] 86 MoNES Berman and Robert L. Schoenfeld 



to the degrees of freedom of the system, as imphed by equations (9) and (12). 

 In this case, however, the statistical variations of the collected data cannot be 

 represented since their dimensions are omitted. Any new data to be collected, 

 however, can be represented in this subspace. The significance of any new data 

 can also be evaluated by the relative reduction in the size of the region in the 

 subspace. A unit of uncertainty may be defined for this subspace as was done for 

 the hyperspace. 



In references (1) and (2) it was shown how information about the system from 

 steady-state measurements and thermodynamic considerations can be combined 

 with tracer data to form a unified methodology in reducing the uncertainty 

 about the system. The treatment presented here can be extended to include such 

 additional information. 



Whereas the concepts presented here are relatively simple, the application to 

 specific problems involves considerable work. One can handle two or three 

 compartmental systems with few degrees of freedom fairly easily using a desk 

 calculator. The handling of more complex systems becomes quite time con- 

 suming. It is hoped that a programming of this on digital computers can be 

 worked out for routine applications. 



REFERENCES 



1. M. Berman: The formulation of biological models from tracer and steady-state data. 

 Ph.D. Thesis, Polytechnic Institute of Brooklyn (unpubUshed) (1957). 



2. M. Berman and R. Schoenfeld: Invariants in experimental data on linear kinetics and 

 the formulation of models. /. Appl. Phys., 27, 1361-1370 (1956). 



3. H. Margenau and G. M. Murphy: The Mathematics of Physics and Chemistry, chap. 10, 

 Van Nostrand, New York (1943). 



