MEASUREMENTS 293 



This is the product of the distance d between any two con- 

 secutive ordinates by double the sum of the odd ordinates, plus 

 a quarter of the extreme ordinates, and minus a quarter of the 

 ordinates immediately adjacent to the extremes. 



The even ordinates need not, therefore, be considered. The 

 highest limit of error is : 



4 Cvi +yn-iyy*}> 



The application of Poncelet's method is easy and gives good 

 results. 



219. Ergometry and Ergography. Ergometry is the name given 

 to the procedure for the measurement of work done, and ergo- 

 graphy is that given to the graphical registration of work done. 

 In testing the output of ordinary machines Prony's brake or some 

 modification thereof, is generally employed ( 39) . In the case of 

 a man using a crank handle, a pulley could be fixed on the axis 

 of the crank handle to transmit the work to a Prcny brake, and 

 the same could be done with a bicycle. But the results wculd 

 be inexact. In fact, in an inanimate machine, we can balance 

 the motor momentum gradually, by tightening the brake, and 

 that momentum has a constant value. The muscles modify their 

 power according to the resistance to be overcome, so that this 

 power varies gradually in proportion to the tightening of the 

 brake, and takes the value which corresponds to the friction at 

 a given moment. An exact estimation of human work, by a 

 Prony brake, is therefore necessarily difficult. The brake is also 

 not very sensitive, and has been of little use in the study of mus- 

 cular dynamics. 



220. Ergographic apparatus is more numercus and more satis- 

 factory than ergometric apparatus. (*) General Morin was the 

 first to take up the subject, and on Poncelet's advice (about 

 1839 or 1940) he had a dynamographic machine constructed to 

 measure the work done during the traction of carriages. 



Marey applied his system of transmission by air as follows : 

 Suppose it is required to lift a load by means of a rope passing 

 over a pulley. In the portion of rope which is moved by the 

 muscles is interposed a dynamograph consisting of a piston P, 

 held in equilibrium between two coiled springs, of which one, 

 which is stiffer than the other, sustains the effort exerted at A. 

 The rod of the piston is attached to a membrane of indiarubber, 



( x ) See below and also Zuntz (Arch. f. PhysioL 1899 p. 375) ; Johanssohn 

 (Skand. Arch.f. PhysioL vol. xi. p. 273, 1901) ; Blix (ibid. vol. xv. p. 122, 

 1904). 



