CATALOGUE. — ASTRONOMY, TIDES. 



343 



Waltnesley on the effect of the tides upon 



the earth's rotation. Ph. tr. 175S. 8O9. 

 Lalande on the tides. A. P. 1772. i. !297. 



H. 1. 

 Lalande Trait6 du flux et reflux. Printed 



in the Astronomy. Note. Ph. M. VII[. 



134. 

 Lalande Astronomic. 

 Laplace on the tides. A. P. 1775.73. 1776. 



1790. 45. Mecan. celeste. 

 Laplace on some high tides. Nich. VL 239. 



Agreeing with the theory. 

 fSaint Pierre Etudes de la nature. 



Deduces the tides from the melting of the circumpolar 

 ice. 

 Suremain's remarks on St. Pierre. Roz. XLT. 



239- 

 Villelerque on St. Pierre's hypothesis. Journ. 



Phys.XLIV.(L)99. 

 Chiminelli's researches on the tides. A. Pad. 



IL 204. 

 Robison. Enc. Br. Art. Tides. 



Observes, that the smallest solar retardation of the tides is 

 »o the greatest, as the difference of the solar and lunar influ- 

 ence is to their sum : that is, from Dr. Maskelyne's obser- 

 vations at St. Helena, as 37 to 87 ; and the sun's effect is 

 therefore to that of the moon as 2 to 4.96. 



Woods on St. Pierre's hypothesis. Ph. M. 

 VIIL 134. 



A Simple Tlieory ofihe Tides. Y. 



It has been sufficiently demonstrated by different authors, 

 that the form which the sea would assume, in consequence of 

 the moon's attranion, if the earth were at rest,is thatof anob- 

 longellipticspheroid.ofwhichtheaxiswouldexceedtheequa- 

 torial diameter by :ibout 10 feet, the whole height of the tides 

 being 5 feet ; but when the effects of the earth's rotation are 

 considered, the investigation becomes much more difficult. 



The spheroid of equilibrium, revolving continually, causes 

 the position of the horizon of any place to vary periodically, 

 so as to perform, in the course of a lunar day, two complete 

 oscillations, resemLling those of aeycloidal pendulum; and 

 the surfac* of any detached portion of the sea, so inclosed 

 by perpendicular and parallel shores, as to be capable of 

 permanent oscillations, is drawn after this variable horizon, 

 in the same manner, as a pendulum suspended from a cen- 



tre, which is itself performing its own vibrations ; the midtjl* 

 of the sea, or lake, remaining nearly at rest. 



Now it may easily be shown, that a pendulum suspended 

 from a centre, which performs regular small vibrations of 

 its own, may vibrate in the same time with the centre,, 

 provided that the extent of its vibrations be to that of the 

 vibrations of the centre, as the length of the thread carrying 

 the centre is to the difference of the lengths of the two 

 threads ;. for, in this case, the situation of the thread of tha 

 pendulum will be always the same as that of a simple pen- 

 dulum of the length of the thread carrying the centre. 

 When this thread is the longer, the vibrations will agreo 

 in direction, but, when shorter, their directions must be 

 contrary to each other ; and, it appears to be in the latter 

 case only, that the pendulum will always tend to acquire 

 such a state of permanent vibration, wi.atever may have 

 been its original situation, although it may sometimes ap- 

 proach rapidly to it, even when the thread of the pendulum, 

 is the shorter. If the breadth of a lake, or sea, from east ta 

 west in miles, be I, and its depth d, the time required for 

 its complete oscillation, or the time, in which a wave might 



b 

 pass over twice its breadth, will be in hours, and the 



lengths of the synchronous pendulums being as the squares 

 of the times, the extent of the oscillations of the lake will 

 be to the extent of those of the temporary horizon, as the 

 square of half a lunar or solar day, to the difference be- 

 tween that time, and the time required for. the oscillation of . 

 the lake ; the motions either agreeing or differing in direc- 

 tion, accordingly as tiie oscillation of the lake would occupy, 

 more or less time than half a day. Supposing the luminaiy 

 vertical, the extent of the oscillation of the temporary sphe- 

 roid will be, for the lunar tide 5 s.c, c being half the breadth 

 of the lake in degrees ; and for the solar tide, 2 s.c ; whentc. 

 .the height of the tides at the eastern and western shores will 



3030000rf , 2830000;/ . , 



be 3 s.c -— ,and2s.c ; — —respectively, 



3030000ci— /'i 283000Ud — bb ■' 



These become infinite, when i=:i7-!0v'<'. and lfi82v'(/, 



and in these cases, the magnitude of the tides would be 



only limited by the resistances; this must hajipcn, ifrfzrl, 



when bzzi 1740, or 2 5° for the lunar tide ; if dzzg, when 



ir:5220, and if d^, or 100 fathoms, when i:=s8^, or 



betweerr %° and g°. If d were 1> and i 6000, the lunar 



tide would be about ,48 feet, and if b were 8216, or go' of 



the equator, it would be ,42, 



At the eastern and western shores of a sea or lake, 90" irt- 

 diameter, the ascent and descent of the water would be pre- 

 cisely the same as in every par< of an open ocean, of the 

 same depth ; and the tides of such an ocean may, th '.refore, 

 be calculated, by making 6^8216, and the height, A wijt 



