317 



of the radii of the convex, whence the radii themselves are easily de- 

 duced. 



Mr. Barlow next inquires into the validity of the empirical rule 

 employed by Mr. Tulley, as stated in Rees's Cyclopaedia, which in 

 many usual cases he finds to give results nearly agreeing with his 

 own computations ; in others, however, it differs too widely to he 

 depended on. 



The author next enters on an experimental inquiry of the limits 

 within which an error in spherical aberration or dispersion may have 

 taken place without producing a sensible defect in the object-glass, 

 by procuring, with the assistance of Mr. Gilbert, glasses to be ground 

 to radii nearly, but not quite agreeing with the results of compu- 

 tation. It results from them, that in some states of the data and 

 assumed radii, much greater deviations may be borne than in others, 

 and the author considers that such combinations should be preferred 

 as admit the greatest latitude in this respect. 



The author concludes this paper by a synoptic statement of a mode 

 of approximate solution applicable (in consequence of the peculiarity 

 of the formula for the destruction of the spherical aberration) to all 

 ordinary states of the data, and comprised in a very short and easily 

 calculable form ; and by a method of practically determining the cur- 

 vatures and indices of refraction of any given convex or concave lens. 



On the Change in the Plumage of some Hen-Pheasants. By William 

 Yarrell, Esq. F.L.S. Communicated by William Morgan, Esq. 

 F.R.S., March 19, 1827. Read May 10, 1827. [PM. Trans. 

 1827, p. 268.] 



The last shooting season having been unusually productive of hen- 

 pheasants, which have assumed more or less the plumage and ap- 

 pearance of the male, much discussion in consequence has arisen on 

 the cause of this change ; and the author having had many opportu- 

 nities of examining the facts, both as respecting the pheasant and 

 domestic fowl, was induced to notice the internal peculiarities which 

 invariably accompany this transformation. According to an opinion 

 of Mr. J. Hunter and of Mr. Butter, this change only takes place 

 at an advanced age ; but the author considers the facts in his posses- 

 sion as at variance with this idea, and that the appearances in ques- 

 tion may occur at any period of life, and may even be produced arti- 

 ficially. 



In all the instances examined by him, the sexual organs were found 

 diseased, and to a greater or less extent in proportion to the change 

 of plumage. The ovarium was shrunk, purple, and hard ; the ovi- 

 duct diseased, and the canal obliterated at the upper part, imme- 

 diately preceding its funnel-shaped enlargement at the bottom of the 

 ovarium. Having opened a hen-pheasant in its natural plumage, for 

 the sake of comparison, he found a similar diseased state of the or- 

 gans to exist ; thus proving that the disease must exist some time 

 before the corresponding change of feathers takes place. 



