CORRESP ONDENCE. 



491 



COREESPONDEITCE. 



"THE TIDES." 



To the Editor of the Popular Science Monthly. 



I MAKE the following comments on Prof. 

 Schneider's second article about " The 

 " Tides." All the objections to the state- 

 ments in the first article remain in full force. 

 The chief points of this second installment 

 are two : 1. The disturbing action of the 

 sun on the moon's motion ; 2. The fall of 

 the earth and the moon below their respec- 

 tive tangents, whereby it is sought to be 

 proved that the moon approaches the earth 

 at the time of opposition. If these two 

 statements are shown to be wholly in error, 

 the second article goes the way of the first. 

 On page 231, December number of this 

 Joprnal, we find this : " Thus our moon 

 moves faster, and, by a radius drawn to the 

 earth, describes an area greater for the 

 time, and has its orbit less curved, and there- 

 fore approaches nearer to the earth in the 

 syzygies than in the quadratures. . . . The 

 moon's distance from the earth in the syzy- 

 gies is to its distance in the quadratures, in 

 round numbers, as 69 to 70." 



This extract, which from its form would 

 seem to be from a single paragraph, is in 

 reality from two widely-separated parts of 

 Newton's works, and is besides inaccurate. 

 The phrase " in round numbers " is neither 

 in the original nor in Motte's translation, 

 but instead of it there is cceleris paribus, 

 and it is hardly necessary to say that the 

 phrases are not exactly equivalent. But let 

 these slips pass. I give two other extracts 

 from the " Principia," book hi., prop, xiv., 

 cor. i. : " The fixed stars are immovable, 

 seeing they keep the same positions to the 

 aphelions and the nodes of the planets." 

 Herein is a double error : 

 Again, book Hi., prop, xxxvii., cor. 3 : 

 " The density of the moon is to the density 

 of the earth. . . . as 11 to 9." 



This is very far from the truth, and 

 scores of other mistakes in the " Principia " 

 are known to those who are familiar with 

 that work. So "the b?st of authority" is 

 sometimes at fault, and his conclusions are 

 not always to be accepted blindly and with- 

 out investigation. But if they are to be so 

 accepted, as Mr. Schneider's way of parading 

 his authority seems to imply, would it not 

 be better to accept Newton's theory of the 

 tides, which is the true theory, and so make 

 an end of it. But that theory excludes 

 Prof. Schneider's. 



If Newton's statement concerning the 

 distance of the earth and moon in the syzy- 



gies and quadratures is to be taken without 

 qualification, then it is plainly wrong ; and 

 the mathematical proof that it is wrong can 

 be found more or less fully developed in any 

 of the following works on astronomy, viz., 

 those of Woodhouse, Herschel, Lardner, 

 Gummere, Loomis, Norton, Olmsted, Robin- 

 son, and others. 



Further, there is the practical proof of 

 the correctness of the other view in the cal- 

 culated and the observed positions of the 

 moon for every hour of every dety in every 

 year, these positions being carefully noted 

 by a score of observers every day. There 

 is no more possibility of universal error in 

 these observations and calculations than 

 there is that a person who says that two and 

 two are four should be in error on that 

 point. 



Prof. Schneider's first statement, then, is 

 all wrong; and, this failing, the second goes 

 with it. But it is also easily shown by his 

 own figures that his conclusion should be 

 exactly the opposite to what he makes it. 

 He says, " The distance the earth falls, in 

 one second of time, toward the sun is about 

 .12144+ of an inch," the moon toward the 

 sun .12084 of an inch, and the moon toward 

 the earth .05386 of an inch. The expres- 

 sion " falling toward the sun " evidently 

 means " falling from the tangent ;" any other 

 meaning is false and absurd. With the cor- 

 rectness of these numbers I have nothing to 

 do. Consider them correct ; then at the 

 end of a second the earth and moon will be 

 farther apart than they were at the begin- 

 ning. Here is the proof: 



In the accompanying figure let Mhe the 

 place of the moon at opposition, E, that of 

 the earth, and S the sun ; A, the place of 

 the moon at the end of a second ; B, that 

 of the earth at the same instant. Then, 

 since the moon at opposition moves in a 

 second about two-thirds of a mile farther 

 than the earth, the curve MA is longer than 

 E B, and A is farther to the right than B, 

 and the moon at A is below the point C by 

 .0538 of an inch : the quantity being ascer- 

 tained by supposing the earth to stand fast, 

 while the moon moves forward with the dif- 

 ference of their motions. On this there 

 can be no disagreement. The distance C A 

 is about two-thirds of a mile. But if A is 

 below the tangent .12084 of an inch, and B 

 .12144 of an inch below its tangent, then B 

 is farther from A then when the bodies were 

 at M and E respectively. When the earth 

 is at B it is at the same distance from the 

 sun as it was at E i. e., E S and 2? are 



