Prof. Ch. V. Zenger on a new Spectroscope. 4*39 



The reader will now perceive that the proof of the conjugate 

 property will be scarcely altered if, instead of the bar, we substi- 

 tute a membrane or plate, whose thickness or material need not 

 be uniform. Denoting the transverse displacement of any point 

 by iu, we have as the variational equation, 



8 V -|- \ \ pivBw da; di/ = 0; 



from which precisely, as before, we deduce 



( p' 2 —p 2 ) \ \ uv dx dy = 0. 



It is, I hope, now clear that great advantage results from the 

 direct employment of the variational equation. The reason of the 

 advantage appears to lie in the fact that every thing required to 

 be known is here embraced in one equation, while the ordinary* 

 differential equation needs to be supplemented by the boundary 

 conditions, which are indeed of the same mechanical importance 

 as itself. 



The same method may be applied to the general system. 

 Lagrange's equation of motion for a vibrating system may be 

 written 



i(fH + - +8V=0 ' 



where T is the kinetic energy. If the actual motion denoted by 

 yfr l &c. be a normal component vibration, each coordinate varies 

 as cospt, and the general equation may be writteu 



- I j 2 8T l -i-BV = } (13) 



where T x is the same function of yfr lt yjr 2 , &c. that T is of ^, &c 

 By the same reasoning as before we infer that if ^jr l &c. refer to 

 one normal component and 8yjr l &c. to another having a different 

 period, 



^ = 87 = (14) 



LVII. On a new Spectroscope. By Professor Ch. V. Zenger*. 



IN the spectroscopes usually employed the maximum of dis- 

 persion is attained by the combination of several prisms ; 

 but this entails a very great loss of light by absorption and reflec- 

 tion at the numerous surfaces of the prisms. It is obvious that 

 feeble intensity of light, or, even when the light is strong, feeble 

 physiological action of the red and violet rays of the spectrum 

 much interferes with exactness and distinctness of vision, espe- 

 cially in the spectral analysis of starlight. 



* Ordinary is here used in opposition to variational, not to partial. 

 t Communicated by the Author. 



