228 Cambridge Philosophical Society : — 



May 10. — Professor Miller made communications — (1) " On an 

 improved Method of finding the position of any face of a Crystal be- 

 longing to the Anorthic System." (2) " On the direction of the Axis 

 of a Zone." (3) On a substitute for the Reflective Goniometer." 



Mr. Godfray read a paper " On a Chart and Diagram for facilita- 

 ting Great-Circle Sailing." 



It has long been known that in many cases a verij great saving of 

 distance would be effected by guiding the ship along the arc of a 

 great circle instead of following the rhumb ; but the tedious calcula- 

 tions which great-circle sailing requires, and the difficulty of tracing 

 the track on the chart, have hitherto stood in the way of its adop- 

 tion. The great advantage which Mercator's sailing oiFers in these 

 respects sufficiently explains the preference given to it, even by those 

 who are fully aware of the longer route it obliges them to follow. 



The object of this communication was to show how the same ad- 

 vantages are secured to great-circle sailing by the adoption of a chart 

 on the central or gnomonic projection, which, with the addition of 

 a diagram, solves the problem of this sailing with the same facility 

 as Mercator's chart does for sailing on a rhumb. 



The great-circle track becomes a straight line joining the two 

 places ; and this being drawn, the various courses and the distances 

 to be run upon each are obtained, as also the distance from the ship 

 to her destination, by a mere inspection of the diagram and without 

 calculation. 



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 1130 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. — The Master of Trinity read the conclusion of his paper 

 " On Barrow, and his Academical Times." 



Nov. 8. — Professor Challis made a communication "On Donati's 

 Comet." 



Nov. 22. — The Public Orator gave a lecture on " The Battle of the 



