Oct. 17, 1884.] 



♦ KNOWLEDGE ♦ 



315 



force applied tangentially to such a globe supposed 

 initially at rest would cause it to rotate uniformly 

 — however slowly — and if no new force were applied 

 this rotation would continue until time should be 

 no more. At least, then, we have a simple account 

 to give of the earth's rotation ; but when we consider the 

 rotation of the sidereal scheme we find no simple expla- 

 nation available. Are the stars rigidly bound together in 

 some way t Then indeed they can rotate with the uni- 

 formity observed in their diurnal motion. But then we 

 become immediately perplexed by the sun, moon, and 

 planets, which, while partaking of the uniform diurnal 

 rotation, have, superadded to this, motions peculiar to them- 

 selves. We must have for each of those bodies a separate 

 sphere rotating about the same axis as the stellar sphere, 

 each body being within its own proper sphere. If the stars 

 are not thus bound together, then each travels uniformly in 

 its proper circle, and at its proper rate [round the polar 

 axis ; and instead of a single rotation accounting for the 

 whole system of stellar motions, we require that each star 

 of the thousands we see should travel independently on its 

 proper diurnal path, and that path millions of miles in 

 circuit, even by what we have already learned. 



This is sufficiently difficult to believe ; but when we add 

 to this the evidence atforded by the telescope, the idea that 

 the stars revolve diurnally round the polar axis becomes 

 altogether incredible. In the first place, for every star 

 visible to the naked eye, the telescope reveals thousands, 

 each following the same law of motion which is observed 

 among the lucid stars. Secondly, the careful telescopic 

 examination of the heavens has revealed the fact that the 

 so-called fixed stars have certain minute motions — a circum- 

 stance which suffices to show that they are not rigidly 

 attached together in any way ; so that we are compelled to 

 dismiss the only possible conception by which the uniformity 

 of their rotation seemed explicable. Lastly, the telescope 

 reveals the existence of pairs of stars revolving around each 

 other — -a circumstance which yet more clearly proves that 

 the stars, like the earth, are suspended in space, free to 

 circle around each other or to sweep onward in solitary 

 state, upon their several orbits. 



The second proof of the earth's rotation is founded on 

 the varying attraction of gravity in different parts of 

 the earth's surface. We have seen that the earth's figure 

 is that of a somewhat flattened sphere. Now without 

 assuming the theory of gravitation as Newton propounded 

 it, we yet know quite certainly that the earth's mass exerts 

 an attraction upon all terrestrial bodies. A thousand 

 experiments convince us that this attraction is appre- 

 ciably uniform in any given place. The swing of a pen- 

 dulum, the flight of a projectile, and many other obvious 

 circumstances serve to prove this. Therefore, quite 

 independently of Newton's theory, we can look on terres- 

 trial gravity as not only an established fact, but one 

 from which we can glean useful information. 



Now, if a pendulum be set swinging at a considerable 

 height above the earth, and its oscillation be compared 

 with that of a pendulum at the earth's surface, gravity 

 is found to decrease according to a certain law. 



Suppose, then, we carry a pendulum from the polar 

 regions to the equator, so that (according to what we have 

 already learned respecting the earth's flgure), the distance 

 of the pendulum from the centre of the earth continually 

 increases. Then it is not difficult fer the mathematician 

 to determine according to what law gravity ought to 

 diminish in consequence of this increased distance. I do 

 not enter into a consideration of the mode of calculation, 

 because it depends on principles rather too abstruse for 

 these pages. Suffice it to say, that these principles are 



thoroughly well established and certain, and that they lead 

 to the conclusion that gravity at the equator should be 

 about l-289th less than gravity at the poles, if we merely 

 took into account the earth's shape. 



But instead of this, gravity at the equator is found to 

 be less than gravity at the poles (or rather than 

 gravity as calculated for the pole from the observed 

 gravity in high latitudes), by fully l-19.^)th part Whence 

 then can the difierence arise 1 This difference is equal to 

 M95-1-289, or 1-599, and is not much less than half the 

 estimated decrease, so that it is a quantity far too im- 

 portant to be neglected. 



Now, it is really calculable that the diminution of weight 

 due to the centrifugal force at the equator, if the earth really 

 rotates once in a sidereal day, is exactly l-599th part In 

 other words, if the earth were a perfect sphere, a body at 

 the poles would weigh more than a body at the equator in 

 the proportion of 599 to 598, supposing the earth really to 

 be rotating. We see that this relation actually holds : — A 

 body at the equator weighs less by 1-59 9th than it should 

 weigh on the supposition that the earth does not rotate. 

 Thus we have direct evidence of great weight, in favour of 

 the view that the earth does rotate. 



The evidence derived from the descent of bodies from a 

 considerable height is one of the most interesting of all 

 the proofs of the earth's rotation. It is also, I believe, one 

 of the least known. 



The general principles on which this proof depends are 

 very easily explained. Let B be a 

 point on the earth's equator, O the 

 centre of the earth. A a point verti- 

 cally above B. Then, clearly, the 

 point A moves faster (if the earth is 

 rotating) than the point B. We see, 

 for instance, that in the time occupied 

 by A in passing to C, B only passes 

 to D, and A C is obviously greater 

 than B D. Hence, if a body be let 

 fall from A, it will not fall directly towards B, but will be 

 carried by the excess of its motion, somewhat towards D. 

 In fact, if we suppose that while the body is falling from A 

 to the ground near B, the point A is carried to C, then the 

 point B will have been carried to D, and our falling body 

 will have reached a point E, such that BE=AC. The 

 small displacement D E will be all that will be noticed by 

 the observer ; and when we remember how very small the 

 distance A B must be in all real cases, when compared with 

 B O, it will be seen at once that D E must always be very 

 small indeed. Still, it has been found possible, by very 

 delicate appliances, to render sensible the displacement of a 

 falling body towards the east (the direction of the earth's 

 rotation). Before describing the experiments made on falling 

 bodies, it may be well to consider the minuteness of the 

 results to be looked for. Suppose we consider the case of 

 a body at the equator, let fall from a height of 1,000 feet ; 

 then, according to the usual formula, the time of falling is 



V 



2000 ,^ , . ., 



__- (taking gravity 



at 32 for convenience); that is, 



the time is rather less than 



on the equator travels about 



8 sec. Now, in S sec. 

 25,000 X 8 



a point 



250 

 miles :=Y^ 



24 X 60 X 60 



miles=:2-3 miles or thereabouts. And in order to see how 

 much farther a point 1,000 feet above the level of the earth 

 would travel, we have only to take the same portion of 2-3 

 miles, that 1,000 feet is of the earth's radiua. Thus we get 



4,000x1760x3 ,, ^, ^ . 2-3 



(in miles) 2-3-4- ^-^qq roughly ; that is, —It. : 



or not quite 7 inches. Now, the slightest breath of air when 



