Prof. De Morgan on Continued Fractions. 15 



librio? These questions might be investigated with profit 

 were not this communication already too extended. 



44. It is proper to state, however, that DeCandolle's theory 

 of the bending of plants towards light has been fully disproved, 

 inasmuch as it is an effect due to the indigo rays, which have 

 not power to decompose carbonic acid and produce lignin, 

 &c. {Man. Soc. d'Arcueil, 1809, p. 104). 



In conclusion, it appears that the following facts have been 

 established : — 



1st. That chlorophyl is produced by the more luminous 

 rays, the maximum being in the yellow. 



2nd. This formation is due to pure light, an imponde- 

 rable distinct from all others. 



3rd. That the ray towards which plants bend occupies the 

 indigo space of Fraunhofer. 



4th. This movement is due to pure light, as distinguished 

 from heat and tithonicity. 



5th. That pure ligh* If capable of producing changes which 

 result in the development of palpable motion. 



6th. The bleaching of chlorophyl is most active in those 

 parts of the spectrum which possess little influence in its pro- 

 duction, and are complementary to the yellow rays. 



7th. This action is also due to pure light. 



We have, therefore, an analysis of the action of every ray 

 in the luminous spectrum upon vegetation. The several ef- 

 fects produced are not abruptly terminated within the limits 

 of any of the spaces, but overlap to a certain extent, a fact 

 which coincides with our experience of the properties of the 

 rays. Whilst heat and tithonicity are capable of causing the 

 union of mineral particles, /^///appears to be the only radiant 

 body which rules pre-eminent in the organic world. To the 

 animating beams of the sun we owe whatever products are ne- 

 cessary to our very existence. 

 New York, October 14, 1843. 



II. On the Reduction of a Continued Fraction to a Series. 

 By A. De Morgan, Professor of Mathematics in Univer- 

 sity College, London*. 



ri^HE mode of reducing a continued fraction to a series has 

 A not received much attention, but as every specimen of 

 law of development may contain useful hints, the following in- 

 vestigation will perhaps interest the mathematical reader. 



It is required to develope into a series of powers of x the 

 continued fraction 



* Communicated by the Author. 



