308 PHILOSOPHICAL TRANSACTIONS. [aNNO 17 17. 



A Treatise on Infinite Series ; Part first. By Peter Remund de Monmort,* 

 F. R. S. To which is added an Appendix, in which several parts are treated 

 in a different Way. By Dr. Brook Taylor, Sec. R. S. N° 353, p. 633. 



This is the first part of a treatise on the Summation of Infinite Series, the 

 remainder of which it does not appear was ever pubHshed. Indeed it seems to 

 be fitter for a separate book, than for a paper in the Philos. Trans. And most 

 of its contents occur in other works ; as those of Ja. Bernoulli, Dr. Taylor, 

 Demoivre, Sterling, &c. 



'^On the Advantages that may accrue from the Observation of the Moon* s frequent 

 Appulses to the Hyades. Or, on the usefulness of observing the Occultations of 

 the Fixed Stars by the Moon for finding the Longitude. N° 354, p. 692. 



Of all the methods hitherto proposed for finding the longitudes of places, 

 for geographical uses, none seems more adapted to the purpose, than that by 

 the occultations of the fixed stars by the moon, observed in distant parts : for 

 those immersions of the stars which happen on the dark semicircle of the moon, 

 and their emersions from the same, are perfectly momentaneous, without that 

 ambiguity to which the observations of the eclipses of the moon, and those of 

 Jupiter's satellites, are subject. Besides, while the moon is horned, and her 

 weaker light less dazzling, an ordinary short telescope, such as by experience is 

 found to be manageable on ship board, suffices to observe those moments, even 

 in the occultations of very minute stars : on which account, this way seems to 

 bid fairest for the desired solution of the grand problem of finding the longi- 

 tude at sea. But since it would be needless to inquire exactly what longitude a 

 ship is in, when that of the port to which she is bound is still unknown, it 

 were to be wished that the princes of the earth would cause such observations 

 to be made, in the ports and on the principle head-lands of their dominions, 

 each for his own, as might once for all settle truly the limits of the land and 

 sea. This work however being likely to be left to the care and curiosity of pri- 

 vate persons, it may not be amiss here to give notice of the present opportunity 

 of performing it, in this our northern hemisphere, by help of the frequent ap- 

 pulses of the moon to the more southerly of the hyades, many of which she 

 eclipses in each monthly revolution, and will continue so to do, during the 

 years 17 18, 17 IQ, and 1720. 



♦ A French mathematician, and author of a treatise on Chances, entitled Essay d' Analyse sur lea 

 Jeux de Hazard, in 4to, 1708. 



+ This paper is probably by Dr. Halley. 



