VOL. LXVII.] VHILOSOPHICAL TRANSACTIONS. 131 



ther appears, by the observations, that the greatest tide falls in December, about 

 the winter stolstice, the least in the month of August, and the mediums in 

 March and September. S. Toaldo adds a slight sketch of the course of the flux 

 of the tide through the Mediterranean Sea ; first entering by the Straits of 

 Gibraltar, it sweeps along by the south side, the coasts of Africa and Egypt ; 

 then turning by the east it sweeps along the north side, passing by Syria, Greece, 

 Italy, Liguria, France, and Spain, and thus issues into the Atlantic Ocean by 

 the Gibraltar side of the Straits. 



X. A Letter from Mr. Peter JVargentin, F. R. S., Sec. to the Acad, of Sciences 

 at Stockholm, to the Rev. N. Maskelyne, B. D., F. R. S., &c. concerning the 

 Difference of Longitude of the Royal Observatories at Paris and Greemuich, 

 resulting from the Eclipses of Jupiter s first Satellite, observed during the last 

 Ten Years. From the Latin, p. l62. 



The manner of deriving the difference of longitude, or difference of time, 

 between two places, by the observation of the eclipses of Jupiter's satellites, is 

 well known ; viz. the same eclipse, either immersion or emersion, being observed 

 at different places ; then, because the eclipse is seen the same moment at each 

 place, the difference of the observed times must give the difference of longitude 

 between the places, estimated at the rate of 15° to an hour of time. In this 

 way, by comparing together a great number of corresponding observations of 

 such eclipses, made at Stockholm, at Paris, and at Greenwich, Mr. Wargentin 

 deduced the differences between the meridians of these 3 places, differing among 

 themselves but by a few seconds only^ then, by taking a medium among all the 

 results of each sort, he concludes that he has obtained the true differences of 

 longitude between the 3 places very nearly. Hence it is ultimately concluded, 

 that the difference in time between Paris and Greenwich, is Q"" 25% and between 

 Stockholm and Greenwich l'' 12^" 2 P. 



XL A Method of finding the Falue oj an Infinite Series of Decreasing Quanti- 

 ties of a certain Form, when it converges too slowly to be summed in the Common 

 JVay by the mere Computation and Addition or Subtraction of some of its hiitial 

 Terms. By Francis Maseres, Esq, F. R. S., Cursitor Baron of the Exchequer. 

 p. 187. 



Let a, b, c, d, e,f, g, h, &c. ad infinitum, represent a decreasing progression 

 of numbers ; and let their differences, a ~ b, b — c, c — d, d — e, e —ff— <r^ 

 g — h, &c. also form a decreasing progression : and likewise, the differences of 

 these differences, which may be called the 2d differences of the original numbers 

 form a decreasing progression ; and the differences of those 2d differences, or 

 the 3d differences of the original numbers also form a decreasing progression ; 



s2 



