32 Dr. Ruppell on the Fossil G^H^r^zPseudammonites 



proposed equation of the fifth degree has two equal roots, and 

 in which consequently the condition (62.) is satisfied, the 

 functiony(x) must be of the form (59.); which was the thing 

 to be proved. 



Corollary. — Setting aside the three excepted cases (60.) 

 (61.) (62.), the coefficients of die equation (50.) of the fifth 

 decree in y will be expressed as follows, 



B' = Q'^ B, b' = Q'l D, E' = Q's E ; . . . (86.) 

 and if we attempt to reduce it to De Moivre's solvible form, 

 by making 



D' = iB'% (50.) 



we find 



Q'^=0, (51.) 



that is, 



Q' =0, (52.) 



so that the relation between y and x reduces itself to the 

 form 



?y = (.r5+B.T3 + D.r+E).45(^), (87.) 



which can give no assistance towards resolving the proposed 

 equation (58.) of the fifth degree in x. 

 Observatory, Dublin, June 11, 1836. 



IX. Observations on the Fossil Geiiera Pseudammonites and 

 Ichthyosiagonites of the Solenhojen Limestone, contained in 

 a Letter to R. 1. Murchison, Esq., V. P.R.S., SfC. By D. E. 

 RiJppELL, M.D., of Frankfort.* 



Dear Sir, 

 T SEND you herewith the few words you requested me to 

 -*• draw up concerning the fossils I wish to exhibit at the 

 Geological Society. 



In a paper which I published in 1829, I ventured to ex- 

 press my opinion upon the generic character of two fossils, 

 fragments of which are commonly met with at Solenhofen, 

 and in other calcareous strata of formations of similar age. 

 Having met with some of these fossils in what I considered 

 to be a more than usually perfect condition, I was led to adopt 



* Communicated on the part of the Author by Mr. Murchison, who 

 takes this method of laying before the public the notice, which would have 

 been read before the Geological Society, at its last meeting of this ses- 

 sion, had not the letter of Dr. Ruppell been missent. The fossils alluded 

 to were exhibited. Mr. Murchison is convinced that this small fragment 

 will be read with interest as coming from the pen of the distinguished 

 traveller whose researches have thrown so much light on the physical geo- 

 graphy and natural history of Nubia and Abyssinia. 



