6oo 



NATURE 



[April 22, 1880 



years before adopted the idea — subsequently, towards the close of 

 the next century, so nearly being given final effect to — of making 

 the seconds pendulum the unit of length. But although he did 

 actually determine the length at Paris, and thus unwittingly laid 

 the first stone of the "absolute" method, it was not until the 

 length had also been ascertained at another place and in 

 another latitude that the firstfruits of the method could be 

 gathered. 



It is conceivable (though unlikely) that the pendulums used in 

 the two places were the 'same. But this is of no consequence, 

 since their lengths were different — the time of oscillation being 

 constant. 



Precisely the same result, in respect of variation of attractive 

 force, would have been deduced had the same pendulum, of 

 unchanged length, been used ; the fact of observation in this case 

 being a diminution of rate. 



In the one case we have the absolute method ; in the other we 

 should have had the differential method. But in the former we 

 have not only an indication of the variation of the force, but also 

 a measure of its magnitude in terms of the measured lengths. 

 Hence the designations. 



It is well to remark here that unless the measurements at the 

 two places refer directly, or can, by intermediary scales, be 

 referred ultimately, to one and the same standard, there i- no 

 exact comparison, and no certain result. Further, that if, from 

 any cause, the standard of reference is of unknown length, or, 

 technically speaking, lost, the result is differential only. Thus 

 we see that observations which were,. in intention, of the absolute- 

 class, may fall into the differential class for want of reliable 

 connection with existing standards of length. 



Measurement of the absolute force of gravity at the earth's 

 surface by means of a pendulum was doubtless c ontemplated by 

 astronomers anterior to Richer's discovery of its variation. It 

 is therefore scarcely permissible to recognise in the prosecution 

 of this discovery the determination of the absolute force as a 

 principal object. The object was distinctly to ascertain the 

 variation at different parts of the surface. Such being the case, 

 we must admit that the absolute method was not the simplest for 

 the purpose. In due time this was recognised. It is doubtful to 

 whom is due the credit of earliest perceiving that the measurement 

 of the pendulum might be dispensed with, provided means were 

 supplied of securing a constant length. Graham and Campbell 

 (in 1732), and Bouguer (in 1735), were the earliest in the field ; ■ 

 and Bradley (in 1736) in describing Campbell's use of Graham's 

 pendulum at Jamaica, very decidedly recommends the use of a 

 pendulum of constant length. Bouguer and Godin at the same 

 period were also using pendulums which were measured. From 

 this time forward to the present day both methods have been 

 practised. 



I confess myself unable to frame arguments in favour of the 

 measured pendulum, as an instrument for its purpose, which can 

 at all account for its prolonged use. I mean of course if we are 

 to presume an intimate acquaintance, on the part of the observer, 

 with the meaning of his labours. Considering how fragmentary 

 and scattered, and often unimportant, not to say mistaken, are 

 the early writings on the use of the pendulum, it is scarcely in- 

 vidious to say that such a presumption is sometimes gratuitous. 

 The men who made scientific voyages in those days doubtless 

 had something else to do than to study. Moreover, study was 

 not [very feasible when books were scarce and libraries few. 

 Nevertheless one caunot help a curiosity as to the charm which 

 protected the absolute method. Was it precedent ? 



There is something seductive, it must be admitted, in the con- 

 ciseness and completeness which attends an absolute determina- 

 tion, as contrasted with the dependence of a differential one. To 

 adjust a pendulum to such a length that it will beat seconds, and 

 then to measure its length against a portable standard who-e 

 length has been ascertained — this is conclusive. When done, 

 the worst that can happen to the instruments used is no worse 

 than prevention of further use. This is true; and if the observer 

 is full of confidence in the accuracy of bis measurements, un- 

 conscious of the errors that lurk in reductions, and innocent of 

 the insidious nature of instrumental mischances, why should he 

 surrender the security of present gain ? Nevertheless these flaws 

 exist, and ultimately they are recognised and found irremediable. 

 The more honour to those who foresee and provide against them, 

 in preparing instructions, in conducting experiments to elucidate 

 difficulties, or in multiplying observations by which the work of 

 others may be consolidated. 



1 Mairan, in the same year, su && , 

 advocated and used one frequently. 



Much of the doubtfulness which attaches to the earlier work 

 is due to want of that knowledge which experience brings. 

 Among the most important causes of error must be reckoned the 

 imperfect comprehension which formerly existed as to the 

 retarding influence of the air on the swinging pendulum. It 

 was of course known that a body being lighter when suspended 

 in a fluid than when in air, the oscillations of a pendulum when 

 swung in air would be slower than when swung in a vacuum. 

 No account was taken of this at first, but the time came when 

 the effect was calculated by determining the diminution of 

 weight due to flotation. Ultimately it was shown that there 

 was also retardation due to the disturbance of the surrounding 

 air, and it was surmised that this depended, not only on the bulk 

 of the air displaced by the pendulum, but on the form of its 

 surface as well. Of course it was immediately apparent that the 

 old remits must undergo some correction depending on the forms 

 of the pendulums used ; and equally, of course, the want of pre- 

 cise descriptions was then felt in a way the original observers 

 never contemplated. 



The difficulty was perhaps less real than apparent. As I have 

 already pointed out, the magnitude of the force was not the ob- 

 ject of the experiments, except as a means of inter-comparison. 

 Hence any shortcoming which invalidated the determination 

 of the absolute magnitude without rendering impossible that of 

 the relative force, was of no real consequence. It was only 

 necessary to abandon the idea of retaining a set of results in the 

 absolute class, and to consider them as differential only ; the 

 sine qua non being that such set were taken with one pendulum 

 or with pendulums of the same size and construction. But I 

 cannot remember a single instance in which the difficulty has 

 been met in this way. 



I have pointed out that the idea of measuring the force at any 

 place absolutely arose anterior to that of measuring it relatively, 

 and was afterwards retained as a means of securing the relative 

 measure. Whatever interest attached to the determination of the 

 force of gravity for itself, it is pretty certain that it went for little 

 in the experiments which succeeded Richer's. It is therefore re- 

 markable that even after the simpler differential method had been 

 inaugurated it should still have held its ground. It is probable 

 that Picard's idea 1 of a base or standard of length dominated to 

 some extent the subsequent line of investigation. At any rate 

 it is to his experiments that we must look for the rudiments of 

 the instrument. I am 2 unfortunately unable to refer to the 

 original memoirs in which these experiments are recorded, but I 

 gather from other accounts that all the experimenters aimed at 

 as near an approach to a "simple'' pendulum as possible, and 

 that even the celebrated form which Borda adopted in 1792 

 scarcely differed at all from the earlier ones. The following 

 notice of Borda's experiments by Lalande, in his " Histoire 

 Abrege de l'Astronomie,-" is noteworthy as sustaining the view 

 which I am led to take of the vitality of the absolute method : — 



" Le decret de I'Assemblee nationale qui, le 8 mai, ordonna 

 la reforme des mesnres en France, en indiquant le pendule a 

 secondes pour mesure primitive, exigeait que la longueur du 

 pendule fut determinee avec une nouvelle precision. En 1735 

 Mairan avait fait ses observations avec bien du soin ; mais alors 

 on ne pouvait guere l'assurer d'un quinzieme de ligne. Borda 

 espera obtenir une precision bien plus grande par des moyens 

 nouveaux ; il l'entreprit done cette annee a l'Observatoire, avec 

 des instruments faits d'apres ses ide'es par C e " Lenoir, et il en 

 resulta enfin une determination du pendule de 36p. 81. 60 reduite 3 

 a la temperature de 10° ; et dans le vide ; ce resultat, qui est a 

 un cinquantieme de ligne, et mieux encore, a ete obtenu avec un 

 pendule de douze pieds de long." 



The old form of pendulum consisted of a weight, of simple 

 geometrical form, suspended by a fine wire or fibre. In 

 Borda's the weight was spherical and attached by adhesion to a 

 cup to which the wire was fastened. The object of this was to 

 vary the position of the ball without detaching the wire. This 

 attachment seems to be the only part of consequence which was 

 without precedent. 



In all these forms it is particularly to be noticed that the 

 ball was made heavy and the suspension light and fine. 

 Although the obvious intention of this was to attain to the 



1 Priority, in point of time, is due to Wren in this matter ; but Mouton, 

 from whom Picard got it (and perhaps also Huygens), no doubt evolved it 

 independently, though some years later. 



' This article was written in Calcutta, and no library ther: possesses tne 

 early volumes of the Paris Acad. Memoirs. t . , 



3 Please to remark the absence of intelligible meaning in th.s. W hat is it 

 1 that is reduced ? and why ? 



