30. Pendulum Observations at Fort Conger

216.1 the Chief Signal Officer] General William Babcock Hazen (1830-1887) was in charge of organizing the Greely expedition. In a letter of 30 November 1888, however, Greely wrote to Peirce (RL 174:7):

The statement in the opening line of your report is incorrect. The Chief Signal Officer did not apply to the Superintendent, but the Superintendent applied to me, asking if I would make the observations, and, as I then understood, this application was made owing to your interest and zeal in the matter.

216.1-2 Superintendent of . . . Survey] Carlile P. Patterson (see ann. 216.4).

216.3 Lieutenant Greely] Adolphus Washington Greely (1844-1935), commander of the twenty-five men expedition that was sent by the U.S. Army to establish a metereological station at Lady Franklin Bay. For Greely's account of the expedition see his Three Years of Arctic Service: An Account of the Lady Franklin Bay Expedition of 188-84, and the Attainment of the Farthest North (New York: C. Scribner's Sons, 1886), and his Report on the Proceedings of the United States Expedition to Lady Franklin Bay, Grinnell Land (2 vols., New York: Government Printing Office, 1888), of which the current selection is appendix 141.

216.4 Lady Franklin Bay] At Lady Franklin Bay, which is on the eastern shore of Ellesmere Island, Greely established his base camp, Fort Conger.

216.4 Carlile P. Patterson] Carlile Pollock Patterson (1816-1881), superintendent of the U.S. Coast and Geodetic Survey from 1874 until his death in 1881.

216.7-8 that he understood . . . scientific work] With this comment, and the comment in the next sentence on hampering scientific inquiry by excessive bureaucratic regulations, Peirce shows discontent with the changes that have been taking place in the Coast Survey under Superintendent F. M. Thorn, who was a politician, not a scientist.

216.12-13 series of Peirce Pendulums] During 188-82 four invariable, reversible pendulums, called Peirce Nos. 1, 2, 3, 4, were constructed at the Office of the Coast and Geodetic Survey after an original design of Peirce. Nos. 1, 2, and 4, were meter pendulums; No 3 was a yard pendulum. For a description of the Peirce pendulum, see Victor F. Lenzen and Robert P. Multhauf, "Development of Gravity Pendulums in the 19th Century," United States National Museum Bulletin 240 (Washington: Smithsonian Institution, 1965), 30-48; esp. 327-31. See also W4, introduction, pp. xxx-xxxi.

216.13 will be elsewhere described] A full description of the Peirce pendulums and the theory behind their development is given in the opening narrative of sel. 36.

216.14-15 invariable reversible pendulums] In a 24 February 1886 letter to Thorn (NARG 23/22), Peirce explained:

We have been using for several years, a kind of pendulum designed by me and known as the "Peirce" pendulums. There has been much controversy as to whether determinations of gravity ought to be made with invariable or with reversible pendulums. Our method consists in using pendulums which are at once reversible and invariable.

216.19 Mr. E. Israel] Sergeant Edward Israel (d. 1884), graduate in astronomy from the University of Michigan at Ann Arbor, was assigned to the Greely expedition along with other members of the U.S. Army Signal Corps. See also ann. 218.8.

216.19 to be instructed . . . the instrument] In a 8 Sept. 1881 letter to Superintendent Hilgard, Peirce explained: "The enclosed paper is a copy of the written instructions given by me to Mr. Israel and Lieut. Greely. They were of course supplemented by careful training of Mr. Israel in all the details of the operations." The paper referred to was probably the document transcribed below, of which two different amanuensis copies exist among the Greely expedition papers (NARG 27 entry 138 NC 3). Both amanuenses were found only after publication of Volume 4, and thus were not included in its Chronological List. Neither is in Peirce's hand, and one is a transcription of the other. For Greely's comments on Peirce's instruction see 244.18-19 with ann.

General Instructions for Observing Oscillating Pendulums.

The point requiring the greatest attention of all is the temperature. The temperature of the pendulum is to be ascertained to a fraction of a Fahrenheit degree throughout the observations. As no thermometer can be attached to the pendulum, it follows that the temperature of the room in which the observations are made must be extremely constant. Should this not be the case, the temperature of two thermometers--one at the top, and the other at the bottom of the pendulum--would not indicate the temperature of the pendulum itself, which requires a long time to take the temperature. It will probably be necessary therefore to seize those opportunities on which during the winter the temperature happens to remain constant for a long time. Should the temperature be erroneously determined, it will be impossible to detect the error, and on this account especially great pains must be taken.

Great solidity of the pendulum-support is absolutely essential. When a horizontal force of one kilogram applied to the middle of the point of support of the knife-edge produces a deflection of 1/30 mm, it is ascertained that with the Repsold's Reversible Pendulum, an error of no less than 1/4 mm in the deduced length of the Seconds Pendulum was due to this cause alone. For the pendulum transmitted, this correction would be considerably larger. The support ought to be so stiff that the deflection produced as above should not exceed 1/200 mm. The piers have to be solidly built of brick, laid with Portland cement, and connected at the top by a 2in plank. These piers should be constructed in the Summer, and the observations should be made in Winter, when the piers will be very solid, and when time can be obtained. The distance between the piers on the inside should be half a metre. The flexure of the piers should be measured under the circumstances under which the experiments have been made. This is done by passing a cord carrying the end of it to the middle point of the tongue upon which the pendulum rests, in such a way as to give a horizontal strain parallel to the motion of the pendulum. A long wooden tongue is then to be attached to the tongue upon which the pendulum rests--its general direction being perpendicular to the plane of the motion of the pendulum, that is, parallel to the knife-edges. At the end of this wooden tongue, which may be of any convenient but accurately measured length, is to be attached a micrometer scale, the plane of which is in the plane of motion of the pendulum, and the direction of measurement of which is parallel to the direction of measurement of the pendulum. A microscope carrying a filar micrometer is then set up so as to observe on this scale, and the kilogram weight is to be alternately taken off and put on, so that its effect in producing flexure can be measured. The micrometer scale is to be mounted in two separate positions--one preferably forward, and the other back of the pendulum-support. By means of an arithmetical proportion we shall then obtain from the flexure at the end of the tongue in the two positions the flexure at the middle of the knife-edge.

In setting up the pendulum, the brass head upon which the pendulum rests will first be attached to the 2in plank, either by plaster of Paris or by some other cement, or preferably, by bolts with leaden washers. The leaden washers have the convenience of enabling us to level the plane upon which the pendulum rests by tightening up the bolts, so as more or less to compress the washers. The pendulum can be lifted off of its support so as to rest in the brass Ys. When the pendulum is first put on, these Ys must of course be raised, so that the knife comes down into them, and care must be taken to see that there is no rubbing, either forward or back. It is needless to say, that the greatest pains must be used in handling the pendulum, as the smallest accident might be serious.

The method of observing the pendulum has been fully studied by Mr. Israel. The arc of oscillation had best be neither greater than 25:1000ths nor less than 5:1000ths of the radius. Extreme accuracy in the observations of amplitude of oscillation is not essential. The difficulty lies much more in the observation of the transits of the pendulum. It is recommended that Mr. Israel should practice further in making this sort of observations. An equal number of transits have to be observed from left to right, and right to left. The point from which they are observed is the zero of the scale, and this is done by placing a wire of the telescope in coincidence with the zero line of the scale. The pendulum is to be experimented with on each day, both with heavy end up, and heavy end down. The oscillation with heavy end down should occupy at least an hour and a half, and that with heavy end up about half an hour. It is recommended that two experiments be made each day with heavy end up. If the whole operation is doubled, so as to give four experiments with heavy end up, and two with heavy end down, with good time observations at the beginning and end of the whole series, so much the better. All the chronometers should be compared about the time of making time observations, and also at the beginning and end of the pendulum experiments. The time should be so observed that the probable error of determination does not exceed one-tenth of a second. After eight different days observations have been obtained resting upon different sets of time observations the knife-edges should be taken out and interchanged. The thumbscrews should then be loosened while the pendulum is in horizontal position, and the knives slipped out carefully and immediately interchanged. The thumbscrews should then be tightened up--as tight as the fingers can readily tighten them. In performing this operation the greatest care must be used that no snow, or any other substance gets between the steel and the brass upon which it bears. After this operation is concluded eight more nights oscillations should be obtained. The pendulum should then be put in its box, soldered up, and returned to Washington at the first opportunity. Great care has been used here to have the pendulum quite dry, and the air in the pendulum-box also quite dry at the moment of packing. It is expected that the box will be opened at a low temperature, when there will be little or no moisture in the air; and should the observations terminate the first winter, no particular precautions need be used in packing it up, since the air will have been dry all the time. On the other hand, should it be necessary to make observations on two winters, the box had better be sealed up during the summer to keep it dry. The pendulum sent is intended to be an invariable one, and the observations when received will be reduced upon that principle. But should the principle of invariability fail owing to any injury which the pendulum may receive, it is expected that the observation will still be valuable, on account of its being a reversible pendulum.

In transmitting the records to the office, they should be accompanied by the record of barometric pressure. It is highly desirable that the chronograph sheets should be read off as soon after the observations are made as possible. Should this not be done, however, they can be sent to the office in a tin box, and all the necessary computations will be made here.

If, as we hope, these important pendulum observations should be successful, the gentlemen concerned in making them will deserve great credit, on account of the unusual difficulties which must attend them, and also on account of the great need that there is of the results to be obtained.

216.21-22 preliminary operations in Washington] In a 27 October 1886 letter to Thorn (NARG 23/22), Peirce explained:

The pendulum was oscillated under my direction in June 1881, by Messrs. Farquhar and Israel . . . This work was done in the C. S. Office, Room No. 6, and Professor Hilgard in an oblivious moment, in my absence, allowed Lieutenant Very to take down the pier. It was ascertained that the pier had a peculiar kind of flexure, owing partly to the bad foundation, and partly to the singular sandstone of which it was built; and all things considered, I doubt whether the work done in June 1881 is of any value.

See also ann. 217.9-10 for Farquhar's discussion of this.

217.6-9 Unfortunately . . . plank.] As is clear from his 27 October 1886 letter to Thorn (see ann. 216.21-22), Peirce is referring to Lieutenant S. W. Very, who used a Peirce pendulum to measure gravity in Patagonia in 1882 (Coast Survey Report for 1890, 652), and who may have taken the stone cap to use as a support for the pendulum head at the South American station.

217.9-10 The result . . . no value.] Peirce hoped initially that the preliminary swingings of the pendulum at the Smithsonian might have some long-range value. His April 1887 submission of the report added, "although some result may possibly be deduced from them hereafter." In "On the Pendulum Observations at Fort Conger" which is included in the same appendix, Henry Farquhar (identified at ann. 220.4), commented (716):

The failure, probably complete, of the observations in room 6 of this building is correctly ascribed to the absence of a reliable determination of the flexure of the support. That the deficiency has been irremediable since the removal of the cap-stone is not denied, though, as the flexure must be largely due to the unfortunate situation of the piers over a brick archway, even this is doubtful. But when it is remembered that in such researches large corrections are usually, especially where their exact determination is difficult, variable corrections, that in this case the yielding is described as having been of such a character as would naturally be produced by a cause like imperfectly-hardened mortar under the recently erected piers, and that it might have become essentially changed by a settling of the archway beneath, an accurate measurement of the flexure at the time of the observations is seen to have been the chief desideratum, and the maintenance of this confessedly unreliable stand to have been of far less importance. Results from a later swinging on the same support would not improbably have been misleading. That observations of flexure were not prevented by lack of time, notwithstanding Professor Peirce's illness at the most unfortunate point, is clear, for the stone was removed in August or September, 1882, the pendulum having been swung from it in June, 1881. And as if to fix the responsibility beyond possible question, Mr. Peirce in this report calls especial attention to the liberal discretion allowed him by Mr. Patterson, who was Superintendent until August, 1881. It is certain that Superintendent Hilgard would not have permitted the removal of the stone had not Mr. Peirce failed to impress upon him the importance of retaining it, or had it been given him to understand that observations essential to the availability of work done months before were yet unmade. The simple truth I believe to be, that because of the want of time for proper preparations, the unsuitability of the place, and the newness of the observer, Mr. Peirce expected no valuable results at the time from the swingings in room 6, and attached no such importance to them as he now appears to attach.

217.13 German Normal Meter] For the precise measuments of length required for absolute determinations of gravity, Peirce acquired a line meter from the German Imperial Standards Office in Berlin. For a description of Standard No. 49, see Victor F. Lenzen, "The Contributions of Charles S. Peirce to Metrology," Proceedings of the American Philosophical Society 109 (1965): 29-46.

217.22 Fort Conger] See ann 216.4.

217.27 The directions accompanying the instrument] See ann. 216.19.

217.33-34 This programme was faithfully carried out] In Three Years of Arctic Service, Greely gave the following account (vol. I, p. 180):

the severe cold made the work of the most trying character to our astronomer, Sergeant Israel. He made the observations on the 14th, in temperatures varying from -54° (-47.8° C.) to -56° (-48.8° C.). A few days later, being exposed for a long time to a temperature of -48° (-44.4° C.) in the open observatory, he froze superficially one of his feet. Apart from this the pendulum experiments, though tedious, and involving exposure and suffering, were most fortunately and successfully conducted.

217.34-218.3 but after . . . can be used] Peirce worked for over a year to account for a significant change in the period of oscillation for swingings conducted after the interchange of knives: on average, the pendulum beat slightly longer seconds with the heavy end down than it did with the heavy end up (see also ann. 217.36-218.1). At the time of his April 1887 submission of the report, Peirce was in the midst of an intense and sometimes heated correspondence with Coast Survey colleagues (and with General Greely himself) over his own contention that the anomalous readings were due to some kind of damage to the pendulum. Peirce's eventual decision was to use only swingings made after the interchange of knives, as these could be corroborated with future experiments with the pendulum (see ann. 222.25-27). Farquhar's supplementary report concurs with Peirce's decision but explains how the change in the pendulum may have been due to an accidental loosening of the heavy-end knife edge (718):

One explanation remains: That there was a real difference in the length of the pendulum, as swung before and after the interchange. The mean periods in the two positions were for temperature -20° F. and pressure 29.75in (using the coefficient .00000489):

s. s.
First days . . . . . . . . . . . . . . T d = 1.004514510 T u = 1.003928747
Last days . . . . . . . . . . . . . . T d = 1.004465620
T u = 1.003900929
Differences . . . . . . . . . . . . .000048922 .000027855
Differences, calculated . . . .0000560 .0001672

The distance of edge 9 from its bearing-plane, as measured by Dr. J. J. Clark in January, 1887, is 504.0, and that of edge 10 is 670.6; difference, 166.6. Hence is calculated the theoretical decrease in period, entered above; nearly the observed amount for heavy end down and very different for heavy end up. It seems highly probable, therefore, that the edge at the heavy end was farther from the center of mass at the earlier observations than at the later. This edge, that is to say, was loose, so as to have a play of an eighth of a millimeter on the average until the transposition was made, and was properly tightened after it. Inspection of the earlier heavy-end-up corrected periods plainly suggests (when the lower expansion-coefficient is used more plainly yet) that the play of this edge may have increased progressively, as they show a pretty steady diminution. . . .

A loosening of the heavy-end edge, after the measures made in 1881, might have taken place in one of several conceivable ways. The observer, whose zeal and industry surpassed his experience, could have turned one of the screws holding this edge in place, about the beginning of the experiments, mistaking it for a similar screw by which the pendulum is raised or lowered. An artisan, in packing the instrument, could accidentally have touched the screw. Dirt of some kind could have remained on one of the brass slides holding the edge in place (a recent examination shows that the slide at the name end of the heavy edge-holder is considerably stained with rust, verdigris, etc., over its inner surface, which may be a trace of it) and this dirt not have been squeezed out till after the measures of length (June 11 to 14, 1881, before the pendulum had been swung even in Washington), but become so, gradually perhaps, before the edges were transposed. Without committing ourselves to any one of these possible explanations, we must admit that the hypothesis of a slight loosening of one edge during the first swings is the only one yet suggested that seems to meet the facts.

217.36-218.1 This seems to . . . the pendulum.] For Greely's reply see 243.6-12. See also sel. 36, 280.25-28. At the conclusion of a typescript (1887.28) prepared for the report Peirce gave the following account (R 1076:11-12):

On the first eight days of the swingings at Fort Conger, before the interchange of the knives, the temperature being -13° F., the period of oscillation of an equivalent simple pendulum, uncorrected for flexure, but corrected to bring the pendulum to the length it had after the interchange of knives (on the supposition that the change of length observed in Washington to have taken place during the journey happened at the time of the interchange of knives), was, according to the observations, 10048432. After the interchange, on the following eight days, the temperature being -23° F., the same quantity appears as only 10047795. The discrepancy cannot be attributed to a change of the distance between the knife-edges, for according to the observations at Washington, there was no material change of length during the whole journey. It cannot be attributed to a permanent damage of a knife, because the pendulum after its return gave an excellent value for the gravity at Washington. It might possibly be attributed to a large improvement in the rigidity of the supporting piers, but General Greely does not think that possible. It seems to me most probably due to some frost having been deposited on one or both knives at the time of their interchange. Whatever the cause may be, however, we shall probably ascertain which value to prefer, when we shall have determined by experiment the effect of an interchange of knives upon the periods in the two positions. These experiments should be conducted at extremely low temperatures, so as to reproduce the same conditions, as nearly as possible.

218.4-6 the head . . . was left behind] See 243.13-15 and 244.37.

218.6-7 The pendulum itself was courageously brought away] In his report in the first volume of the Proceedings, Greely elaborated (61):

The pendulum being a heavy and cumbersome instrument, I informed the men that while the saving of it was much to be desired, from the value of subsequent comparative observations, yet it could not weigh against the chances of any man's life, and that whenever any one thought his life endangered by hauling it or anyone insisted on its abandonment I would do so. To the credit of the party no man ever hinted at the abandonment, and most of them were outspoken for its retention to the last.

218.8 the survivors . . . Israel was not one] As supply and relief ships failed to reach the base camp in 1882 and in 1883, Greely and his men decided in August of 1883 to try to make their way south by boat. They reached Cape Sabine, where they were stranded. With dwindling provisions they wintered there. When relief finally arrived on 23 June 1884, only Greely and six of his twenty-four man party were still alive. Sergeant Israel had died of starvation on May 27.

218.9-11 It seems almost inconceivable . . . intact.] See 243.29-36 and 245.4-6.

218.11-12 The chronometer . . . to pieces.] In Three Years of Arctic Service, Greely wrote (vol. I, p. 130):

In default of a break-circuit chronometer, for use with the chronograph in time observations, Professor Pierce [sic ] kindly loaned his own chronometer, which was used in the pendulum work. As a recognition of this action, I felt it incumbent on me to see that the instrument was returned, and so, in all the dark days of our retreat, that chronometer was carefully looked after, and has since been delivered to Professor Pierce.

In a letter of 10 April 1888, to Superintendent F. M. Thorn, Peirce described the damage to the chronometer as follows (NARG 23-22):

A day or two before Lieut. (now Genl.) Greely sailed for Lady Franklin Bay, he found himself in sudden straits for want of a breakcircuit chronometer. By direction of the Acting Superintendent, I let him take Frodsham 2490. When he came back he surrendered it in a terrible state. It was then put in running order and regulated to mean time. I used it at Ann Arbor; but it was found to go very irregularly, and it is probable that some of the spindles or other parts have been slightly bent in a way impossible to detect or remedy and to cause irregular going.

218.14 1/30000] Peirce appears to have used the fractional ratio as an approximation of the increase in the length of the pendulum. The actual increase is closer to a value of 1/31100, according to the measurements summarized at 218.15-17.

218.17 429.3 microns] This value represents the number of microns by which the pendulum exceeded the length of the meter standard (after corrections) as expressed at 240(c7).5. The actual value should be 439.3 microns, unless there is an error in one or more of the correction factors in the table. If the actual value is 439.3, then the fractional variation in pre- and post-expedition length measurements expressed at 218.14 should read 1/23700. Since the calculations underlying the correction factors have not been recovered, the pendulum length value as expressed in the copy-text is retained.

218.17-18 The pendulum was oscillated at the Smithsonian] To remedy the removal of the piers in Room No. 6, the pendulum was compared with the other Peirce pendulums, as Peirce explained in a 27 October 1886 letter to Thorn:

I bestowed much care on the comparison of the pendulum with the other Peirce pendulums. These operations, which were conducted at the Smithsonian by Mr. W. B. Fairfield and myself, lasted almost continuously from 1884 December 19 to 1885 February 18, all the Peirce pendulums being oscillated.

218.36-37 lost from 10 to 15 grammes] For Greely's comments, see 243.23-36. In an earlier hectograph of the report (1887.18), Peirce presented the issue as follows:

Now, on the return of the pendulum it was weighed and found near 10436 grams, so that it must certainly have lost at least fifteen grams upon the journey from Fort Conger to Camp [Clay], unless we are to suppose some great error had been committed in the weighing. Moreover, we find that at Fort Conger, during the last eight days swingings, the difference in time of the oscillation of the pendulum in its two positions was 00005689, this was at about -30° C. On the return of the pendulum to Washington, the same difference was found to be 00007514 at +20° C. The difference of temperature would account for about two thirds of this discrepancy; the rest must have been due to a change in the pendulum, unless it can be accounted for by the difference of the flexure of the supports. On the whole, then, we seem to have positive evidence that some piece of metal of considerable size came away from the pendulum. I was extremely desirous of making further experiments upon the pendulum before the knives were removed, but contrary to my earnest representations, and without my knowledge, they were taken out of the pendulum in January 1887; and doubtless sustained some injuries at that time. At any rate, the invariability of the pendulum has been destroyed; and it will be fortunate if the whole value of the magnificent work done by Greely and his party, in the determination of gravity and the figure of the earth, does not turn out to have been brought to naught in a single day, by an act which might well be called criminal, were officials considered bound to exercise intelligence.

218.37-220.1 Camp Clay] The encampment at Cape Sabine, named after Henri Clay who wrote an article for the Louisville Courier predicting the disaster awaiting the expedition, and urging that Cape Sabine be provisioned. A copy of this article was included among the provisions brought to Cape Sabine which allowed the expedition to survive the winter (see ann. 218.8).

220.1-8 The centre . . . a change] In his supplementary report Farquhar commented (716):

The loss to the service from the necessity of using for the Peirce pendulums a center-of-mass apparatus adapted to a smaller stem Professor Peirce slightly overrates. In consequence of the forced removal of parts of the apparatus the measure is rendered more difficult with the new pendulums; but as two independent determinations of the distance hu, made last January, gave (when reduced to edge 9 at heavy end) 25.140cm and 25.135cm, it is improbable that the uncertainty of the result can be so great as to admit the earlier value, 25.105cm, as an equally exact observation of the same quantity. I have not examined the 1881 observations with care, but I believe them to have been less complete than those of 1887.

220.4 Mr. Farquhar] Henry Farquhar, Coast Survey employee who assisted Peirce in his Photometric Researches and in pendulum research; see W4:116 (1879) and W5:8 (1884). Farquhar wrote a report discussing the charges made by Peirce, which was added to the appendix in which Peirce's report appeared.

221.3-6 Still . . . consequences] The greatest obstacle Peirce encountered in reducing the Arctic gravity data involved the 47° C difference in temperature between the calibration station in the Smithsonian and the Arctic field station at Fort Conger. The initial submission (1887.21) identifies the first- and second-order atmospheric effects on such pendulum operations, and also speculates about "other atmospheric effects, not yet taken into account in reducing pendulum operations." In rewriting the report, Peirce came to the conclusion that these factors were, in effect, cancelled out "as long as the pendulum is treated as reversible." This conclusion allowed him to remove the lengthy tables of atmospheric effects, which appeared in the initial submission (1887.21), the subsequent typescript (1887.28), and the uncorrected first galleys (1887.3) between pages 236 and 237. In 1889, Peirce prepared a more fully developed form of the atmospheric notations and tables for the 1889 Gravity Report (sel. 36).

221.10 U.S.C.S.--C.S.P.--1878--B] As measurements are made at different temperatures, the coefficients of expansion of the pendulum and of the meter scales need to be determined. To establish this the pendulum meter, which is assumed to have the same coefficient as the pendulum, was compared at different temperatures with meter No. 49. To determine the coefficient of expansion of No. 49 itself, Peirce compared it with one of two meters he had made for the purpose, which are marked U.S.C.S.--C.S.P.--1878--A and U.S.C.S.--C.S.P.--1878--B respectively (also called Meter A and Meter B). See also ann. 350.19-20, and W4:120ff. (1879). For a description of the comparison of meter bars and the use of a comparator, see Victor F. Lenzen, "The Contributions of Charles S. Peirce to Metrology" (cited at ann. 217.13), pp. 34ff.

221.13-14 "Measurements . . . at Initial Stations."] W4:79-145 (1879).

221.15-16 D. C. Chapman] Coast Survey mechanician; see also ann. 286.28-29.

221.31-222.8 The coefficient 18.24 . . . 17.61] In his supplementary report Farquhar provided the following comment, reemphasizing his rival hypothesis of a loose knife-edge (719):

The probability of a loose knife-edge is the real justification of the course properly followed by Mr. Peirce in depending on the latter half of the observations alone for a value of gravity. One correction to his final result appears, however, to be needed: An increase of the expansion allowance by 0.0000074.s He states that his expansion "coefficient 18.24is for the temperature of 24.6° C.," apparently because the comparisons between Pendulum No. 1 and Meter B were made about that temperature. But the observations of Meter A, on which the adopted coefficient for B depends, were made (1876 Report, page 274) about 8° C.; taking this as the temperature at which the coefficient 18.24 holds good, we have as the value for -7.7° C. 17.93.

221.32 Fizeau] Armand Hippolyte Louis Fizeau (1819-1896), French physicist. On page 1129 of the paper referred to, Fizeau gives an expansion coefficient for yellow brass of 18.59 millionths at 40° C with a variation of 1.96 millionth per 100° C. This gives an expansion coefficient at 24.6° C of 18.29 millionths (rounded up).

222.17 Repsold pendulums] For a detailed description of this type of pendulum and Peirce's involvement with it, see Lenzen and Multhauf, "Development of Gravity Pendulums in the 19th Century" (op. cit.), 320-27.

222.25 Minneapolis] Peirce suggested this location to examine the influence of low temperatures on the pendulum, so as to better evaluate the results obtained on the Arctic expedition. Reacting to the Survey's refusal to honor his requests for further cold-weather observations, Peirce ended the first draft of his report with the following attack on the Coast Survey (1887.18):

Consequently, it would be utterly impossible, in the present state of our knowledge, to make the slightest use of Greely's observations to determine the force of gravity at Fort Conger. For the error due to erroneous expansion through 40° C might easily, and indeed probably would surpass the error of the general formula from the form of the earth as known. Meantime, until the Coast Survey does the part which it agreed to do, the observations remain monument to the strict scientific care, industry, and skill of Greely and his companions; and if they are not rendered nugatory by the various blunders of the Survey may at some future time (when scientific questions shall again be treated as matters of legitimate inquiry by those in whose hands the power of government resides), completed according to the original plan, furnish an important contribution to human knowledge.

222.25-27 But . . . be used] In galley revision, this brief passage replaced a long section in the April 1887 initial submission describing how expansion (due to temperature) and the apparent change of length of the pendulum during the Arctic journey prevented Peirce from calculating a value for gravity at the Arctic station. In the original submission, Peirce provided a version of the linear interpolation for temperature expansion, but cautioned against using it for the extreme range of temperatures involved in the Arctic work (R 1076:11):

At present, I can only say that for moderate differences of temperature the expansion should be taken at about 22 microns per degree centigrade. But over a range of 47 degrees, this might involve an error of over a third of a millimeter.

Peirce continued the original discussion by revisiting the issue of damage to the pendulum, which he felt occurred at the time of interchange of the knives. Without further observations at low temperatures, Peirce felt that "the reductions can proceed no further." Peirce's subsequent decision to use "only the observations made after the interchange of knives" (218.1-3) apparently cleared the way for him to use linear calculations to determine expansion per degree centigrade and to complete the gravity determinations.

222.28-32 Elaborate . . . detail.] This statement appears in the initial submission after the table at 241, which concludes the data run on the descent of the pendulum arc during oscillations. In the original, Peirce commented further on Farquhar's corrections for arc (1887.21, 10): "His reductions have a value in showing the general uniformity of the descent of arc. An improved method of reduction will, however, be given in my description of the Peirce Pendulums." Neither this reference, nor Peirce's description of the pendulums appeared in the final report; he eventually completed a draft of the description for the 1889 Gravity Report (sel. 36).

235(c19).3 1.0045337] Calculation from previous data shows that this uncorrected period should read 1.0045386.

236(c17).11 1275.218] Calculation from previous data shows that this interval should read 1275.319.

236(c17).32 3190.275] Calculation from previous data gives an interval of 3190.305.

237(t1,c15).1 1.0045498] In his offprint copy, Peirce has made additional working calculations around the mean value for the period of swings made with the heavy end down and before interchange of the knives. The result is a correction of +0.0000428 seconds, correcting the mean period of oscillation for these swings to 1.0045926 seconds. The calculations for this correction cannot be verified, nor can it be known if this correction alters subsequent stages in the determination of gravity for the Arctic station. Given this degree of uncertainty, the original copy-text reading is retained.

238(t1,c11).10 1.0039554] Given the previous data, this corrected period value ought to read 1.0039464. The error affects the subsequent corrected period.

238(t1,c11).13 1.0038852] Based on previous data, this corrected period value ought to read 1.0039174. The error affects the subsequent corrected period.

238(t1,c15).1 1.0039485] In addition to the correction of mean period of oscillation for heavy end down swingings of the pendulum prior to exchange of knives, Peirce also made further calculations in his offprint for the mean period of heavy end up swings prior to exchange of knives. The result is a correction of +0.0000261 seconds, correcting the mean period for these swings to 1.0039746 seconds. The basis for these calculations is unknown, as is the effect on subsequent stages in the gravity determinations; with no certain basis for emendation, the original copy-text reading is retained.

239(c13).16 392.9] Based on previous data, this corrected excess ought to read 393.9.

240(c7).5 +429.3] The final addition should give 439.3. See ann. 218.17.

240.2-3 Mr. W. B. Fairfield] See ann. 286.23.

241.1-242.1 In comparing . . . north pole] Farquhar continued his discussion of the increase of the expansion allowance by describing the effect on the station error in Peirce's final results (719):

Increasing Td, Tu, and the "reversible pendulum" period by 0.0000074s, we must increase the double logarithm by 0.0000064, when the "station error" becomes -0.0000097, and the conclusion in favor of a term in odd powers of the sine of the latitude is correspondingly weakened. It should be remembered that this result is subject to three uncertainties: Whether the latter observations were alone made with a pendulum of the length found in 1884; whether, in correcting periods of the simple pendulum for temperature, allowance for the expansion of the metal is sufficient, and whether the unusually rapid decrement of arc at this station was due to a cause that left the period unaffected. Another point, which does not appreciably affect this result, is nevertheless worth noting. If the reversible-pendulum period equals (74.914 Td - 25.160 Tu):49.754, 3/2 Td - 1/2 Tu must be increased by 0.0057(Td - Tu) = 0.0000040s at the Smithsonian, 0.0000037s at Fort Conger. This might be diminished by 2 in the seventh place to allow for the factor under the radical in the first formula above. Professor Peirce, at the end of his report, uses a quite different correction.

241.2-3 a figure of the earth which I have deduced] Peirce is probably referring to his "On the Mean Figure of the Earth from Determinations of Gravity. Second Paper. The formula for the Earth's ellipticity in terms of the variation of gravity with the latitude" (1888.4).

241.3-4 Kater invariable pendulums] Henry Kater (1777-1835), English geodesist who introduced in 1819 an invariable compound pendulum with a single knife-edge of which thirteen were constructed and swung throughout the world. See also W4:148 (1880); W4:529 (1883).

241.4-5 the expedition of Mr. Edwin Smith] Assistant at the U.S. Coast Survey. This is probably the expedition for the determination of gravity at various points in the Pacific Ocean under Smith's charge. This expedition used a Kater pendulum that was on loan from the Royal Society. See Peirce's 24 February 1886 letter to Thorn (NARG 23/22).

243.7-8 No accident . . . to this pendulum] In his report in the first volume of the Proceedings, Greely also stressed that no damage came to the pendulum (15):

The instructions of Assistant Charles Peirce, of that service, were followed as closely as practicable, and fortunately no accident or mishap occurred in the course of the observations. The pendulum itself was brought back in good condition, so that further comparable observations may be made with that instrument.

In reply to a letter Peirce wrote after seeing Greely's memorandum, Greely again explained (RL 174:6, 30 November 1888):

I have never considered this question otherwise than impersonally and I should in no way have considered the question as involving any imputation upon Mr. Israel or myself. It would have been a grave reflection upon both of us if the scientific world believed that an accident having occurred, the commanding officer failed to fully and clearly set forth the nature of such accident. The whole question for the scientific world to pass upon is whether your hypothesis is correct or not.

243.12 again soldered up in the original tin box] See ann. 216.19.

243.13-15 The statement . . . left behind] See 218.4-7, and 244.37-38.

243.23-36 Later the statement . . . and life.] See 218.26-220.1, and 244.39-245.1.

243.37 as suggested in the following Supplementary Report] Henry Farquhar's "On the Pendulum Observations at Fort Conger" which he was requested to write by Superintendent Thorn (716): "to clear up the question of responsibility with regard to certain charges explicitly or implicitly made by Assistant C. S. Peirce against the management of this office in his report on the Pendulum Observations at Fort Conger." See also 245.7-11.

243.44-244.2 On one occasion . . . one-quarter of the usual time] In a 30 November 1888 letter to Peirce, Greely explained (RL 174:6):

On one occasion, when the decrease of arc of oscillation was so rapid as to show conclusively that the vibration would not continue more than one-fourth the usual time, Mr. Israel suggested that one of the screws might be loose, and on that occasion he entered the pendulum house alone and stopped the pendulum, readjusted the screws, and set the pendulum again in motion.

244.18-19 the former . . . written instructions] See ann 216.19. Also, in Three Years of Arctic Service, Greely wrote (vol. I, 130): "My astronomer, Sergeant Edward Israel, had received from Professor Pierce [sic ] careful and detailed instructions concerning the pendulum work."

244.33 imputing blame] See the Peirce-Greely correspondence in RL 174:3-10.

245.4-5 was absolutely unavoidable] After seeing Greely's memorandum, Peirce wrote to Greely on 27 November 1888 (RL 174:4; draft):

Looking at the question from a purely impersonal point of view myself, and advancing my hypothesis as a means of strengthening, and not of weakening, the determination, I did not realize that you would consider an accident, which in my opinion was absolutely unavoidable, as involving any imputation upon you or Mr. Israel.

245.9-10 a certain derangement of apparatus] See 217.6-9 and corresponding ann.