This report describes the development and design details of an instrument that measures current in the range 10-6 to 10-13 a. and indicates or records this current on a single logarithmic scale. It is frequently desirable to measure a wide range of low current values without range switching. Since no instrument with such characteristics is commercially available, this study was made to determine whether or not the Beckman Model V Micromicroammeter could be modified to provide a logarithmic response. The feasibility of operating this instrument over six decades of input current has been demonstrated. As many as seven decades can be accommodated if a slight non-linearity in the lowest decade is tolerable. This non-linearity is insignificant in most applications. Fewer decades with increased readability and precision can also be obtained.