AN INQUIRY INTO RECRUITMENT OF APPRENTICES TO SKILLED TRADES IN WESTERN AUSTRALIA INDICATED LITTLE CORRELATION BETWEEN THE NUMBER OF NEW APPRENTICES AND THE LEVEL OF INDUSTRIAL EMPLOYMENT OR THE TOTAL NUMBER OF APPRENTICES. THIS ARTICLE ATTEMPTS TO OUTLINE A MATHEMATICAL MODEL OF AN APPRENTICESHIP SYSTEM AND DISCUSS ITS IMPLICATIONS. THE MODEL, A FORMULA USING "TOTAL NUMBER OF APPRENTICES,""EMPLOYMENT,""APPROPRIATE APPRENTICE-EMPLOYMENT RATIO,""COEFFICIENT OF OPTIMISM,""LEVEL OF INTAKE,""QUALIFIED RECRUITS," AND "TIME" SHOWED A HIGH DEGREE OF AGREEMENT BETWEEN ACTUAL AND CALCULATED APPRENTICE INTAKE WHEN APPLIED TO THE MOTOR VEHICLE REPAIR AND CLOTHING MANUFACTURING INDUSTRIES FOR THE PERIOD 1948 TO 1958. IMPLICATIONS OF THE MODEL ARE--(1) COMPARATIVELY SMOOTH CHANGES IN INDUSTRY EMPLOYMENT CAN GIVE RISE TO LARGE APPRENTICE INTAKE CHANGES THUS CAUSING DIFFICULTIES IN THE FORMAL EDUCATION OF APPRENTICES, (2) CHRONIC SHORTAGES OF APPRENTICES WILL OCCUR IN OCCUPATIONS FOR WHICH SUPPLY LIMITATIONS PREVENT "NATURAL" INTAKE PEAKS FROM BEING ACHIEVED, AND (3) THE VIRTUAL IMPOSSIBILITY OF DISCHARGING AN APPRENTICE RESULTS IN A LOW "COEFFICIENCY OF OPTIMISM" WHICH MAY RESULT IN A LOWER INTAKE THAN OBJECTIVE CONSIDERATION WOULD JUSTIFY. THE IMPLICATIONS SUGGEST THE NEED FOR FLEXIBLE APPRENTICESHIP ARRANGEMENTS SUCH AS MAKING THE FIRST PART OF APPRENTICESHIP COMMON TO A NUMBER OF TRADES, OR INDENTURING APPRENTICES TO AN APPRENTICESHIP BOARD RATHER THAN TO INDIVIDUAL, THUS MAKING TRANSFER POSSIBLE. THIS ARTICLE IS A REPRINT FROM THE "BRITISH JOURNAL OF INDUSTRIAL RELATIONS," VOLUME 5, MARCH 1967. (EM)