Hoy al Society, 231 



mately a geometric series with a ratio — -. The author has also in- 



vestigated a series proceeding according to ascending powers of c— ar, 

 which converges more rapidly than the former when x approaches c. 

 By the use of these two series, /(a;) may be calculated by means of 

 series which are ultimately geometric series, with ratios ranging 

 from to ^. 



The unsymmetrical form of the trajectory, and the largeness of 

 the deflection produced by the moving body, come out from the in- 

 vestigation. I3y means of the numerical values of f{x) the author 

 has drawn a figure representing the trajectory for four different ve- 

 locities. The expression for the central deflection, however, becomes 

 infinite when x becomes equal to 2e, which shows that it is neces- 

 sary to take into account the inertia of the bridge ; although, if the 

 bridge be really light, the solution obtained when the inertia of the 

 bridge is neglected may be sufficiently exact for the greater part of 

 the body's course. 



ROYAL SOCIETY. 



[Continued from p. 154.] 



June 14, IS^Q. — The President announced, that in accordance 

 with the resolution of the Society, requesting him to communicate 

 the thanks of the Society to the Government of the United States 

 for the steps taken by them to ascertain the fate of the Expedition 

 under Sir John Franklin, he had addressed the following letter to 

 His Excellency the American minister: — 



My dear Sir, 3 Connaught Place, June 8, 1849. 



I have the honour to inform you that at the annual meeting of 

 the Royal Society, held the 7th inst., a communication was read 

 from Admiral Sir Francis Beaufort, in which he ajiprised the So- 

 ciety that the American Government had nobly undertaken to send 

 an expedition in search of Sir John Franklin. Upon which a vote 

 of thanks was moved by Sir Charles Lemon, seconded by Lord 

 Northampton, and carried with the utmost enthusiasm, expressive 

 of the gratitude of the Royal Society to the American Government, 

 and of their deep sense of the kind and brotherly feeling which had 

 prompted so liberal an act of humanity. Allow me to assure you, 

 that it is peculiarly gratifying to me to have the honour of being 

 the humble instrument in conveying to you the thanks of the Royal 

 Society on this occasion, and permit me to express a hope that this 

 most generous act of the United States may, if possible, draw closer 

 the bonds of friendship between the two kindred nations. 



That the United States may continue to progress with the same ex- 

 traordinary rapidity in the arts of peace and civilization, and to hold 



