•204 



The great-circle track is not always practicable, on account of its 

 taking the ship into too high a latitude, where the ice would render 

 it dangerous or impossible to penetrate. When this is the case, the 

 same chart and diagram will, with just as much facility as before, 

 point out that which, under the circumstances, is the shortest route. 

 Some parallel of latitude is fixed upon for the maximum, and the 

 track to be followed will then consist of a portion of that parallel 

 and of the portions of two great circles which are tangents to it, — 

 one passing through the ship, the other through the destination. 

 On this great-circle chart the track will be the two straight lines 

 drawn from the two places, so as to touch the circle of highest lati- 

 tude and the part of this circle between the points of contact. 



The paper explains the construction of the chart and diagram, 

 and illustrates their use by two examples : the first, from the south- 

 ern extremity of Africa to Perth in Australia, which shows a gain of 

 204 miles; the other, from 30° S. lat., 18° W. long, to Melbourne, 

 gives a gain of 1 1 30 miles, without going into a higher latitude than 

 55° south. 



A chart and diagram on this principle have been engraved by the 

 Hydrographic Office, Admiralty. 



May 24, 1S5S. 



The Master of Trinity read the conclusion of his paper " On Bar- 

 row, and his Academical Times." 



November S, 1858. 

 Professor Challis made a communication "On Donati's Comet." 



November 22. 1858. 



The Public Orator gave a lecture on " The Battle of the Trebbia," 

 the object of which was to compare the different authorities, and 

 to illustrate them by a description of the neighbourhood of Pia- 

 cenza, which he had recently visited. He showed that Polybius's 

 narrative was the most valuable, as being in all probability the ori- 

 ginal source of all subsequent accounts, and as deriving an especial 

 interest from the author's personal knowledge of the localities. Livy 

 in the main followed Polybius, amplifying and varying the details 

 rather with a view to an effective and ornamented style than to the 

 actual truth of his statements. Some particulars, however, appeared, 

 in this part of his work as elsewhere, to have been borrowed from 

 L. Cincius Alimentus, or some other historian of the Second Punic 



