428 Prof. Powell's Remarks on Mr. Barton's Paper 



Difference. 



•001 inch. 



•003 



•002 



•001 



•010 



•011 



This calculation is not carried to any great accuracy ; but 

 it will suffice to show that even without affecting the value of 

 (b) (which is open to much uncertainty), the differences are 

 fairly within the limits of error. We might proceed to calcu- 

 late the errors in (b), or to estimate their joint effect ; but what 

 is here given, is, I believe, quite enough for our purpose. 



Mr. Barton enters on a calculation in some measure the 

 counterpart of this to find from the assumed length of an 

 undulation, and Newton's values of (c), what ought to be the 

 values of (b). This is done by taking the value of (X) deduced 

 as before from the 1st of Newton's experiments; but since 

 that value has been found to be different in each of the expe- 

 riments, it would have been more fair to take the mean value 

 from all the experiments : and still more to the purpose of the 

 inquiry, to take Fresnel's value of (X) (as I have before done), 

 and ascertain the amount of error which might account for the 

 discrepancy ; and even if this should turn out considerable, it 

 would be no more than accords with the admission that Fres- 

 nel's measures were more precise than those of Newton. 



The author then refers to certain experiments of M. Biot, 

 in which, with a given aperture, he measures the distance at 

 which the centre of the screen first becomes a dark point in 

 homogeneous red light. Upon Biot's data for (b) and (c), 

 Mr. Barton computes what must have been the values of (a) by 

 the same formula as before ; which in this case, upon transposi- 

 tion and squaring, will give, 



_ c l b 



a ~~ 7*03 A 6— c~' 



The circumstance that the denominator may become nega- 

 tive indicates of course that there are certain limits of distance, 

 consistent with the other conditions, within which the formula 

 cannot be applied to any real case. Mr. Barton finds in the 

 first three of Biot's experiments that the formula thus applied 

 gives rise to the absurd result of a negative value of (a), and 

 thence concludes that the values of (a) are incorrect. The 

 source of error may surely just as probably lie in the values 



