FOCCACLT'S EXPERIMENT.] NAVIGATION NAUTICAL ASTRONOMY. 



107J 



the distance, that hypothesis must be modified till it 

 accounts for it."* 



From these statements the student will perceive that 

 one of the two fundamental hypotheses of astronomy- 

 the hypothesis of gravitation is not irrefragably estab- 

 lished like a proposition in Euclid ; nor is it a truth set 

 at rest, once and for ever, by observation and experi- 

 ment. Indeed, no physical truth can be regarded as thus 

 unalterably fixed, like a necessary truth of geometry. 

 The laws of nature may change ; the supposition of such 

 a change would involve no such absurdity as that which 

 would be implied in the supposition that the three angles 

 of a triangle could ever exceed or fall short of two right 

 angles. This truth would remain undisturbed, however 

 the properties of matter might be modified, and even 

 1 hough matter were to be altogether annihilated. It is 

 obvious that we reckon upon the continuance of the 

 properties of matter, and the return of natural pheno- 

 mena, only to the extent to which we reckon upon the 

 j/ermanence of the existing natural laws. And Laplace, 

 in extension of this idea, has oven calculated the proba- 

 bility that the sun will not rise to-morrow. 



But, assuming the unchangeableness of nature's laws, 

 we are authorised in regarding certain of its phenomena 

 as unalterable truths. For instance, if the planet we 

 inhabit is clearly ascertained now to be a round body, we 

 conclude that it will remain round as long as it lasts. If 

 it be as clearly seen to rotate, we conclude, in like man- 

 ner, that it will always rotate ;" its rotation ceases then 

 to be an hypothesis it becomes an observed fact, the 

 evidence for the truth of which is not increased by the 

 confirmations of future experience, nor by its satisfac- 

 torily accounting for 'whatever phenomena may be re- 

 ferred to such rotation. It is a matter of some impor- 

 tance, therefore, that the rotation of the earth is taken 

 out of the category of hypothesis, and classed among 

 observed physical truths, as we now proceed to show. 



FOUCACLT'S PENDULUM EXPERIMENT. Let the reader 

 conceive before him a circular table, upon which, passing 

 through its centre, the meridian line is drawn. If the 

 earth have no rotation about an axis, this line can never 

 change its direction ; if it do rotate, the direction must 

 continually vary, except the place of observation be at 

 the equator : this will readily appear from the following 

 considerations. 



Let our horizontal meridian line be indefinitely ex- 

 tended ; we shall thus have an indefinite straight line, in 

 the plane of the terrestrial meridian, and touching the 

 surface of the earth, the point of contact being the centre 

 of the table ; we may, of course, regard the table-top as 

 lying horizontally on the ground. 



For any place of observation between the equator and 

 the ]>ole, it is obvious that if the earth turned round its 

 axis, this tangent line will, in one complete rotation, 

 describe a conical surface enveloping the globe ; and, as 

 the vertex of the cone is necessarily at a finite distance, 

 the line which generates its surface thus always pointing 

 to a fixed determinate point (the vertex) must con- 

 tinually change its direction, which, however, it cannot 

 do if the earth be at rest. 



lint if the place of observation be at the equator, what, 

 in the case just considered, is a conical surface, would 

 evidently be a cylindrical surface; the straight line gene- 

 rating it would thus always be parallel to itself, and, 

 fore, though the earth should really rotate, there 

 would be no more change of direction in the meridian 

 line than if it were at rest. 



If, however, the centre of the table were directly over 

 the pole, then, taking any diameter of the table for a 

 meridian line, the changes in its direction if the earth 

 rotate would clearly be more rapid and more consider- 

 able ; it would pass through a revolution of 360 for 

 every complete rotation, and the surface described by the 

 line would be a plane surface. 



It is thus easy to see what must necessarily happen, as 

 to the direction of the horizontal meridian, if the eartli 

 have any rotation about its axis. At the equator, the 



" IMirriral Aftroromr," in the Encyelnpc-din Mrlnpolilaiia, by Sir J 

 F. \V. Ilcncbelj p.GIS. 



Fig. 22. 



direction would remain undisturbed, and the line would 

 generate a cylindrical surface ; at a small distance from 

 the equator, the cylinder would become a cone, and the 

 direction of the line would regularly, but only slightly 

 change. At a greater distance from the equator the cone 

 would differ more palpably from the cylinder, and the 

 angular deviation of the line always directed to the 

 vertex of the cone would be more considerable. As the 

 place of observation approaches the pole, the cone would, 

 as it were, widen out more and more, the deviation of 

 the line would become greater and greater, in a given 

 time, till at length, when the pole is reached, the cone 

 would spread into a plane, and the change of direction 

 would be the greatest possible. 



The reader will find it of much assistance, towards 

 clearly apprehending what is to follow, if lie keep con- 

 stantly before his mind the idea of the enveloping cones. 

 Every parallel of altitude is to be regarded as the circle 

 of contact of a cone, the apex of which becomes less and 

 less remote as the parallel approaches the pole ; we shall 

 call the cone adapted to any particular parallel, the cone 

 of Irititude of that parallel a designation which is suffi- 

 ciently significant. The extreme cases of the cone of 

 latitude are the cylinder and the plane the former be- 

 longs to the equator, the latter to the pole ; the angle of 

 the former is 0, that of the latter 180. The straight 

 line from a point of contact to the vertex of the coue^ is 

 the horizontal meridian of that point of contact. The 

 imaginary cone, of course, rotates with the earth, if the 

 latter rotate, but not else ; and the axis of the earth is, 

 when prolonged, also the axis of the cone. All this is 

 obvious. 



Let now P (Fig. 22), be the centre of the circular top 

 of the table, P P' half its meridional diameter, N S the 



axis of the earth, 

 prolonged to meet 

 the vertex of the 

 cone of latitude in 

 N. The angle. N 

 will be equal to the 

 latitude of the point 

 of contact P ; be- 

 cause, if a line P C be drawn from P to the centre of the 

 eartli, the angle P C N will evidently be the complement 

 of the latitude ; consequently, since N P C is a right 

 angle, the angle N is the latitude. 



Over the point P, let now the bob of a pendulum freely 

 hang the longer the wire or cord by which it is sus- 

 pended the better ; but it must be so attached to the 

 support above, as to be equally free to vibrate in any 

 direction. Let the pendulum be made to vibrato in the 

 direction of the meridian line N 1" ; and, if the earth 

 rotate, let us try to anticipate the phenomena that will 

 be presented to us. 



The point P immediately under the bob, at rest, must 

 rotate slaicer than the points in the meridian line more 

 remote from the apex of the cone ; so that, as the bob 

 sweeps over these points, they must keep proceeding in 

 advance of it, that is, towards the ea^t, if P be in the 

 north latitude, as here supposed. The rate of rotation 

 of the bob round the cone must be the same whether it 

 oscillate or not; because the fact of its oscillating cannot 

 interfere with any motion of revolution round the cono 

 it may have had, when hanging freely. We see, tliere- 

 fore, that the path of the pendulum, that is, its line of 

 vibration, must appear to be gradually receding from the 

 meridian line P P' towards the west, making with P P' 

 an angle of deviation, which increases at every oscilla- 

 tion. 



Actual experiment fully justifies these anticipations: 

 the deviation of the track of the bob is seen to be in com- 

 plete accordance with them ; and although, in the fol- 

 lowing mathematical investigation of the exact amount 

 of deviation in a given latitude and in a given time, 

 allowance must be made for mechanical imperfections, 

 and for the accidental impulse to the right or left com- 

 municated to the bob by the hand in giving the initial 

 impulse, and which will give rise to what is called an 

 apjidal motion, yet, with only very ordinary care, the 



