402 THE PRINCIPLES OF SCIENCE. 



If we measure over and over again the same angular 

 magnitude by the same divided circle, maintained in 

 exactly the same position, 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 can hardly be in the same 

 direction, the average result will be nearly free from 

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

 than one divided circle. 



Even when we have no clear perception of the points of 

 our apparatus at which fixed error is likely to enter, we 

 may with advantage vary the construction of our appa- 

 ratus with the hope that we shall accidentally detect 

 some latent imperfection. Baily's purpose in repeating 

 the experiments of Michell and Cavendish 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 sur- 

 rounding air, &c., would yield different results. He per- 

 formed 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 mo- 

 tion of a pendulum, Baily employed no less than 80 

 pendulums of various forms and materials, in order to 

 ascertain exactly upon what conditions the resistance de- 

 pends. Regnault, in his exact researches upon the dilata- 

 tion of gases made arbitrary changes in the magnitude of 

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

 modification the results are unchanged, the errors are 

 probably of inconsiderable amount"; but in reality it is 

 u Jaiuin, ' Cours de Physique,' vol. ii. p. 60. 



