32 



An error in the rate accepted for 6711 of 1 second per diem means an error of approximately 

 59 x 10~" second in the time of swing of the pendulums. 



3. A second source of uncertainty, already alluded to by Mr. BERNACCHI, is the absence of 

 observations for determining the so-called "flexure" correction, which arises from the absence of absolute 

 rigidity in the pendulum and its supports. Flexure experiments were made at Kew before the Expedition 

 set sail, and after its return, but the results apply strictly only to the conditions existent at Kew. It has 

 seemed on the whole best to apply no flexure correction to the results obtained during the Expedition, and 

 to compare these results with those obtained at Kew, also unconnected for "flexure." This is equivalent to 

 the assumption that the " flexure " with the piers used at Winter Quarters, Christchurch, and Melbourne 

 was the same in each case as that with the pier used at Kew. Judging by Mr. BERNACCHI'S description 

 and the photograph, the pier used at Winter Quarters was fairly similar to that used at Kew, so it is 

 probable that the plan adopted will lead to but little error. The " flexure " tends to lengthen the time of 

 swing, and so, if uncorrected or underestimated, leads to too low a value for </. Whether the method 

 adopted is equivalent to an overestimate or an underestimate it is, of course, impossible to say. On the 

 Kew pier, on the average of experiments with three pendulums, the flexure correction to the period was 

 69 x 10~~ second. The error in g corresponding to the total omission of a correction of this size is 

 approximately 0'027 C.S.~-, or about 1 part in 36,000. The error actually arising seems hardly likely to 

 have exceeded a third of this, and may, of course, be absolutely nil. 



4. The last source of uncertainty to be mentioned is the fact that during their three years' absence on 

 the Expedition the pendulums seem all to have altered slightly. The apparatus had really four 

 pendulums, Nos. 36, 37, 38, 39, but with a view to possible changes in the Antarctic it was considered 

 advisable to retain one pendulum, No. 36, at Kew. The times of swing observed at Kew in 1901 and 

 1904 were as follows, all the ordinary corrections temperature, pressure, arc, and clock-rate having 

 been applied : 



The apparent change in No. 36 does not exceed the probable error of the observations. Thus the 

 presumption is that during the Expedition no appreciable change took place except in the pendulums 

 themselves. That some change actually took place in Nos. 37, 38, 39 can hardly be doubted. There is 

 independent evidence of the fact from the observations at Christchurch, presently to be discussed. The 

 changes in Nos. 37 and 38 are, fortunately, not large, but that in No. 39 appears much more serious. 

 Comparatively few observations were made with this pendulum at Kew before the Expedition set sail, and 

 it is quite possible that the change in it is overestimated, but in any case the results derived from it must 

 be regarded as appreciably more uncertain than those derived from Nos. 37 and 38. 



5. Table I., p. 26, gives particulars of all the observations taken during the course of the Expedition. The 

 reductions, involving a large amount of laborious calculation, were made by Mr. BERNACCHI. They were 

 then done independently by Mr. E. G. CONSTABLE. The results obtained by Mr. BERNACCHI were 

 accepted as correct unless Mr. CONSTABLE'S differed by more than 1 in the seventh figure. In cases where 

 larger differences existed I investigated the cause myself. I also revised the rates accepted for the 

 chronometer during the observations. The usual set of observations gave four values for the period of 

 each pendulum, two with the pendulum facitig D (or direct), and two with it facing E (or reversed). But 

 on February 6, 1903, at Winter Quarters, the R position alone was used, and at Melbourne, in 1901, the 

 D position only was used. If one compares the results for the D and R positions in Table I., when both 



