April 22, 1880] 



NATURE 



599 



possible to land and winter. Continuing their course to the west, 

 they intend running along by the " Southern Continent," where 

 the existence of land is certain, and endeavour to penetrate 

 through the ice, as did D'Urville, Wilkes, and Ross. The hope 

 is that canals in the ice might be found through which they 

 might attain a remote latitude, or, running along them when 

 massed into a continent, arrive at Kemp or Endermet, where 

 they could pass the second winter. 



A JAPANESE paper states that the Swedish skipper Johannesen, 

 who has already done a good deal of exploration in the Spitz- 

 bergen seas, is to set out this month from Yokohama in the 

 steamer NordenskjiUd to make the North-East Passage in an 

 opposite direction to that taken by the Vega, viz., from Behring 

 Straits to Europe. 



Prof. NordenskjoLD reached Copenhagen at the end of last 

 week, in the Vtga, and was received on landing by the acclama- 

 tions of 20,000 per- ons. Every one has united to do him and 

 his companions honour, from the Royal Family dow nw aids. 



The death is announced, on the 16th inst., of Mr. Robert 

 Fortune, well known as a botanical collector in China and 

 Japan, and author of several volumes describing his Iravels in 

 those countries in search of new plants. It was he who intro- 

 duced the tea-plant from China into the North-West Provinces 

 cf India. He was born in 1812. 



ON THE EMPLOYMENT OF THE PENDULUM 

 FOR DETERMINING THE FIGURE OF 

 THE EARTH 



]\ 1 V object in writing this paper is principally to draw attention 

 to the course « hich the employment of pendulums has taken, 

 from the time when Kicher's first experiment at Cayenne, in 

 1672, attracted the attention of Newton ; and to show in what 

 respect the present aspect of the question is different from that 

 which successive observers, as well as writers upon the subject, 

 have at various times taken. It is no part of my object to 

 discuss the observations themselves, or to discriminate between 

 them, still less to enter upon any investigation of the figure of 

 the earth, except incidentally in alluding to the conclusions 

 which different writers have accepted. But as it is nearly 

 impossible — perhaps not altogether desirable — to hold no inde- 

 pendent opinions, I may aid that I hope to be able to influence 

 the future course of such operations in a certain direction which 

 will be recognl-able as we proceed. 



The literature of the subject is very extensive, — not so much in 

 respect of the pendulum itself, or of the use which has been 

 made of it, as on account of the intimate relation which the laws 

 which govern its motion have to larger questions. It is the 

 discussion of these that experiments with the pendulum have 

 influenced, and in general it is only with reference to such 

 influence that the experiments have been instituted, described, 

 and considered ; and that in close connection with other opera- 

 tions of wholly different character. It is thus nearly i 

 to have a thorough knowledge of the history of pendulum 

 operations without at least a general acquaintance with the 

 history of geodesy, and of that part of astronomical and mathe- 

 matical literature which deals with the probable forms and 

 constitutions of cosmical bodies. This would be less the case 

 than it is if some of the many writers on the figure of the 

 earth had written less exclu ively from their own point of view, 

 and (at any rate in writing of pendulum operations) had dealt 

 more fully with the historical aspect of this particular branch of 

 the general subject : I mean in the modern sen-e of the word ; 

 describing not only the sequence of experiments, but also the 

 development of the comprehension of the questions in is>ue. 1 

 have felt the want of this myself si strongly that now that a 

 somewhat protracted study hus partly supplied that want I am 

 fain to attempt this review, in aid of those who may have to 

 pro-ecute the work. 



It is of course impossible to present the course of pendulum 

 operations without continually referring to their intention. At 

 the same time one learns at last that, with one or two exceptions, 

 the intention itself w as not well grasped by those who conducted 

 the experiments. Indeed one may almost say that even on the 

 part of those who directed them the intention is not very clear ; 

 or more correctly, that it was more confined than we now might 

 wish had been the case. Laplace was not perhaps the first to 

 give utterance to the opinion that the anomalies noticeable in 



pendulum results were probably due rather to inequalities of 

 figure than to errors of observation. Nevertheless it is with 

 something of surprise, considering that the importance of his 

 opinion lay latent so long as a practically unrecognised con- 

 sideration, that we find him saying as follows : — " We shall 

 here remark that the same anomalies. . . arising without doubt 

 from the irregularity of the parts of the earth, are also perceived 

 in the ob-erved lengths of pendulums." That such irregularities 

 existed was doubtless always a suspicion, but the fact was very 

 slow of being recognised, and to this day it does not govern the 

 observations. 



In reviewing the course cf pendulum operations then we 

 must be prepared to put this [aside as a fact which has not 

 entered into account. It may be strange, but such is the case. 

 It follows that a very considerable portion of the discussions 

 and calculations, based on results which I am very far from 

 wishing to impeach, must also be set aside as almost entirely 

 without present value other than as evidence that the breadth of 

 the question had not been measured. 



If the absence of a true appreciation of the influence of local 

 irregularity is apparent in the narrowness of the discu-sionof 

 individual observations, or of small groups of results ; it is also 

 noticeable in the rejection of many, en the sole ground that the 

 methods of observation were inferior ; without any proof being 

 adduced that the probable error was greater than the probable 

 effect of local irregularity. This may be taken as indicating 

 that there was also on the part of those who set themselves to 

 review the produce of experiment a reluctance to accept as 

 facts the irregularities which now we recognise as necessary 

 concomitants. 



Here again it follows that we must be ready to turn aside from 

 conclusions which are seen to rest on the exclusion of an impor- 

 tant consideration. But it by no means follows that, in thus 

 finding reason on all hands to go back to the original sources, 

 and to discard more or less summarily much which has been at 

 one time or another accepted as legitimate deduction, there 

 is any occasion to slight these deductions.' Mere trials as 

 they have often been, they have served many purposes which 

 we cannot disdain, and (in ways which it is vain now to 

 examine) have placed us in the more advanced position. There 

 is one thing however which they must have no power to effect, 

 and that is to obstruct us in further advance. 



At the same time I confess that, for my own part, I cannot 

 turn over the innumerable pages of vain, calculations without 

 profound regret that they represent so much labourV^-not thrown 

 away — but without further use. I would give' instances, but 

 perhaps it is better to refrain. If auything could excuse it, it 

 would be the hope of saving some other learner from spending 

 time over them, and that object can perhaps be otherwise 

 secured. 



From another point of view I have also been led to perceive 

 a want of distinctness in the plan of operations, which accounts 

 for an otherwise inexplicable diversity in the individual con- 

 tributions. In studying the history of these operations we are 

 reminded of an edifice which presents different styles ; and parts 

 which make up a whole, not so much after any known design 

 as casually. The two principal styles, to continue the metaphor, 

 have indeed a common element which is a key to the whole 

 construction ; but though we can perceive that it is there in 

 every part, and was present to the mind of every worker, it 

 scarcely ever amounts to an expressed design by which future 

 work is to be regulated. I allude to the absolute and differential 

 methods. As we cannot properly appreciate the value of the 

 work which has been done without understanding the relation in 

 which these stand to each other, it is necessary to preface the 

 merely historical account By a description* of those methods 

 in their relation both to the general purpose and to each other. 



The conception of the earth as an oblate spheroid probably 

 preceded the first use of the pendulum as an instrument by which 

 its oblateness could be proved and measured. But the uncer- 

 tainty which characterised geodetic measures — an uncertainty so 

 great that it was, at a later date, actually the subject of vehement 

 controversy whether the elipticity was not prolate — was such 

 that Kicher's di-covery (in 1672) that the length of a pendulum 

 beating seconds at Cayenne was notably less than that of a 

 pendulum beating seconds at Paris, was from its very sim- 

 plicity and conciseness, a revelation which promised inestimable 

 doasequences. 



This was not the first time that a measurement of the seconds 

 pendulum figures in the annals of geodesy. Picard had two 



