240 PHILOSOPHICAL TRANSACTIONS. [aNNO 166&, 



set myself to watch this difference of the time of the tides, and to find out some 

 rule how to proportion the time of the tides between the spring tides and the 

 neap tides, and I found by many trials, that the true time of the tides might be 

 found out to be somewhat shorter and shorter from the new and full moon unto 

 the quarters ; yet not in an equal manner, neither gradually decreasing from the 

 new and full moon until the quarters ; but rather that there was some little 

 difference of alteration, both at the new and full moon, and also at the quarters; 

 and that the greatest difference fell out in the midst between them, agreeing 

 very well to a circular proportion after this manner : (See fig. 5, pi. 7.) — First, 

 Divide a circle into 12 equal parts, or hours, according to the moon's motion 

 or distance from the sun, from the new moon to the full. — 2d. Let the dia- 

 meter of the circle be divided into 90 parts or minutes, that is, according to the 

 time of the difference of tides between the new or full moon, and the quarters ; 

 which is one hour and a half. — 3d. Make perpendicular lines cross the diameter 

 of the circle, from hour to hour. — 4th. Reckon the time of the moon's coming 

 to the south in the circumference of the circle, and observe the perpendicular 

 line that falls from that point on the diameter ; then the proportional minutes 

 cut thereby, will show how many hours or minutes are to be subtracted from 

 the time of high tides at the new and full moon, that you may have the true 

 time of the tides that present day. 



For example : At London, on the day of new and full moon, it is high 

 tide there at three o'clock, that is when the moon is three hours past the 

 meridian : so that by the common rule, the moon being about four days old, 

 it will be south about three o'clock, and it will be high tide three hours after- 

 wards, that is at six o'clock. But now by this rule, if you count this time of 

 the moon's coming to the south in the circumference, the perpendicular line 

 which eomes from three to nine cuts the diameter in the half, or at 45 m. which 

 shows that so much is to be abated from the time of high tide in the new and 

 full moons. So that it is high tide 45min. before six o'clock, that is, at five 

 hours 15min. and not at six o'clock, according to the common rule. 



The like you may do for any other port or place, knowing the time of high 

 water at the new and full moon in that place : And it will be done the more 

 readily, if you set down the time of high water at the new and full moon under 

 the diameter, as I have done for London, where it is high tide at three o'clock. 

 So that when the moon is south at three o'clock, the perpendicular cuts the 

 diameter at 2 hours 15 m. which added to the time of the southing, makes it 

 5 hours .15 m. and so when the moon is south at nine o'clock, by adding 2h. 

 15 m. you have the time of high water, which is llh. 15 m. 



And thus you may easily make a table, which by the southing of the mooii 

 shall readily show the time of high tide at any time of the moon. 



