reference voltage supply of —10 volts, becomes: 



-10 



R/IO 



O 



z 



In the operation of the integrating network, i.e. 

 only determines the value of N, (condenser charge) 

 at the beginning of the computation. It is cut off 

 the instant computation begins, and current flow is 

 then confined to the feedback loop. That is why 

 i.e. does not appear as a variable in the block dia- 

 gram. The figure "1" by the integrator input refers 

 to the input resistor. Operation of the integrator 

 is such that the input is multiplied by a factor 

 100/7?f when /?, = input resistance in kilohms. 



With the knowledge now at hand we can proceed 

 to set up a circuit in which Z is divided into its 

 components F and M. The equation becomes 

 .V, = /?fi~"^+"" and the diagrams are: 



BLOCK DIAGRAM 



CIRCUIT DIAGRAM 

 -10 



Study of the circuit u.sed here (fig. 2) reveals it to 

 be essentially an elaboration of the basic feedback 

 loop. A multiplier has been added to take care of 

 the nonlinear Gompertz growth curve, and other 

 elements have been added as described in the text. 

 The "time-base" {t) is generated bj^ a simple inte- 

 grator output. Biologists interested in further in- 

 formation on analog computer programming will 

 find an excellent brief introduction in Strong and 

 Hannauer (1902) or a more extended treatment in 

 Ashley (19(53). 



The plotter has a pen actuated by two servo- 

 motors. One moves it along the "X" axis and the 

 other along the "Y" axis in proportion to an input 

 voltage supplied by the computer. Thus the pen 

 moves to any point A', Y in a system of rectangular 

 coordinates on the plotting surface, corresponding to 

 input voltages T'^ and V^. Since the computer in- 

 tegrates with respect to time, a voltage directly 

 proportional to time is usually fed into "A'." The 

 input for "!'" can be taken from any point on tlie 

 computer circuit to plot the variable(s) desired 

 against time. 



As an alternative method of output display, an 

 oscilloscope can be used. This combination requires 

 that the computer be modified for "repetitive opera- 

 tion." Problem solutions are repeated 10 to 100 

 times per second, so that they appear as curves on 

 the oscilloscope screen. For a permanent record 

 the screen can be photographed as mentioned by 

 Doi (1902). 



This oscilloscope display is particularly valuable 

 for curve fitting, since points can be plotted on the 

 face of the tube. In this manner the effect of the 

 potentiometer adjustment in improving the fit is 

 instantly seen. 



The work described below was performed on a 

 Pace TR-10 analog computer in conjunction with 

 an EAI Variplotter 1 1 10. The TR-10 is one of the 

 smallest general-purpose analog machines. Since 

 both computer and plotter are fully transistorized, 

 they are small and can be used conveniently atop a 

 desk or small table. The set of units available in 

 the computer as I used it was as follows: 



Unit Number 



Amplifier (u.-^ed with integrator, multiplier, etc.) 10 



Coefficient potentiometer (ussed as above) 18 



Null potentiometer (used to set coefficient 



potentiometers) 1 



Integrator (used as above) 4 



Multiplier (used as above) 1 



Dioile function generator (use described later 



in text) 1 



Comparator (use described later in text) 1 



GENERATION OF SURVIVAL CURVES 



The differential eciuation needed for generating 

 the survival curve of a given weight of recruits, R^, 

 is obtained by differentiating expression (4): 



(5) 



3G 



U.S. FISH .\N"D WILDLIFE SERVICE 



