../fftw-2.1.3/fftw/.libs/libfftw.a -lm
Source: $(OBJECTS) $(LIBRARIES)
        gcc -static -o source $(OBJECTS) $(LIBRARIES)
CFLAGS=-g -Wall -gstabs # used by the implicit rule $(CC) -c $(CPPFLAGS)
$(CFLAGS)
        
# Dependencies of source files which create the named objects
source.o: source.h header1.h

# Dependencies of header files
header1.h: header2.h

By writing the makefile in this way, I expected that changes in header2.h
would cause source.c to get recompiled to source.o, since source.o depends
on header1.h and header1.h depends on header2.h. But this is not the case.
>From make's debug (-d) output, the dependencies of header1.h were not
considered.

How can I accomplish what I want, without putting header2.h in as an
explicit dependency wherever I have header1.h now?