43^ 



NA TURE 



[Sept 14, 1S76 



various to account for all that we learn trom geological evidence 

 of earthquakes, of upheavals and subsidences of solid, and of 

 eruptions of melted rock." ^ 



Leaving altogether now the hypothesis of a hollow shell filled 

 with liquid, we must still face the question, how much does the 

 earth, solid throughout, except small cavities or vesicles filled 

 with liquid, yield to the deforming (or tide-generating) influences 

 of sun and moon ? This question can only be answered by 

 observation. A single infinitely accurate spirit-level or plummet 

 far enough away from the sea to be not sensibly affected by the 

 attraction of the rising and falling water, would enable us to find 

 the answer. Observe by level or plummet the changes of 

 direction of apparent gravity relatively to an object rigidly con- 

 nected with the earth, and compare these changes with what they 

 would be were the earth perfectly rigid, according to the known 

 masses and distances of sun and moon. The discrepance, if 

 any is found, would show distortion of the earth, and would 

 afford data for determining the dimensions of the elliptic spheroid 

 into which a non-rotating globular mass of the same dimensions 

 and elasticity as the earth would be distorted by centrifugal force 

 if set in rotation, or by tide-generating influence of sun or moon. 

 The effect on the plumb-line of the lunar tide-generating influence 

 is to deflect it towards or from the point of the horizon nearest 

 to the moon, according as the moon is above or below the 

 horizon. The effect is zero when the moon is on the horizon or 

 overhead, and is greatest in either direction when the moon is 

 45° above or below the horizon. When this greatest value is 

 reached, the plummet is drawn from its mean position through a 

 space equal to i-js oo^ooo tt of the length of the thread. No 

 ordinary plummet or spirit-level could give any perceptible indi- 

 cation whatever of this effect ; and to measure its amount it 

 would be necessary to be able to observe angles as small as 

 TaTT ooftoo u of the radian, or about ^^". Siemens' beautiful 

 hydrostatical multiplying level may probably supply the means 

 for doing this. Otherwise at present no apparatus exists within 

 small compass by which it could be done. A submerged water- 

 pipe of considerable length, say twelve kilometres, with its two 

 ends turned up and open might answer. Suppose, for example, 

 the tube to lie North and South, and its two ends to open into 

 two small cisterns, one of them, the southern, for example, of 

 half a decimetre diameter (to escape disturbance from capillary 

 attraction) ; and the other of two or three decimetres diameter 

 (so as to throw nearly the whole rise and fall into the smaller 

 cistern). For simplicity suppose the time of observation to be 

 when the moon's declination is zero. The water in the smaller 

 or southern cistern will rise from its lowest position to its highest 

 position while the moon is rising to maximum altitude, and 

 fall again after the moon crosses the meridian till she sets ; and 

 it will rise and fall again through the same range from moonset 

 to moonrise. If the earth were perfectly rigid, and if the 

 locality is in latitude 45°, the rise and fall would be half a milli- 

 metre on each side of the mean level ; or a little short of half a 

 millimetre if the place is within 10° north or south of latitude 45°. 

 If the air were so absolutely quiescent during the observations as to 

 give no varying differential pressure on the two water surfaces to the 

 amount of y^^ millimetre of water, or xv^ts of mercury, the observa- 

 tion would be satisfactorily practicable, as it would not be difficult 

 by aid of a microscope to observe the rise and fall of the water in 

 the smaller cistern to 1^ of a millimetre ; but no such quies- 

 cence of the atmosphere could be expected at any time, and it 

 is probable that the variations of the water-level due to difference 

 of the barometric pressure at the two ends would in all ordi- 

 nary weather quite overpower the small effect of the lunar tide- 

 generating motive. If, however, the two cisterns instead of 

 being open to the atmosphere were connected air-tightly by a 

 return pipe with no water in it, it is probable that the observa- 

 tion might be successfully made : but Siemens' level or some 

 other apparatus on similarly small scale would probably be pre- 

 ferable to any elaborate method of obtaining the result by aid of 

 very long pipes laid in the ground ; and I have only called your 

 attention to such an ideal method as leading up to the natural 

 phenomenon of tides. 



Tides in an open canal or lake of twelve kilometres length 

 would be of just the amount which we have estimated for the 

 cisterns connected by submerged pipe ; but would be enormously 

 more disturbed by wind and variations of atmospheric pressure. 

 A canal or lake of 240 kilometres length, in a proper direction 

 and in a suitable locality, would give but ten millimetres rise 



X- V'l^^^'il^'^ Cooling of the Earth." Transactions of the Roj'al Society of 

 iidinburgh, 1862 (W. Ihomson), and Thomson and Tait's " Natural Philo- 

 sophy," §§(««), (//). 



and fall at each end, an effect which might probably be analysed 

 out of the much greater disturbance produced by wind and 

 differences of barometric pressure ; but no open liquid level 

 short of the ingens cequor, the ocean, will probably be fcund so 

 well adapted as it for measuring the absolute value of the dis- 

 turbance produced on terrestrial gravity by the lunar and solar 

 tide generating motive. But observations of the diurnal and 

 semi-diurnal tides in the ocean, do not (as they would on smaller 

 and quicker levels) suffice for this purpose, because their amounts 

 differ enormously from the equilibrium values on account of the 

 smallness of their periods in comparison with the periods of 

 any of the grave enough modes of free vibration of the ocean as 

 a whole. On the other hand, the lunar fortnightly declinational 

 and the lunar monthly elliptic and the solar semi-annual and 

 annual elliptic tides have their periods so long that their amounts 

 must certainly be very approximately equal to the jequilibrium 

 values. 



But there are large annual and semi-annual changes of sea 

 level, probably both differential on account of wind and differ- 

 ences of barometric pressure and differences of temperature of 

 the water, and absolute depending on rain-fall and the meU- 

 ing away of snow and return evaporation, which altogether 

 swamp the small semi-annual and annual tides due to the sun's 

 attraction. Happily, however, for our object there is no 

 meteorological or other disturbing cause which produces periodic 

 changes of sea-level in either the fortnightly declinational or 

 the monthly elliptic period ; and the lunar gravitational tides in 

 these periods are therefore to be carefully investigated in order 

 that we may obtain the answer to the interesting question, how 

 much does the earth as an elastic spheroid yield to the tide- 

 generating influence of sun or moon ? Hitherto in the British 

 Association Committee's reductions of Tidal Observations we 

 have not succeeded in obtaining any trustworthy indications of 

 either of these tides. The St. George's pier landing-stage pontoon, 

 unhappily chosen for the Liverpool tide gauge cannot be trusted 

 for such a delicate investigation ; the available funds for calcula- 

 tion were expended before the long-period tides for Helbre Island 

 could be attacked, and three years of Kurrachee gave our only 

 approach to a result. Comparisons of this, with an indication of 

 a result with calculations on West Hartlepool tides, conducted 

 with the assistance of a grant from the Royal Society, seem to 

 show possibly no sensible yielding, or perhaps, more probably 

 some degree of yielding, of the earth's figure. The absence from 

 all the results of any indication of a i8'6 yearly tide (according 

 to the same law as the other long-period tides) is not easily 

 explained without assuming or admitting a considerable degree 

 of yielding. 



Closely connected with the question of the earth's rigidity, and 

 of as great scientific interest and even of greater practical moment, 

 is the question — how nearly accurate is the earth as a time- 

 keeper ? and another of, at all events, equal scientific interest — 

 how about the permanence of the earth's axis of rotation ? 



Peters and Maxwell, about thirty-five and twenty-five years 

 ago, separately raised the question, how much does the earth's 

 axis of rotation deviate from being a principal axis of inertia ? 

 and pointed out that an answer to this question is to be ob- 

 tained by looking for a variation in latitude of any or every 

 place on the earth's surface in a period of 306 days. The model 

 before you illustrates the travelling round of the instantaneous 

 axis relatively to the earth in an approximately circular cone 

 whose axis is the principal axis of inertia, and relatively to space 

 in a cone round a fixed axis. In the model, the former of these 

 cones, fixed relatively to the earth, rolls internally on the latter, 

 supposed to be fixed in space. Peters gave a minute investiga- 

 tion of observations at Pulkova in the years 1841-42, which 

 seemed to indicate at that time a deviation amounting to about 

 /^" of the axis of rotation from the principal axis. Maxwell, from 

 Greenwich observations of the years 1851-1854, found seeming 

 indications of a very slight deviation — something less than half a " 

 second — but differing altogether in phase from that which the 

 deviation indicated by Peters, if real and permanent, would have 

 produced at Maxwell's later time. On my begging Prof. New- 

 comb to take up the subject, he kindly did so at once, and 

 undertook to analyse a series of observations suitable for the 

 purpose, which had been made in the United States Naval Ob- 

 servatory, Washington, A few weeks later I received from him 

 a letter referring me to a paper by Dr. Nysen, of Pulkova Ob- 

 servatory, in which a similar negative conclusion as to constancy 

 of magnitude or direction in the deviation sought for is arrived 

 at from several series of the Pulkova observations between the 



