70 Linncean Society. 



But by the properties of the ellipse, the reciprocal of r is equal to 

 a series of terms involving the excentricities, and involving also co- 

 sines of the mean anomaly and its multiples : and hence the variation 

 of this reciprocal is equal to a similar series, involving sines and co- 

 sines of such arcs, and involving also the variations of the elliptic 

 elements. By substituting the variations of the elliptic elements given 

 by the formulae above mentioned, when we put for R its expansion, 

 we have a certain series of sines and cosines with their coefficients 

 multiplied into certain other sines of the same kind. 



It is found tliat the sines and cosines thus multiplied produce, by 

 trigonometrical transformations, arcs identical with those which were 

 found in the value of the reciprocal of r obtained by the former 

 method ; and the coefficients are also found to be identical with those 

 resulting from the former transformations and reductions. 



We have not thought it necessary to verify the somewhat complex 

 reductions by which Mr. Lubbock has shown the identity of the results 

 obtained by these two methods. The mode of proceeding is per- 

 fectly satisfactory, and the truth of the conclusion might have been 

 foreseen. I'he reductions, however, by which identity was to be 

 exhibited were by no means obvious : and we conceive it not un- 

 likely that the development of them may sometimes be of use in 

 enabling us to judge which of the two methods of solution may be 

 applied with most convenience in particular cases. 



We are of opinion that this Paper is well worthy of being printed 

 in our Transactions. (Signed) W. Whewell. 



Geo. Peacock. 

 h. coddington. 



LINNiEAN SOCIETY. 



June 5. — A paper was read, entitled, " Additional Observations 

 on the Sexual Organs and Mode of Impregnation in Orchidece and 

 Asclepiadea:," by Robert Brown, Esq. V.P.L.S. 



These additional observations to a paper communicated to the 

 Society in November, and of which an abstract is given in the 

 Phil. Mag. and Annals for December last, relate entirely to Orchidece. 



The author begins by remarking, that as the tubes forming the 

 mucous cords were never observed in the cavity of the ovarium 

 until after the application of the pollen to the stigma, and as these 

 tubes very nearly resemble those immediately derived from the 

 pollen, he had in the paper referred to considered them as having 

 the same origin. 



But as he has since ascertained in several cases, especially in 

 Bonatea speciosa, that the application of a small portion of a pol- 

 len-mass to the stigma is sufficient for the production of mucous 

 cords of the usual size, and as the number of tubes thus produced 

 is much greater than that of the grains of pollen actually applied, 

 he is now led to believe, that these tubes do not immediately pro- 

 ceed from the pollen, though its application to the stigma is neces- 

 sary for their production. In what manner they arc generated, 

 however, he does not attempt to explain. He finds in Bonatea 



