PHYSICAL SCIENCE 



XXVll 



to east, at the same time that it is drawn down 

 towards the plane of the ecliptic, is to preserve 

 the inclination of these two planes unchanged, 

 but to make their intersection move in a direc- 

 tion opposite to that of the diurnal rotation, that 

 is, from east to west, or contrary to the order of 

 the signs; 10" appeared to be the part of the 

 effect due to the moon's attraction, and 40" to the 

 attraction of the sun. How Newton obtained 

 these numbers does not appear ; his data seem 

 scarcely sufficient for the purpose ; yet as his 

 results are correct, the probability is that he was 

 in possession of data which he has not stated to 

 Tiis readers. The subject was completed at the 

 interval of a century, by the exertions of 

 Lagrange and Laplace. 



Newton next turned his attention to the pheno- 

 mena of the tides, the dependence of which on 

 the sun and moon was sufficiently obvious to 

 common observation. That the moon has the 

 greatest effect in producing the tide, is evident 

 from this, that high water always occurs at a 

 place nearly at the time when the moon is in 

 the same meridian, and that the daily retardation 

 of the tide is synchronous with the retardation of 

 the moon in her diurnal revolution. It is equally 

 evident that the sun is concerned in the tides, as 

 the highest tides happen when the sun, moon, 

 and earth are all three in a straight line, and the 

 lowest tides when the lines drawn from the sun 

 and moon to the earth make right angles with 

 each other. 



Newton perceived that the waters revolving 

 round the earth are nearly in the condition of a 

 satellite revolving about its primary, and liable 

 to the same kind of disturbance from a third 

 body. High water always takes place in the 

 hemisphere where the moon is, and in the op- 

 posite hemisphere where the moon is not, nearly 

 at the same time. Now if the action of the moon 

 disturb the equilibrium of the ocean, just as the 

 action of one planet disturbs the motion of a 

 satellite moving round another, this is exactly 

 what might be expected. It had been proved 

 that the moon, when in conjunction with the sun, 

 had her gravitation to the earth diminished, and 

 when, in opposition to the sun, has it diminished 

 very nearly by the same quantity. For at the 

 new moon the moon is drawn to the sun more 

 than the earth is, and at the full moon the earth 

 is drawn to the sun more than the moon is, and 

 nearly by the same quantity ; the relative motion 

 of the two bodies is, therefore, affected the same 

 way in both cases, and the gravity of the moon 

 to the earth is in both cases lessened. 



The action of the moon on the waters of the 

 ocean must be regulated by the same principle. 

 In the hemisphere where the moon is, the waters 



are more drawn to the moon than the earth is ; 

 and its gravity being lessened, the column to- 

 wards the middle of the hemisphere lengthens in 

 consequence of the pressure of the waters, which 

 are at a distance from the middle point of which 

 the weight is less diminished, or at the horizon 

 even increased. In the opposite hemisphere the 

 earth is more drawn to the moon than the 

 waters, and their relative tendencies are changed 

 in the same direction, and nearly by the same 

 quantity. 



The attraction of the sun and moon conspire 

 to elevate the waters of the ocean, whether these 

 luminaries be in opposition or conjunction. In 

 both cases the solar and lunar tides are added 

 together, and the tide actually observed is the 

 sum of both. At the quadratures these two tides 

 are opposed to one another, the high water of 

 the lunar tide coinciding with the low water of 

 the solar tide, and vice versa ; so that the tide 

 actually observed is the difference between the 

 two. 



Newton had no data for measuring the lunar 

 force in producing the tides. But a measure for 

 the solar force, as it acts on the moon, had been 

 obtained. It had been shown to be T ^th of the 

 force which retains the moon in her orbit. This 

 last is TeVoth of the force of gravity at the earth's 

 surface; and, therefore, the force with which the 

 sun disturbs the moon's motion is 1^7 X TSSTJ f 

 gravity at the earth's surface. This is the solar 

 disturbing force on the moon, distant sixty semi- 

 diameters from the earth's centre ; but on a body 

 only one semi-diameter distant from that centre 

 (that is, on the water of the ocean) the disturb- 

 ing force will be sixty times less, or only 

 Ig4 | 80 - of gravity at the earth's surface. 



Now this being the mean force of the sun, is 

 that by which it acts on the waters ninety degrees 

 distant from the point where it is vertical, where 

 it is added to gravity, and tends to increase tho 

 weight and lower the level of the waters. At 

 the point where the sun is vertical the force to 

 raise the water is about double this ; and, there- 

 fore, the whole force tending to raise the level 

 of the high above that of the low water, is three 

 times the preceding, or about nfisZoo of gra- 

 vity. Newton had previously shown that the 

 centrifugal force, amounting to -^^ of gravity, 

 was able to raise the level of the ocean above 

 seventeen miles. This enabled him to conclude, 

 that the elevation of the waters, produced by 

 the solar force, will come out 1 '92 French feet. 

 From a comparison of the spring and neap tides, 

 that is, of the sum and difference of the lunar 

 and solar forces, it appears that the force of the 

 moon is to that of the pun as 4 '48 to 1. Hence 

 the moon will raise the waters 8-63 French feet, 

 n E 2 



