168 Mr, Herschel on the Action of [March, 



outlined the successive loci of the minima of illumination, and 

 laid down the poles, found the values of a 6 in the several lem- 

 niscates, as in the following table : 



The nature of the illumination not allowing the delineation to 

 be performed with the same freedom and precision as in a fuller 

 light, the values of a 6 in the second column are the means of a 

 great number of measures, taken in every part of their respective 

 curves. The numbers in the fifth column exhibit the excesses of 

 the terms of the arithmetical progression in the fourth (whose 

 common difference is 1*59, the mean of all the differences in the 

 third column) above the observed values of a b, and are so small 

 •as fully to authorize the conclusion, that these values, and of 

 course those of the parameter by increase in arithmetical pro- 

 gression with the order of the rings ; or, in other words, that the 

 number of periods performed in a given space (= 1) by a lumi- 

 nous molecule going to form any point M in the projection of any 

 ring is proportional to the rectangle of the distances P M, P'' M, 

 of that point from the two poles. 



Now, if we extend our views to crystals in which the distance 

 between the axes is considerable, we may reasonably expect that 

 the usual transition which takes place in analytical formulae from 

 the arc to its sine, when we pass from a plane to a spherical sur- 

 face, will hold good. If this be the case, we shall have at once, 

 and in all cases 



4, (d, 6") = sin. Q . sin. &" 



and the nature of the isochromatic curve for the wth complete 

 period will be expressed by the equation 



sin. 6 . sin. 6^ = ~ . cos. ^ = ji h . cos. f 



(e) 



putting h for — . If the plate be cut at right angles to the optic 



axis 



