III. On the Possibility of accounting for the Absorption of Light, by supposing it due 

 to the Motion of the Particles of Matter. By the Rev. M. O'Brien, late Fellow 

 of Cuius College. 



[Read Feb. 14, 1843.] 



When we take into account the motion of the particles of matter (see Cambridge Transactions, 

 Vol. VII. p. 421*), we arrive at the following equation for determining the velocity of propagation 

 («^), viz. 



_ TO C m C 



~ v' - mB "'" v" - mB' 

 the disturbance being proportional to cos k (vt — u). 

 If we put kv = n, this equation becomes 



w'(w^-raB) (yi^-m^B) = C {m, («= - mB) + m{v'-mB)\v'' (1). 



which is a quadratic equation for determining v^ when n is given, i. e. when the colour is given, 



Stt . , . „ ., 



since — IS the time of vibration. 

 n 



This equation affords a complete explanation of the dispersion of light, and it may also be 



applied to account, apparently in a satisfactory manner, for the absorption, as follows. 



Suppose that the roots of the equation are impossible, then we shall obtain four values of v, 



which we may put in the form, -= ±6±J7\/— 1. 



V 



Now a = ae"\ "i/ "' is an integral of the equations of motion; hence we have four integrals 

 included in the formula 



Q _ gg»«-(±«±>)\/~i)«)\/^, or a e*"'''' . e""*'"'^"". 

 From these imaginary integrals we obtain the real integrals 



a = ae*""" . cos w (< ± eu). 



Now we must not suppose a continually increasing intensity of vibration ; and therefore the 

 upper sign of the exponential coefficient must be rejected, as is usually done in similar cases : we 

 have therefore 



a = ffle"'""" COS w (< ± 6m). 



This expression indicates a continually decreasing intensity of vibration different for different 

 colours (since >j is evidently a function of n), and thus the supposition that the roots of (l) are 

 impossible, leads to an explanation of the absorption of light. 



It is easy to follow out this explanation into detail, and to shew that it agrees with experiment 

 .so far as it goes ; but the object of the present paper is to prove, very briefly, that there is a serious 

 objection against the supposition that the equation (l) has impossible roots, and therefore against 

 the explanation of absorption depending on the motion of the particles of matter. To do this, we 



• Since the paper here referred to was printed, I have been 

 informed that ProfesBor Lloyd had previously read a paper on 

 the same subject, in which he gave an explanation of tlie Dis- 



persion and Absorption of Light; but 1 am not aware that 

 liis paper has been printed, for I have not been able to pro- 

 cure it. 



o2 



