25J8 M. Fraunhofer on the Laws 



Let r denote the angle which a coloured ray kfter the mo- 

 dification makes with the plane of the system of lines, (in ver- 

 tically received rays therefore, the complement of ^,) and y 

 denote the straight line drawn from the micrometer wire of 

 the telescope employed in the observation, perpendicularly on 

 the plane of the system of lines, * the aggregate of all my 

 observations may then, with all the accuracy to be attained in 

 experiments of this kind, be represented by the following equa- 

 tion : 



(III) tangr — =-^^^= ~7, / ■ — r-^^ = — -^ 



^ -^ ° ^7 (^ sin. 0"+ V6j) 



This equation I have developed without approximation after 

 the principles of interference which were published in the year 

 1802 by Dr Thomas Young, and which were afterwards 

 treated with merited attention for the first time by Arago 

 and Fresnel. w here generally denotes the length of a wave 

 of light. Although this is an infinitely small magnitude, we 

 may deduce it with a very high degree of accuracy, from the 

 experiment which I have already described in my treatise 

 " on the New Modifications of Light^"^ &c. the results of 

 which are there set down for the diff^erent coloured rays in 

 general terms. From the experiments with the glass sys- 

 tems of lines we ascertain this magnitude so accurately, that 

 for the lighter colours scarcely the thousandth part of w can 

 be uncertain. From the experiments with the finer systems 

 of lines on glass, by means of the angle for the first spectrum, 

 with the light received vertically, if (C w) denote the length 

 of a wave of light, for the ray C, and (D w) for the ray D, &c. 

 I obtained in parts of a Parisian inch, f 



• If, therefore, t is the distance of the micrometer wire, (and conse- 

 quently the distance of the place where the image of this phenomenon is 

 produced,) from the system of lines, then we liave > = a sin r. 



f The fixed line B, towards the end of the red, was, on account of the 

 great extension of the image, not so easily seen that its- place could be 

 determined witli certainty. I shall endeavour to make a still greater num- 

 ber of fine systems of lines upon glass, in order to determine, if possible, 

 still more accurately the value of « for the various coloured rays. It is, how- 

 ever, already accurately enough known to be certain whether the experi- 

 ments confirm the theory. If the value of (D «), (E •), &c. is deduced 

 from the experiments with coarser systems of lines upon glass, they are 



