" On the Inflexion of Light" 427 



Newton has given us in his Optics, Book iii. the detail of 

 these measurements, and their exactness is amply sufficient 

 for the nature of his inquiry. Here is another point which 

 should always be borne in mind in criticizing experimental re- 

 searches. Newton does not apply these results for computing 

 the lengths of the "Jits ;" their accuracy might be quite suffi- 

 cient for the general establishment of the facts, though it should 

 not be so for such a very delicate computation as this. Yet 

 Mr. Barton takes Newton's measurements, in these experi- 

 ments, as data from which to calculate, by Fresnel's theorems, 

 the value of the length of an undulation. 



I think it must be admitted that such a mode of comparison 

 is hardly fair either to Newton or Fresnel. The data assumed 

 to reason upon are inches and parts of an inch by measure- 

 ment; the results turn upon differences in calculated mil- 

 lionths; the distance of the aperture or knife-edges from the 

 origin of light, and from the screen, and the width of the aper- 

 ture, are obviously determinations open to small errors ; and 

 no consideration seems to be made of the amount to which a 

 small uncertainty here might influence the almost infinitesimal 

 values which are to be deduced. Mr. Barton, however, cal- 

 culating by Fresnel's formula on these data, finds the resulting 

 lengths of an undulation to differ among themselves in the 

 different experiments, and the greatest of them he finds to be 

 less than Fresnel's value by about one fifth. 



Now it appears to me that a fairer mode of comparison would 

 be, to assume the length of an undulation according to Fresnel, 

 and see what degree of inaccuracy, in the confessedly looser 

 data, will suffice to give an accordance with that result. 



If we adopt (for convenience of calculation) A = -000025 

 inch, which is somewhat less than Fresnel's value for red rays, 

 the distance (a) from the origin to the slit being 101 inches, 

 the formula used by Mr. Barton on substituting the above 

 values and transposing will give us very nearly, 



1875 = c y 2 ° 2 + 2& " 



From which we may obtain the calculated values either of (b) 

 the distance from the slit to the screen, or of (c) the width of 

 the aperture, the other being assumed, in each of Newton's 

 experiments for the supposed value of (x) ; and we may com- 

 pare them with the measured values. It will suffice for our 

 purpose to do this with respect to the values of c ; thus we 

 shall have as follows : — 



3 I 2 



