﻿M. S. Merz on a small Universal Stellar Spectroscope. 129 



tides impinging upon it is, when the piston is in motion, 



times as great as it was when the piston was at rest. It will 



therefore create times as much momentum in m particles 



in the one case as in the other. The momentum of m particles 

 after reflection from the piston at rest was mv. It is therefore 



u-\-v 



— ^— .mv or m.u + v when reflected by the moving piston. But 



the number of particles which impinge upon the piston in the 



u ~\~ v 



time dt is in the second case times what it was in the first, 



v 



and therefore the average velocity which these must receive in 



order to acquire the same aggregate momentum will be 



m . (u + v) 



i ■— i. = 17. 



u-Vv 



m. 



v 



U -I- V 



It thus appears that the moving piston reflects times as 



many particles as the stationary one in the same time, but with- 

 out altering their velocity. But the pressure of the gas depends 

 upon the frequency of these reflections when their velocity is un- 

 altered) and the energy of the gas depends upon the alteration of 

 the velocity • so that when the motion of the piston is uniform, 

 as in the present case, the increment of the condensing energy 

 all goes into pressure, and none of it into motion. When the 

 motion of the piston is accelerated, the excess of energy which 

 causes the acceleration then increases the vis viva. 



XIX. On a small Universal Stellar Spectroscope. 

 By M. Sigmund Merz. 



[With a Plate.] 



To Dr. Francis, F.L.S. fyc. 

 Sir, Munich, November, 1870. 



IN Carl's Repertorium der Physik, vol. vi. p. 273, there is con- 

 tained the description of a small universal star-spectroscope 

 constructed by me, accompanied by an explanatory Plate. As, 

 however, since that article appeared this compendious little in- 

 strument has been improved in various essential particulars, at 

 the suggestion of a friend I make bold to forward to you a shor 

 description thereof, and also a corrected sketch of its arrangement 

 The instrument consists of two principal parts, or, in othei 

 Phil. Mag. S. 4. Vol. 41. No 271. Feb, 1871. K 



