406 M. H. Becquerel's Experimental Investigations 



4th. The greater or less accuracy in the measurement of 

 the temperature and pressure of the gases. 



5th. The accidental displacement of the luminous point. 



The influence of the last four causes of error is very slight 

 in comparison with the first. In determining the maximum 

 value of the latter, let us consider the maximum value to 

 which the errors in our measurements might attain. Let R 

 be the magnetic rotation for a given gas, submitted to the 

 action of an electric current of the intensity I, and A the 

 wave-length of the luminous rays to which the observations 

 are being directed, let p be the rotation which is to be mea- 

 sured, i and \ the wave-length of the light studied. It will 

 be shown afterwards that we can express 



E p I 760 ■ A 



By taking the logarithms of the two numbers and differ- 

 entiating, we have 



dR_dp 2dX di d& adt 



R ~~p \ T H 1 + at 



Each of the terms of the second member represents the 

 relative error due to the variation of each element, and may 

 be positive or negative. It is clear that the most unfavour- 

 able case for the measurements will be that where the terms 

 have the same sign and are additive. y 



Now it has been seen above (p. 395) that — cannot exceed 

 0-001. l 



The possible variation of \ may be deduced from experi- 

 ments made with carbon bisulphide (p. 398). It is easily 

 seen that the variations in brilliancy of the incandescent lime 

 through the same coloured screen do not give for the expres- 



2<7\ r/IT 



sion — r— greater values than 0*05 ; -^j- does not amount to 

 A- Jo. 



0*002 ; and an error of 1° must be made in the temperature of 



the gases in order that the expression — shall be 0'003. 



J. "T~ at 



There remains, then, the error -A With a shaded appa- 



r 



ratus the position of equality of tint is easily determined to 

 nearly V ' . As the rotations sought are deduced from the 

 difference between the two measurements, the maximum 

 error cannot exceed 2' . 



Let us admit this limited value dp = 2 r , and let us calculate 

 the relative error for two gases — air, which produces the 

 smallest rotations, and defiant gas, which produces the 



