THE ANIMAL AS A MOTOR. 



79 



25. Equations connecting the time, effort, and work 

 of animals have been proposed, all of which are only- 

 approximate, at best ; since the conditions of each 

 case are certain to differ more or less from the mean, 

 and are always difficult to evaluate. Rankine follows 

 Maschek, who gives the expression 



ie, + + ~ ^ ' 



in which R^, V^, T^, are respectively one third, each, 

 of the maximum load, maximum speed, and maximum 

 time in the day's work. Thus a maximum day's work 

 is obtained under the load R = R^, at the speed 

 V — V^, and T — T^, working eight hours per day. 

 Any departure from this adjustment is presumed to 

 give sensible loss of result. Bouguer proposes and 

 Gerstner endorses the following, R^ and being max- 

 imum loads and speeds : 



Gerstner, taking R^ and at their mean values, as 

 per table, would write the equations thus : 



For small variations from the times, loads, and speeds 

 of best effect, the total effect may be taken as varying 

 with those variations. 



In ascending inclines, the work may be taken as 

 approximately increasing with the inclination and at 

 a rate proportional to the ratio i -\- {a -r- 11.5°) ; since 



