364 THE PRINCIPLES OF SCIENCE. [CHAP 



which will form an appropriate transition to the succeeding 

 chapters on the Method of Mean Eesults and the Law of 

 Error. 



5. Method of Reversal. 



The fifth method of eliminating error is most potent 

 and satisfactory when it can be applied, but it requires 

 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 suspen- 

 sion 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 re- 

 versing the weights, and it may be estimated by adding 

 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 arithmetic 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- 

 tion is differently conducted, but the principle is the same ; 

 the telescope is fixed to the circle, which moves with it, 

 and the angle through which it moves is read off at three, 

 six, or more points, disposed at equal intervals round the 

 circle. The older astronomers, down even to the time oi 



