ASTRONOMICAL PHENOMENA AND PROGRESS. 



49 



ing modified by local circumstances ; and consequent- 

 ly the tides have not been hitherto considered an 

 available means for determining the mass of the moon. 



In addition to the constant, to be determined by 

 observation, introduced into the conditions by La- 

 place for determining the moon's mass, Mr. Ferrel 

 has introduced another, depending upon friction. 

 Hence, there being three unknown quantities to be 

 determined, including the moon's mass, he uses the 

 condition depending upon the moon'sparallax in ad- 

 dition to the two used by Laplace. Without the in- 

 troduction of this additional constant and the addi- 

 tional condition for eliminating it, Laplace's condi- 

 tions for the determination of the moon's mass 

 entirely fail when applied to the Boston tides. 



Laplace selected Brest, where the tide has a direct 

 and short approach from deep water, and, neglecting 

 the effect ot friction referred to, obtained, as is well 

 known, the value of *&<>, in terms of the earth's 

 mass, for the mass of the moon. At Brest the ratio 

 of the half-monthly inequality to the coefficient or 

 half range of the constant tide is about .358, that of 

 the constant tide being about 2.25 metres, and that 

 of the mean spring-tides about 3.05 metres. At Bos- 

 ton the same ratio is only about .14, the coefficient 

 of the constant tide being 4.91 feet, and that of the 

 mean spring-tides 5.58. From data so widely differ- 

 ent Mr. Ferrel has deduced, by means of the intro- 

 duction of the term depending upon friction, two 

 values exhibiting a remarkable agreement, viz., from 

 the Brest tides TTTT, and from those at Boston rsW. 



Lunar Action and the Earths Shrinkage. 

 In a communication to the National Acad- 

 emy of Science, Prof. Benjamin Peirce briefly 

 considers the relations between lunar action 

 and the supposed shrinkage of the earth from its 

 original bulk. The most obvious cause of this 

 shrinkage is the cooling of the earth ; but to 

 shrink two per cent, linearly, which is the 

 amount deduced by Mr. Lesley from the ob- 

 served geological phenomena, involves a prob- 

 able cooling of the whole earth of not less 

 than 2,000 Cent., which would require that 

 its original temperature should be higher than 

 would be consistent with the solidity of the 

 shrunken strata. Another source of shrink- 

 age in different directions in different parts of 

 the earth is to be found in the diminution of 

 oblateness arising from the diminished velocity 

 of rotation upon the axis. This, as Mr. Ferrel 

 has shown, would be caused by the action of 

 the moon in producing the tides, and Prof. 

 Peirce inquires how great this amount can be 

 under any circumstances. He says: 



It is sufficient for the present object to regard the 

 earth as homogeneous. Under this condition, La- 

 place has shown that the time of the earth's rotation 

 could not be less than about rV of a day, which cor- 

 responds to a ratio of the axis of the equator to that 

 of the pole, equal to 2.7197, and an equatorial circum- 

 ference 94 per cent, greater than the present one. 

 Such is, then, the amount of shrinking which might 

 have taken place, if any cause could be assigned 

 capable of producing so great a reduction of the 

 earth's velocity. The whole surface of the earth 

 would have been about 130 per cent, larger than at 

 present. 



But the only cause at present known which would 

 produce a sensible reduction of the earth's velocity 

 is the lunar action upon the tides. But, in this mu- 

 tual action between the moon and the earth, the com- 

 mon rotation area of the earth and moon must remain 

 unchanged. The question then arises, How great a 

 reduction of the rotation area of the earth would 

 have passed into that of the moon? In this inquiry 

 VOL. xi. 4 A 



it may be assumed that the moon revolves in a circu- 

 lar orbit in the plane of the earth's equator. 



Now, the moon's rotation area is 3.716 times the 

 earth's. But, if, in the origin, it had revolved just 

 in contact with this earth, its rotation area would not 

 have been less than 0.480 times the earth's, so that 

 it could not have absorbed a rotation area from 

 the earth greater than 3.236 times the earth's pres- 

 ent rotation area, and therefore the earth's rota- 

 tion area could never have exceeded 4.236 times 

 that which it has at present. But, with the maxi- 

 mum velocity of rotation given by Laplace, the 

 earth's rotation area would have been 37i times 

 greater than at present. It can never, therefore, 

 have been reduced to so -great an extent by the 

 moon's action on the tides. But, since, when the 

 oblateness is small, the rotation area is nearly pro- 

 portional to the velocity, and the excess of the square 

 of the equatorial above that of the polar axis is 

 nearly proportional to the square of the velocity, this 

 excess may have been originally nearly 18 times as 

 great as at present, or about 15i per cent, of the 

 square of the polar axis. This would correspond to 

 a figure of the earth in which the equatorial radius 

 would have been about 2i per cent, greater than at 

 present ; so that it is sufficient to account for the ob- 

 served phenomenon. 



This peculiar form of shrinkage would produce 

 the highest mountains at the equator, and the ten- 

 dency of the mountain-ranges would then be to 

 assume the direction of the meridian. But nearer 

 the poles the mountains would be less elevated, and 

 would rather tend toward the direction of the paral- 

 lels of latitude. 



It is, next, expedient to consider the mechanical 

 question of the loss of living force in the case of the 

 moon's action upon the waters of the earth, and its 

 effect upon their different motions. In this connec- 

 tion, there are problems worthy of the attention ^of 

 geometers ; such as the relative motions of bodies 

 rotating above the same vertical axis ? toward which 

 they are drawn by weights, and acting upon each 

 other through the friction on the axis. For one of 

 the bodies a rotating wheel may be substituted. 

 There is also the case of two planets revolving about 

 a primary, and acting upon each other through some 

 form of friction. 



In this way it will be seen that the planet or satel- 

 lite once formed is constantly removed from the pri- 

 mary, and that planets tend to approach each other. 

 It is interesting to consider whether this may not be^ 

 one of the actual problems of Nature. 



Proposed Observations of Venus. The Ob- 

 serving Astronomical Society of Great Britain 

 have decided to undertake a series of system- 

 atic observations of the planet Venus during 

 one complete revolution. They have in view 

 the obtaining of results that shall lead to> 

 becoming better acquainted with the markings 1 

 visible on the Yenusian surface and a correct 

 knowledge of their form and permanency.. 

 They remark that, in most modern astronomi- 

 cal works, the information about Venus is very- 

 meagre, and that, in the majority of cases,, 

 she is depictured only as a black crescent.. 

 But, in turning to ancient observations of the- 

 planet, they find a large number recorded,, 

 and many well-defined markings shown, indi- 

 cating that a study of the planet is not so diffi- 

 cult as is generally supposed. The committee 

 having the work in charge have divided it into- 

 three branches : 1. The formation of a sub- 

 committee of astronomical observers (includ- 

 ing non-members of the society) for the purpose 

 of continually observing Venus during one com- 



