VOL. XVI.] PHILOSOPHICAL TRANSACTIONS. 333 



illustrated his method of quadratures by several figures which have been already 

 considered by geometricians. As for the circle and hyperbola, he asserts that 

 their indefinite quadratures are impossible ; and therefore, in these and such 

 like cases, he expresses the area by an infinite series, which is easily done by 

 his method, except the series consist of irrational terms ; for in these he has 

 recourse to Leibnitz's method of finding tangents, where the calculation will 

 be more tedious. By resolving the area of the hyperbola into an infinite series, 

 he arrives at the same expression with that of N. Mercator: and in measuring 

 the zone of a circle, his expression coincides with that invented by Mr. Isaac 

 Newton, as Mr. David Gregory relates in his treatise. He has subjoined a 

 method of measuring the curve superficies made by the rotation of any curve 

 upon its axis ; with a small animadversion on the method of quadratrices, pub- 

 lished in the Acta Lipsiensia Eruditorum of October, l683. 



An Account of the Course of the Tides in the Port of Dublin, in Ireland. By 

 fViUiam Molyneux, Esq. R. S. S. With a remark upon it. N° 184, p. 192. 



-rtlj> . i. -.it) Ui. 



' At the bar of Dublin, on the new and ' fuir'moons, a S.S.E. moon makes 

 high water, that is, at half an hour after 10. At Ring's-End, at three quarters 

 after 10. — At the Custom-house at Dublin, at 11. 



On the quarter days, high water on the bar at 5 o'clock. — At Ring's-End, at 

 a quarter past 5. — At the Custom-house, half an hour past 5. A southerly 

 wind between S.S.E. and S.S.W. blowing fresh, makes it flow near half an 

 hour longer than its usual course. 



Note. This observation makes the tides, on the quarter moons, come in 

 later, in respect of the moon's southing, than on new and full moons, by hah 

 an hour : whereas in the River Thames, as high as London, the quarter moons 

 make high water above an hour and quarter sooner in that respect, than the 

 new and full ; as may be seen by the accurate tide-tables of Mr. Flamsteed : but 

 it is from hence evident that the same tables are not applicable to the sea-ports, 

 where there is not the same reason for the anticipation of the neap tides on the 

 quarter moons. The cause of this phenomenon seems to be, that the impulse 

 of the ocean in the quarter moons is not so vigorous as in the new and full ; 

 nor the motion of the waters so quick : hence it happens, that in the open sea, 

 and in ports on the sea-coast, as this of Dublin, the high water is later than 

 when the motion is more rapid in the new and full ; but on the contrary, in 

 "rivers, at any considerable distance from the sea, the resistance of the weight 

 of the fresh water, which is kept suspended during the time of the flood, is 

 longer overcome by the more potent impetus in the new and full, than by the 



