-110 THE PRINCIPLES OF SCIENCE, 



5. Method of Reversal. 



The fifth method of eliminating error is most potent 

 and satisfactory whenever it can be applied, but it re- 

 quires that we shall be able to reverse the apparatus and 

 mode of procedure, so as to make the interfering cause 

 act alternately in opposite directions. If we can get two 

 experimental results, one of which is as much too great as 

 the other is too small, the error is equal to half the dif- 

 ference, and the true result is the mean of the two 

 apparent results. It is an unavoidable defect of the 

 chemical balance, for instance, that the points of sus- 

 pension of the pans cannot be fixed at exactly equal 

 distances from the centre of suspension of the beam. 

 Hence two weights which seem to balance each other 

 will never be quite equal in reality. The difference is 

 detected by reversing the weights, and it may be esti- 

 mated by adding sufficient small weights to the deficient 

 side to restore equilibrium, and then taking as the true 

 weight the geometric mean of the two apparent weights 

 of the same object. If the difference is small the arith- 

 metic mean, that is half the sum, may be substituted for 

 the geometric mean, from which it will not appreciably 

 differ. 



This method of reversal is most extensively employed 

 in practical astronomy. The apparent elevation of a 

 heavenly body is observed by a telescope moving upon 

 a divided circle, upon which the inclination of the 

 telescope is read off. Now this reading will be erroneous 

 if the circle and the telescope have not accurately the 

 same centre. But if we read off at the same time both 

 ends of the telescope, the one reading will be about as 

 much too small as the other is too great, and the mean 

 will be nearly free from error. In practice the observa- 



