262 THE HUMAN MOTOR 



experimenter's body may affect results. It is often difficult, if 

 not impossible, accurately to evaluate the amount of such errors. 



Whatever precautions may be taken, a single measurement is 

 insufficient ; there must be at least two, from which the average 

 may be taken. 



194. In practice the concordance of several observations is not 

 absolute ; there \\i\\ always be differences between them. We 

 can take the arithmetical mean of n readings, fl lt a 2 , a z .,,, (in \ 



_ 



Each of those observed values will differ, more or less, from the 

 average a m . W T e shall have n differences, represented by 8. If 

 the differences are small, and the number n of the observations 

 comparatively large, the average a m will give approximately 

 the desired quantity. But for greater precision we apply the cal- 

 culus of probabilities^ 1 ) Let 5 be the sum of th- squares of all 

 the differences, a sum obviously positive, and e be the average 

 error, then 



It can be shown that the probable error is about f of e. Con- 

 sequently, the desired value will be : 



2 

 = &, .y e, 



tS 



a m being the arithmetical mean. We endeavour to make the 

 sum of the squares of the differences, 5, as small as possible. 

 Hence the name, the law of least squares, given to the method. 



It is a good plan to make calculations without waiting till the 

 end of a series of experiments, so as to make sure, before going 

 further, that there has been no error. Note should always be 

 made of the temperature, the atmospheric pressure at the "time, 

 the date and the place. If the experiment is on man, the sex' 

 name, occupation, age, stature, etc., should be noted. ' 



195. Methods of Graphical Registration. Errors are reduced 

 both by the accuracy of the instruments employed, and their 

 frequent calibration, and also by arranging that, where possible 

 they shall be self-recording. The demands on the attention of 

 the observer are thereby greatly reduced and the possibility of 

 visual errors in observation eliminated. The apparatus em- 

 ployed in producing the various graphical records described in 



, J l) ,?: Ca t 110 ' Le Calcul des Probabilities et ses Applications, 1912 p 118 

 ifmphcity }> ThlS W rk 1S distin e uish ed by its clearn^' and 



