on Magnetic Rotatory Polarization in Gases, 407 



largest : 



For air. . . p= 6' : 4^=0'3, ^=0'35 ; 

 r p It ; 



For olefiant gas p = ±0 / 'Q ^ = 0'05, ^=0'10J 



Strictly speaking, then, in a single determination it would 

 be possible to commit an error which would vary between 

 the third and the tenth of the rotation, according to magnitude 

 of the rotation. 



These numbers are far from giving the precision which 

 may be attained by increasing the observations. For ex- 

 ample, we made on the two gases that we have just cited about 

 a hundred and fifty measurements, which mutually tested each 

 other, and enabled us to see which observations were too in- 

 exact and ought to be rejected. 



Not being able to determine separately the value of the 

 most important causes of error, we attempted to make the 

 precision of each series evident by means of the greater or 

 less agreement in the measurements. Suppose that the 

 average of the numbers for a series of observations is the true 

 value of the rotation sought ; the individual measurements 

 can then be compared with this average, and the positive or 

 negative deviations calculated in each case. Giving the same 

 sign to all of them, and taking the average, a number will 

 result that we will call the " average deviation," and which 

 will give an idea of the precision of each of the measurements 

 in a series. In this calculation all the observations were 

 taken into account, even those which presented exceptionally 

 large deviations due to accidental causes. In the following 

 Tables we have put in opposite columns the numbers 

 adopted, and the value of the average deviation calculated in 

 this way for each series ; but it must be observed that this 

 deviation is not the error which is probably to be feared. 

 As might be anticipated, it is much smaller, as, indeed, the 

 agreement of the results deduced from different series de- 

 monstrates. The average deviations are only superior limits of 

 the errors. 



If the only cause of error were that which relates to the 

 optical measurements, the different series ought to give the 

 rotations sought with a precision proportionately greater as 

 the image reflected is of a higher order ; for the same error 

 would enter into a multiple of unknown quantity, and the 

 application of the method of least squares would be clearly 

 indicated ; but certain perturbations, such as a variation in 

 the wave-length of the light studied, enter into the value of 



