1. IN A SUBAQUEOUS DRILLING RIG COMPRISING A FLOATING SUPPORT ANCHORED ON A BODY OF WATER SUBJECT TO TIDAL FLUCTUATIONS AND ABOVE A POINT ON THE MARINE BOTTOM, A DRILL PRIME MOVER MOUNTED ON SAID SUPPORT, AND AN OPENING IN SAID SUPPORT IN PROXIMITY TO SAID PRIME MOVER ADAPTED TO ALLOW PASSAGE OF A DRILL STRING THROUGH SAID SUPPORT; THE IMPROVEMENT WHICH COMPRISES A WATER LEVEL COMPENSATING DRILL CASING ASSEMBLING SAID ASSEMBLY COMPRISING: (A) HOLLOW CONDUCTOR CASING MEANS MOUNTED IN SAID OPENING AND DEPENDING FROM SAID SUPPORT FOR A DISTANCE GREATER THAN THE TIDAL VARIATION IN WATER LEVEL AND LESS THAN THE LOW TIDE DEPTH OF THE BODY OF WATER; (B) A HOLLOW PILOT CASING HAVING AN UPPER END AND A LOWER END, SAID LOWER END BEING EMBEDDED VERTICALLY IN THE MARINE BOTTOM AND SAID UPPER END BEING IN TELESCOPIC ENGAGEMENT WITH SAID CONDUCTOR CASING; (C) FLEXIBLE SEALING GLAND MEANS MOUNTED ON SAID PILOT CASING ADJACENT THE UPPER END THEREOF, SAID GLAND MEANS FORMING A SLIDING SEAL BETWEEN SAID PILOT CASING AND SAID CONDUCTOR CASING; AND (D) MEANS FOR SUPPLYING DRILLING MUD TO SAID GLAND MEANS COMPRISING A MUD PIT, SAID MUD PIT BEING PROVIDED WIH AN OPENING ADAPTED TO PERMIT THE PASSAGE OF SAID DRILL STRING, SAID OPENING BEING SUPERIMPOSED ON THE OPENING IN SAID FLOATING SUPPORT AND MEANS CONNECTING SAID CONDUCTOR CASING TO SAID MUD PIT, THE INTERIOR OF SAID CONDUCTOR CASING BEING MAINTAINED IN FLUID COMMUNICATING RELATIONSHIP WITH THE INTERIOR OF SAID MUD PIT.