175 



Therefore the position and magnitude of the image of any object is 

 found by a simple proportion. 



In one important class of instruments there are no principal foci 

 or focal centres. A telescope in which parallel rays emerge parallel 

 is an instance. In such instruments, if m be the angular magnifying 



power, the linear dimensions of the image are — of the object, and 



TO 



the distance of the image of the object from the image of the object- 

 glass is — of the distance of the object from the object-glass. Rules 



were then laid down for the composition of instruments, and sug- 

 gestions for the adaptation of this method to second approximations, 

 and the method itself was considered with reference to the labours 

 of Cotes, Smith, Euler, Lagrange, and Gauss on the same subject. 



November 6, 1856. 



A paper was read by Dr. Donaldson " On the Structure of the 

 Athenian Trireme, considered with reference to certain difficulties 

 of Interpretation." 



The author's intention was to show in this paper that the arrange- 

 ments for seating the three tiers of rowers in the trireme, which Dr. 

 Arnold has called " an indiscoverable problem," may be adequately 

 explained by an examination of the terms which are used to discri- 

 minate the rowers, and of other words referring to the different parts 

 of the war-galley. The name of the zygitce, or rowers of the middle 

 tier, implies that they sat on the (vya, or transverse planks connect- 

 ing the opposite sides of the vessel, also called aeXfxara, and in 

 earlier times nXrjTSes. The thalamitce, or rowers of the lowest tier, 

 must, in accordance with their name, have had their seats attached 

 to the ribs of the vessel in the OdXa/xos, or hold. And the thranitas, 

 or rowers of the highest tier, sat on dprjvves, or benches like low 

 stools, extending for seven feet along the alternate t,vya. The epi- 

 batce, or marines, whether as working the supernumerary oars, or 

 as fighting, occupied platforms running along the bulwarks. This 

 view of the matter explained the fact that there was a gangway 

 from the stern to the prow for the passage of the officers, &c. along 

 the aek/xara or £vyd, between the ends of the stools on which the 

 thranitse sat. This gangway was called the oekis, and the same 

 name was given to the passages leading down to the orchestra from 

 the upper part of the theatre between the rows of seats occupied by 

 the spectators. Hence was derived a philological explanation of the 

 words in Aristoph. Equites, 546 : — 



aipeatf airw ttoXv to podiov, Trapcnrifxipar e^' eVciem Ka>7rcus 

 66pvj3ov ypTf)aTov Xrjva'iTr/v' 



for there were eleven tiers of seats between each diazoma of the 

 theatre, which were divided again by the sells ; so that the spectators 



