A LARGE FRACTION OF THE BLACK HOLE LOW-MASS X-RAY BINARIES (BH LMXBS) ARE TRANSIENT SYSTEMS. THEY OCCASIONALLY GO INTO OUTBURST DURING WHICH THEIR LUMINOSITIES CAN INCREASE BY FACTORS OF MORE THAN A MILLION. THE OCCURRENCE OF AN OUTBURST IS DIFFICULT TO PREDICT. NEW OUTBURSTS ARE GENERALLY FIRST NOTICED BY ALL-SKY MONITORS OR WIDE-FIELD CAMERAS. HOWEVER GIVEN THE LIMITED SENSITIVITY OF SUCH INSTRUMENTS A TRANSIENT'S FLUX IS TYPICALLY ALREADY A FACTOR OF 1E3-1E4 ABOVE ITS PRE-OUTBURST LEVEL WHEN IT IS FIRST DETECTED AND FOLLOW-UP OBSERVATIONS WITH MORE SENSITIVE INSTRUMENTS OFTEN DO NOT START UNTIL THE FLUX HAS RISEN BY AN ADDITIONAL FACTOR OF 5-10. AS A RESULT THE EARLY RISING PHASE OF BH LMXB OUTBURSTS IS RELATIVELY POORLY STUDIED.