A CFI ADMITTED THAT HE ALLOWED HIS STUDENT TO GET THEM INTO IMC WHILE ON A VFR XCOUNTRY IN ZBW'S AIRSPACE.

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WHILE ON A VFR XCOUNTRY TRAINING FLT; STUDENT AND INSTRUCTOR ENCOUNTERED THIN OR PARTIAL CLOUDS AT VFR CRUISING ALT OF 4500 FT MSL APPROX 18 SM SE OF LEBANON; NH (LEB). STUDENT ELECTED TO FLY BELOW THE CLOUDS IN ORDER TO MAINTAIN PROPER VFR CLOUD CLRNC REQUIREMENTS. THE LEB ATIS WAS RPTING 10 SM VISIBILITY AND CLOUDS SCATTERED AT 12000 FT. THE STUDENT ELECTED TO CONTINUE THE FLT TO LEB AT 3500 FT MSL MAINTAINING CLOUD CLRNC AND PROPER GND CLRNC OVER THE MOUNTAINOUS TERRAIN. THE APCH AND LNDG AT LEB RWY 36 WERE UNREMARKABLE AND WITHOUT INCIDENT. STUDENT TAXIED FOR IMMEDIATE DEP ON RWY 7 FOR THE RETURN TRIP. UPON CLBOUT OF LEB; THE INSTRUCTOR GAVE THE STUDENT THE TASK OF DIVERTING TO CLAREMONT ARPT (CNH) 15 MI TO THE S OF LEB. STUDENT CONTINUED CLBING TO NE WHILE CALCULATING NEW HDG. STUDENT WAS PREOCCUPIED WITH TASK AND DID NOT NOTICE VISIBILITY DECREASING AT 3000 FT MSL. THE STUDENT CONTINUED TO CLB AND TURN ON COURSE THAT BROUGHT THE ACFT 3 MI E OF LEB AT 3500 FT. THE INSTRUCTOR NOTIFIED TWR OF POS; AND WAS CLRED TO CHANGE FREQ AT THAT TIME. THE STUDENT CONTINUED TO CLB AND VISIBILITY CONTINUED TO DECREASE. STUDENT THEN REALIZED THE GRAVITY OF THE SIT AND ATTEMPTED A DSNDING 180 DEG TURN. SINCE THE INSTRUCTOR HAD SOME LCL AREA KNOWLEDGE; AND SINCE THE SUN WAS VISIBLE THROUGH THE OBSCURATION; THE INSTRUCTOR ADVISED THE STUDENT TO CLB IN ORDER TO PREVENT FROM DSNDING INTO THE MOUNTAIN THAT WAS NOW TOTALLY OBSCURED. THE INSTRUCTOR TOOK CTL OF THE ACFT AND RADIO COMS. THE INSTRUCTOR REQUESTED A CLRNC TO CLB THROUGH THE CLOUDS AND PROCEED DIRECT WITH ZBW (134.75). DUE TO THE IMMEDIATE NEED TO CLB THROUGH THE CLOUDS AND PROCEED TO THE AREA OF KNOWN VFR 10 MI TO THE SE; THE ACFT CLBED THROUGH THE CLOUD TOPS AT 5000 FT MSL WHILE STILL RECEIVING A XPONDER CODE FROM ZBW. IN LESS THAN 10 MI FROM RECEIVING THE CODE; THE ACFT RETURNED TO AN AREA OF VMC WITH UNLIMITED FLT VISIBILITY AND UNRESTR CEILINGS. THE INSTRUCTOR BELIEVES THAT SINCE THE ENTIRE AREA WAS RPTING VFR CONDITIONS; THAT THE XPONDER CODE AND FOLLOWING COMS WERE NOT A CLRNC TO CLB IFR; BUT A VFR FLT FOLLOWING CODE. IN A MATTER OF 10 MINS; THE AREA OF SCATTERED THIN CLOUDS AT 4500 FT TURNED INTO OVCST WITH CLOUD BASES OF 3500 FT AND TOPS OF 4500 FT TO ALMOST 5000 FT MSL. THE STUDENT AND INSTRUCTOR BELIEVED THAT THERE WOULD NOT BE A PROB EXITING THE AREA SINCE THEY ONLY ENTERED MINS BEFORE; AND ALL WX DESCRIPTIONS (CURRENT AND FORECASTED) SHOWED VFR THROUGHOUT THE NEW ENGLAND AREA. THE INSTRUCTOR BELIEVES THAT MOST PRUDENT COURSE OF ACTION WAS THE ONE TAKEN -- TO CLB ABOVE THE LAYER INSTEAD OF 'SCUD RUNNING' AT LOW ALT THROUGH MOUNTAINOUS TERRAIN. ONE OF THE CONTRIBUTING FACTORS WAS THE FALSE BELIEF THAT FLYING BELOW THE CLOUDS IN MOUNTAINOUS TERRAIN WAS THE BETTER CHOICE. THE BETTER COURSE OF ACTION WOULD HAVE BEEN NOT TO ATTEMPT THE LNDG AT LEB BUT CONTINUE N OR E IN THE AREA OF UNRESTR VISIBILITY. THE STUDENT AND INSTRUCTOR DISCUSSED WX AND CRITICAL DECISION MAKING IN THE COCKPIT. ALSO DISCUSSED WAS THE MAX ELEVATION FIGURE FOR THAT AREA WAS 3600 FT; AND THAT DSNDING BELOW THAT ALT NEAR A KNOWN (AND OBSCURED) MOUNTAIN WOULD NOT HAVE BEEN A WISE CHOICE.