Apra 22, 1880] 



NATURE 



601 



nearest practical model of a simple pendulum, I cann \ help 

 seeing in it also an unconscious recognition that there was resist- 

 ance to be met in the air as well as buoyancy. It is not credible 

 that the resistance of the air to a body moving through it w as 

 11 it thought of, though it is intelligible that the effect of such 

 resistance was ..-o underrated or misunderstood as to be supposed 

 insignificant. 



Having mentioned Borda's pendulum in this connection, I 

 will add that I do not find grounds for assenting unreservedly to 

 the practice of assigning to him so large a share in the merit of 

 inventing the measurable pendulum. He improved somewhat 

 on an already existing form, and experimented with greater 

 accuracy, if not with gp ater care, than his predecessors ; but we 

 must, I think, in ju-tice ass iciate Picard's name, and still more 

 Graham's, with that form. 1 



About the year 1786 Whitehurst, carrying out an abortive idea 

 of Hatton's, presented to the Royal Society, and afterwards 

 withdrew and published independently, a paper describing 

 experiments with a pendulum of the ball-and-wire construction, 

 the use of which depended on a change in the length of the wire. 

 I have not hi access to the original paper, but if we may trust 

 Saigey's account the experiments were singularly correct in their 

 result. In all experiments with very long pendulums — indeed 

 whatever be the length, but especially with long ones — the ulti- 

 mate precision turns on the measurement of the distance between 

 the upper and lower planes. The liability to error in such 

 measurements is much better understood now than it was in 

 Whitehurst's time, and it is somewhat doubtful if the correctness 

 of hi result may be accepted as an argument in favour of his 

 method. But even if we had not ground for anticipating 

 advantages in a method which secures, to some extent, the 

 elimination of certain errors, the fact that Bessel adopted the 

 same method in preference to employing either Borda's or 

 Kater's pendulum, some forty years later, would go far to require 

 that full recognition should be accorded to Whitehurst. 



Thj result of the use of the single ball-and-wire pendulum, in 

 whatever form, depends ultimately, as I have said, on the accuracy 

 with which the di-tance can be measured between the p lint of 

 support and the lower contact plane. The measurement, and 

 perhaps also the distance itself, will vary with the temperature. 

 The length of the pendulum also, and therefore its rate, will 

 vary either with the temperature (if the suspension is by a wire) 

 or with the dampness of the air (if by a fibre). If the tempera- 

 ture varies much during the time occupied by the experiment, 

 the effects will be so complex — owing to the difference of the 

 masses of the wire, the scale, and the support — that great 

 precision can scarcely be expected. To some extent the 

 uncertainties are eliminated when the experiment takes the 

 form of a comparison between the rates of two pendulums of 

 different lengths, but otherwise identical. In any case, how- 

 ever, there is an element of uncertainty peculiar to the quest of 

 length distinct from th t which is peculiar to the quest of rate. 



It is not, I think, possible to form a correct conception of the 

 prx gress of the research which was prosecuted by the help of the 

 pendulum — still less to understand its present aspect— without 

 grasping firmly the idea that the use of the absolute pendulum 

 contemplated two distinct objects which had no essential con- 

 nection, viz., the force of gravity and the figure of the earth ; 

 while the u-e of the differential pendulum contemplated one 

 only of these. Of course I do not mean to imply that this 

 distinction was not perceived ; but I do suggest that no small 

 portion of the difficulties which have attended the research are 

 traceable to the frequent absence of a sufficient perception of the 

 independence of the two quests. From the time of Graham, 

 Bradley, and La Condamine, to the present day, while the 

 ostensible main purpose, has been one, the methods have been 

 "1 one of these was encumbered with a hardly ac- 

 knowledged second purpose whose presence created a set of 

 difficulties from which the single-minded purpose and method 

 were free. This is so obvious, so well known, that it seems 



1 On another point also, namely that of the general association of Borda's 

 nanie with the inventi< n of the method of coincidences, I am glad to find 

 myself not ah.nc in demurring. LeRentil distinctly says that he followed 

 nfuran in this; and Meyer alludes (1865) to the same misconception when 

 Die v n Mairnn erfundene Methode der Coincidenzen, die 

 gewOhnlich de Borda augeschr.eben wird " i.Pog£' Ann., exxv. p 

 The merit due to Borda in this connection would seem to be limited to his 

 employment of a cross mark on the clock-pendulum as an object with which 

 the thread of the free pendulum was to be in concert — just as Kater after- 

 wards used a white disk and an opaque slip ; out of which in after years 

 arose a somewhat complicated and very differently understood question of 

 precision. 



almost an impertinence to bring it forward. It is not so, how- 

 ever. Fully recognised and admitted as |it must be allowed to 

 be, the fact remains that notwithstanding the comparative failure 

 of the absolute method and the acknowledged success of the 

 differential, the tendency at this day is still to have recourse to 

 the former, although the second purpose is now scarcely thought 

 of as a real desideratum, the whole interest centring in variation, 

 and variation only. 



Let us consider the two objects of the absolute method 

 separately ; or rather, let us consider that one especially which 

 is its peculiar object — the length of the equatorial seconds 

 pendulum. 



What is the equatorial seconds pendulum? It is a simple 

 pendulum beating seconds under the force of gravity at, or near, 

 the equator. We are obliged to add the qualifying words, 

 because it is certain that the rate varies along the actual equator. 

 It is necessary, therefore, either to specify some spot, or to define 

 in some other way the force to be designated. How is this to 

 be done ? 



As I remarked at the beginning of this paper, I do not propose 

 to approach the question of the figure of the earth more nearly 

 than is necessary. But it is perfectly clear that as soon a> it is 

 admitted that the form which we are to study by means of a 

 pendulum actuated by gravity is to be expressed as a more or less 

 complicated mathematical equation, the force of gravity enters 

 as a principal variable. The limits and law of variation it is 

 not necessary here to attempt to define. All that is necessary is 

 to perceive that there will be one or more maxima at or near the 

 equator, one or more minima at or near the pole, and as many 

 means as we choose to invent functions expressing what may 

 be called means. 



The idea of a seconds pendulum as a definite length rests on 

 the idea of gravity as a definite force. The idea of an equatorial 

 seconds pendulum as a determinable length rests on the idea of 

 equatorial gravity as a determinable force. We are therefore 

 driven to consider in what sense, and by what means, it was, 

 and perhaps is, supposed determinable. 



Had France been an equatorial country there need be no 

 doubt that, not Paris, but some equatorial village, would have 

 been chosen as the site of experiment to be repeated again and 

 again as time went on. But as this was not the ca.se French 

 philosophers went some thousand miles and sojourned for years 

 in an equatorial country, in search of this stone. And in after 

 time, when confirmation was wanted, voyagers experimenting in 

 foreign latitudes made a point of getting as near to the equator 

 as possible. 



Gradually the idea of determining gravity by experiment at the 

 equater gave place to the idea of determining it by experiment 

 elsewhere. The summit lost its immediate attraction in the 

 interest of perfecting a road to it. By degrees it became 

 apparent that there was no summit, or at any rate that the summit 

 could only be designated by a careful study of all the approaches ; 

 and lastly, that it was in fact only an idea. Only an idea, and 

 that an undefined one. 



The history of physical research is full of instances of this 

 kind of baffled inquiry. From a distance the goal is clear, 

 distinct, definite, precise ; we can in thought put a finger on it. 

 We approach, and the aspect changes, foreshortened distances 

 extend, and small things become great ; forms are changed, and 

 though we penetrate into the very midst of what we ran for, we 

 recognise it no longer. Had we run open-eyed we should have 

 been prepared for the transformation and have realised better 

 the suco 



So it is with equatorial gravity. What was seen at a distance 

 was that very idea, which, close at hand, we cannot readily 

 define. 



Some such difficulty appears to be the explanation of the 

 vigour with which the more concrete idea of the actual force at 

 a definite spot was grasped ; and perhaps we may recognise in 

 the almost extravagant pretensions of the London and Paris 

 seconds pendulums a sense of retreat from, and abandonment of, 

 the hopeless equatorial representative. 



But in falling back from the equator upon Paris and London 

 there was no abandonment of the length cf the seconds pendu- 

 lum as a linear standard. This came somewhat later, when the 

 difficulties of precise determination even at one and the same 

 spot were more apparent. Meanwhile the local lengths were 

 retained as provisional units. 



This appears to me to be the key of the position. It was 

 anticipated that|the exact relation of gravity at Paris and at 



