3rvn.l THE LAW OF ERROR. 397 



angular magnitude by the same divided circle, maintained 

 in exactly the same ])ositioa, it is evident that the same 

 mark in the circle will be the criterion in each case, and 

 any error in the position of that mark will equally affect 

 all our results. But if in each measurement we use a. 

 different part of the circle, a new mark will come into use, 

 and as the error of each mark cannot be in the same 

 direction, the average result will be nearly free from 

 errors of division. It will be better still to use more 

 than one divided circle. 



Even when we have no perception of the points at 

 which error is likely to enter, we may with advantage 

 vary the construction of our apparatus in the hope that we 

 shall accidentally detect some latent cause of error. Baily's 

 purpose in repeating the experiments of JNIichell and Caven- 

 dish on the density of the earth was not merely to follow 

 the same course and verify the previous numbers, but to 

 try whether variations in the size and substance of the 

 attracting balls, the mode of suspension, the temperature 

 of the surrounding air, &c., would yield different results. 

 He performed no less than 62 distinct series, comprising 

 2153 experiments, and he carefully classified and discussed 

 the results so as to disclose the utmost differences. Again, 

 in experimenting upon the resistance of the air to the 

 motion of a pendulum, Baily employed no less than 80 

 pendulums of various forms and materials, in order to 

 ascertain exactly upon wliat conditions the resistance 

 depends. Jiegnault, in his exact researches upon the 

 dilatation of gases, made arbitrary changes in the magni- 

 tude of parts of his apparatus. He thinks that if, in spite 

 of such modification, the results are unchanged, the eri'ors 

 are probably of inconsiderable amount ;i but in reality it 

 is always possible, and usually likely, that we overlook 

 sources of error which a future generation will detect. 

 Thus the pendulum experiments of liaily and Sabine were 

 directed to ascertain tlie nature and amount of a correction 

 for air resistance, which had been entirely misunderstood 

 in the ex})erinients by means of the seconds pendulum, 

 uj)on which was founded the definition of the standard 

 yard, in the Act of 5th George IV. c. 74. It has already 



' Jaiiiiu, Cours de Physique, vol. ii. [i. 60. 



