Include path being ignored in a gnu make file - makefile

Question

The makefile is included below. It's just a long list of object files and two targets. The problem seems to be that the $(INC) is being ignored for the first target. For example, the output starts with "g++ -c -o main.o main.cpp" instead of "g++ -I/usr/home/jrm/tmp/proteus_beta -c -o main.o main.cpp".
TIA
PROG = proteus
# list of object files
OBJS = main.o \
dataset.o \
genetic_codes.o \
likelihood_engine.o \
options.o \
parsimony.o \
parsimony_engine.o \
seq.o \
site_collection.o \
site_pattern.o \
tools.o \
optare/crs.o \
optare/point.o \
optare/newton_1d.o \
optare/golden_section.o \
models/model.o \
models/DNA/DNA_model.o \
models/DNA/DNA_ssm.o \
models/CODON/CODON_model.o \
models/CODON/CODON_modelA.o \
models/CODON/CODON_modelB.o \
models/CODON/CODON_modelC.o \
models/CODON/CODON_modelD.o \
models/CODON/CODON_M0.o \
models/CODON/CODON_M1.o \
models/CODON/CODON_M2.o \
models/CODON/CODON_M3.o \
models/CODON/CODON_M0gtr.o \
models/CODON/CODON_FEBC1.o \
models/CODON/CODON_FEBC1b.o \
models/CODON/FESC/CODON_FESC1.o \
models/CODON/CODON_nh/CODON_M0nh1.0 \
models/CODON/CODON_nh/CODON_M1nh1.0 \
models/CODON/CODON_nh/CODON_M1nh1.0 \
models/CODON/CODON_nh/CODON_M3nh1.0 \
models/CODON/CODON_nh/CODON_M0nh2.0 \
models/CODON/CODON_nh/CODON_MmodelAnh2.0 \
matrices/matrix.o \
matrices/DNA_matrix.o \
matrices/CODON_matrix.o \
matrices/AA_matrix.o \
matrices/int_matrix.o \
matrices/str_matrix.o \
matrices/eigen.o \
incidere/slice_sampler.o \
dendrology/forestry.o \
dendrology/node.o \
dendrology/DNA_node.o \
dendrology/tree.o \
alphabetia/alphabet.o \
alphabetia/DNA_alphabet.o \
alphabetia/CODON_alphabet.o \
alphabetia/AA_alphabet.o
CC = g++
INC=-I/home/jrm/tmp/proteus_beta
.C.o:
$(CC) $< -c $(INC)
$(PROG): $(OBJS)
$(CC) -o $# $(OBJS) -lm

Answer 1

According to your post, you have a file named main.cpp, not a file named main.C. But you provide an implicit rule for converting .C files to .o. Make will compile main.cpp using its built-in rule for .cpp to .o compilation. You have two options to do what you want:
(1) Change your implicit rule to .cpp.o (and consider using new-style rules, i.e. %.cpp: %.o)
(2) Declare a CXXFLAGS variable (which is automatically included in Make's C++ compilation implicit rule) such as the following:
CXXFLAGS = $(INC)
and then remove your .C.o implicit rule.
The second option will simplify your makefile, and it will work with C++ files, regardless of the extension.

Answer 2

Do your source files end with .C or .cpp?
The compilation rule for .C.o lists $(INC) after the other parts of the rule, not where you expect the output to come:
CC = g++
INC = -I/home/jrm/tmp/proteus_beta
.C.o:
$(CC) $< -c $(INC)
You should see:
g++ file.C -c -I/home/jrm/tmp/proteus_beta
But it appears to be ignoring your rule altogether. You mention main.cpp; that will never be compiled by your rule.
So, is .C a recognized suffix? Are your source files .C files? Are you running on a case-insensitive file-system? Why are you setting the C compiler (CC) -- you've probably got case problems with your source.