TRANSACTIONS OF THE SECTIONS. 13 



The publication of M. Plana's work constitutes a new era in the 

 question, from the circumstance that the results are therein deve- 

 loped by M. Plana according to powers of the eccentricities, inclina- 

 tions, &c., and also of the quantity m, which denotes the ratio of 

 the sun's mean motion to that of the moon. The methods employed 

 by M. Plana are otherwise similar to those of M. Damoiseau, but 

 M. Plana's results possess the inestimable advantage of permitting 

 each term of which a coefficient is composed to be verified sepa- 

 rately. The form in which M. Plana's results are presented also 

 enables us to examine them with facility and to judge of their con- 

 vergence. Unfortunately we soon find that the expressions for the 

 coefficients in many cases do not converge, so that it will be difficult, 

 if not impossible, to push the approximation so far as to arrive d, 

 priori at expressions upon which reliance can be placed for the prin- 

 cipal inequalities, such for example as the annual equation in longi- 

 tude*. 



In consequence of this difficulty I wish to call the attention of the 

 Section to the importance of deducing the numerical values of these 

 coefficients from the best observations empirically , and of thus con- 

 structing new Lunar Tables, which may serve to check the results 

 obtained by theory, and which may be inform unobjectionable. The 

 Tables of Burckardt, otherwise of great merit, and the best empiri- 

 cal Tables of the Moon at present in existence, were constructed 

 before theory had been brought to its present state ; and their form 

 is such that it would be difficult to render them available in the 

 manner I have pointed out. 



M. Plana has pushed the approximation to so great an extent that 

 if his figures could be depended upon the subject might perhaps be 

 considered as exhausted practically ; but notwithstanding M. Plana's 

 great skill and care, of which I am well convinced, it is unlikely that 

 calculations of such prodigious difficulty and complexity should be 

 free from errors. 



The construction of empirical Lunar Tables such as I have recom- 

 mended resolves itself into a question of expense ; for we have com- 

 puters in this country who are competent to undertake a work of 

 this nature under proper guidance. 



On the Action of Crystallized Surfaces upon Common and Polarized 

 Light. By Sir David Brewster, K.G.H., V.P.R.S.Ed. 



In the year 1819 I submitted to the Royal Society a series of ex- 

 periments on the action of crystallized surfaces on common and 

 polarized light. These experiments established in the clearest man- 



* According to M. Plana this coefficient contains the following terms : 

 ,735 , , 1261 , , 142817 



3257665 , 964470235 , . 



J _ Tifi -A ■ m' -+■ &c. 



^ 576 ^ 55296 ^ 



