236 A Short History of Astronomy [Cn. ix. 



that on the solid earth, and that on the water farthest from 

 the moon is less. Consequently the water moves on the 

 surface of the earth, the general character of the motion 

 being the same as if the portion of the ocean on the side 

 towards the moon were attracted and that on the opposite 

 side repelled. Owing to the rotation of the earth and 

 the moon's motion, the moon returns to nearly the 

 same position with respect to any place on the earth in 

 a period which exceeds a day by (on the average) about 50 

 minutes, and consequently Newton's argument shewed 

 that low tides (or high tides) due to. the moon would follow 

 one another at any given place at intervals equal to about 

 half this period ; or, in other words, that two tides would 

 in general occur daily, but that on each day any particular 

 phase of the tides would occur on the average about 50 

 minutes later than on the preceding day, a result agreeing 

 with observation. Similar but smaller tides were shewn 

 by the same argument to arise from the action of the 

 sun, and the actual tide to be due to the combination of 

 the two. It was shewn that at new and full moon the 

 lunar and solar tides would be added together, whereas 

 at the half moon they would tend to counteract one another, 

 so that the observed fact of greater tides every fortnight 

 received an explanation. A number of other peculiarities 

 of the tides were also shewn to result from the same 

 principles. 



Newton ingeniously used observations of the height of 

 the tide when the sun and moon acted together and 

 when they acted in opposite ways to compare the tide- 

 raising powers of the sun and moon, and hence to estimate 

 the mass of the moon in terms of that of the sun, and 

 consequently in terms of that of the earth ( 185). The 

 resulting mass of the moon was about twice what it ought 

 to be according to modern knowledge, but as before 

 Newton's time no one knew of any method of measuring 

 the moon's mass even in the roughest way, and this result 

 had to be disentangled from the innumerable complications 

 connected with both the theory and with observation of 

 the tides, it cannot but be regarded as a remarkable achieve- 

 ment. Newton's theory of the tides was based on certain 

 hypotheses which had to be made in order to render the 



