C  Reply-To:  AURIEMMA@ROMA1.INFN.IT                                            
C  Subject: Gran Sasso Rock overburden                                          
C     Dear Dr. Kashara,                                                         
C       thanck you for your fax of Jul. 25. I can answer your questions         
C      upon the rock overburden of the G.S. Laboratory, but please keep         
C      in mind that this are only preliminary data. We know from                
C    satellites accurately, the thickness of the rock in almost any             
C    direction, exception made for   65<phi<105 and 45<theta<75;                
C    108<phi<105 end theta>60; 133<phi<148 and theta>70, where we have          
C    no direct informations.  the following program gives the rock              
C    thickness:                                                                 
C           To convert phi into angle from the north (counterclockwise)         
C you can apply the transformation    PHIPRIME=MOD(360.-PHI+128.4,360)          
C and this should be the azimuth from the NP ( +x axis of the detector          
C point phiprime=128.4 deg).  The liomits above are given in azimuth            
C from the NP.  The above codes needs to read a file GSROCK.DAT, which          
C I'm sending as separate mail.                                                 
C                                                                               
C                                                                               
C                      C A U T I O N S                                          
C I do not think that assuming a uniform density gives you a good result        
C We are limited untill now by statistics, but the local variations             
C seems to be of order of 5-10% on a grid of 10x10 deg**2.  However the         
C best estimate of the density is 2.7+/-.05 gr/cm**3 Average Z=11.3 ;           
C average Z/A=.4991 ; average Z**2/A=5.65 which is close to the values          
C of world average limestone.  When I tryed to calculate energy loss            
C using as inputs the average values I found a difference of about 8-10%        
C from the correct values of dE/dx of the mixture.  With regular mail           
C I'm sending a Memo that I wrote recently, which I think might be              
C interesting to You.  We are still analisyng our multiple muons data. I        
C put your name in our mailing list for preprints, and I'll appreciate          
C you doing the same for me.                                                    
C                         Regards         Giulio Auriemma                       
C                                                                               
     FUNCTION GSROCK (PHI, TET)                                                 
C....    This function returns the depth (in m) of the Gran Sasso rock          
C       in the direction                                                        
C         tet = zenith angle (degrees)                                          
C         phi = azimuth angle (degrees)                                         
C         output in meters                                                      
C   the phi azimuth angle is in the detector system                             
C                                   ---------------                             
C   phi = 0 points approximately south east                                     
C                                                                               
C   important     0 .le. tet .le. 80.                                           
C                 0 .le. phi .le. 360.                                          
C                                                                               
C   there is no check in the program of the input ]                             
C................................................................               
        DIMENSION DEPTH(41,91)                                                  
C                                                                               
        OPEN(UNIT=10,FILE='GSROCK.DAT', STATUS='OLD',                           
C                           ~~~~~~~~~~                                          
        1         FORM='UNFORMATTED')                                           
        READ(10)DEPTH                                                           
C.....   phi = 0  in detector system  points approximately toward South East    
C   phi in the rock system (data  values) points  East                          
      fi = phi - 40.                                                            
      if (fi .lt. 0.)  fi = 360. + fi                                           
C....    bilinear interpolation in theta and phi                                
C   the structure of the grid is `hard wired' in the code                       
      jt = tet/2. + 1                                                           
      jf = fi/4. + 1                                                            
      d1 = depth (jt,   jf)                                                     
      d2 = depth (jt+1, jf)                                                     
      d3 = depth (jt,   jf+1)                                                   
      d4 = depth (jt+1, jf+1)                                                   
      t1 = 2.*(jt-1)                                                            
      f1 = 4.*(jf-1)                                                            
      r = (tet - t1)/2.                                                         
      u = (fi  - f1)/4.                                                         
      gsrock = (1.-r)*(1.-u)*d1 + r*(1.-u)*d2 + (1.-r)*u*d3 + r*u*d4            
      end                                                                       
