1. A programmable integrator for measuring the use of a system comprising: an integrator including a coulometer having a bored tube; a pair of columns of electrolytically platable metal positioned in the bore of said tube, said columns being separated by a gap filled with an electrolyte; and a pair of electrodes at each end of said tube in contact with said metal columns; a source of light positioned to one side of said tube; a pair of light sensitive means positioned on the side of said tube opposite said light source, said light sensitive means being spaced from one another along the longitudinal axis of said tube; switch means for connecting said coulometer across a source of voltage, said switch being closed when said system is in operational use; logic input means for effectively reversing the connection of said coulometer with said voltage source at the start of each of a succession of integrating intervals, said integrating interval being completed when said gap moves from a position between said light source and one of said light sensitive means to a position between said light source and the other light sensitive means, said logic input means being alternately connected to a source of high and low potential during successive integrating intervals; means connected to said logic input means for indicating when said logic input means is connected to neither said high or low potential sources; output means for indicating when said integrating interval is completed, said integrating interval representing a predetermined period of operational use of said system; and means controlled by said logic input means for effectively connecting to said indicating means at the beginning of an integrating interval the light sensitive means at the opposite end of the coulometer tube from the electrolytic gap.

4. A programmable integrator for measuring the use of a system comprising: an integrator including a coulometer having a bored tube; a pair of columns of electrolytically platable metal positioned in the bore of said tube, said columns being separated by a gap filled with an electrolyte; and a pair of electrodes at each end of said tube in contact with said metal columns; first and second means, spaced from one another along the longitudinal axis of said tube, for detecting the presence of the electrolytic gap when it is adjacent a detecting means; means for connecting said coulometer across a source of electrical energy; means for effectively reversing the connection of said coulometer with said electrical energy source at the start of each of a succession of integrating intervals, said integrating interval being coMpleted when said gap moves from a position adjacent one of said first and second detecting means to a position adjacent the other of said detecting means; output means for indicating when said integrating interval is completed, said integrating interval representing a predetermined period of operational use of said system; and means distinct from said reversing means for preventing further movement of said electrolytic gap in said tube between the time said gap moves into a position adjacent one of said detecting means and the time the connection of said coulometer is reversed.

8. A programmable integrator for measuring the use of a system comprising: an integrator including a coulometer having a bored tube; a pair of columns of electrolytically platable metal positioned in the bore of said tube, said columns being separated by a gap filled with an electrolyte; and a pair of electrodes at each end of said tube in contact with said metal columns; first and second means, spaced from one another along the longitudinal axis of said tube, for detecting the presence of the electrolytic gap when it is adjacent a detecting means; means for connecting said coulometer across a source of electrical energy; logic input means for effectively reversing the connection of said coulometer with said electrical energy source at the start of each of a succession of integrating intervals, said integrating interval being completed when said gap moves from a position adjacent one of said first and second detecting means to a position adjacent the other of said detecting means, said logic input means being connected during successive integrating intervals to a source of a first potential and a second potential, respectively, said first and second potentials being different; output means for indicating when said integrating interval is completed, said integrating interval representing a predetermined period of operational use of said system; and means connected to said logic input means for indicating when said logic input means is connected to neither said first or second potential.

9. A programmable integrator for measuring the use of a system comprising: an integrator including a coulometer having a bored tube; a pair of columns of electrolytically platable metal positioned in the bore of said tube, said columns being separated by a gap filled with an electrolyte; and a pair of electrodes at each end of said tube in contact with said metal columns; first and second means, spaced from one another along the longitudinal axis of said tube, for detecting the presence of the electrolytic gap when it is adjacent a detecting means; means for connecting said coulometer across a source of electrical energy; logic input means for effectively reversing the connection of said coulometer with said electrical energy source at the start of each of a succession of integrating intervals, said integrating interval being Completed when said gap moves from a position adjacent one of said first and second detecting means to a position adjacent the other of said detecting means; means for indicating when a fault has occurred in said logic input means; and output means for indicating when said integrating interval is completed, said integrating interval representing a predetermined period of operational use of said system.