Letter from Charles S. Peirce to Carlile P. Patterson
(Paris, 02.03.1876)

Spanish translation and annotations


Paris, Avenue Matignon 11
1876 March 2


C. P. Patterson Esq.

Supt U. S. Coast Survey

Washington D. C.

Dear Sir,

I write to you tonight under peculiarly disadvantageous circumstances and must therefore ask your indulgence if my letter is more unsatisfactory than usual. I finished today my experiments in Paris and got my instruments all packed up. My trunks and boxes are also very nearly packed and unless something unforseen occurs I shall leave Paris the morning of Sunday the 6th. I am obliged to wait till then on account of instrument makers’ work not being ready. Everything has been in pell-mell in my room for the last ten days owing to the man who does my work being ill, and two days ago he died. You can therefore imagine that my thoughts are disarrenged like my surroundings.

My Geneva work was practically all computed some


time ago, but I find there was a difference in the resistance of the knife-edges, which will lead to my elaborating the computations very much. Meantime, treating the matter in a simpler way, I find the results satisfactorily harmonious, although I could have wished them to be more so. I proposed sending a special report on the Geneva work but on consideration, I concluded that too much time would be wasted in doing so, at a moment when it was important to have the time for other matters. I might however send you a summary of the results and will do so in my next letter. I cannot do so now as the papers are packed up.

The conditions of the experiments in Paris have been much better than in Geneva, but still not in every respect all that could be wished. They have been made in the same hall where Biot made his experiments. But I must say that it is not a remarkably good place. It is in the second storey of the building and although built on arches of great solidity, it is not so solid as a stone or brick pier. But it is necessary to choose between a building the great thickness of whose walls etc. render the error of temperature (the worst point in pendulum experiments) a minimum and a temporary building with


a more solid foundation. Where I have made my experiments, a person walking on the floor close to the pendulum (of course nothing of the sort was permitted) would cause a deflection of the stand of 1/30 of a second of arc. Borda’s stand being screwed to the wall was I suppose more stable. On the other hand Borda most unaccountably swung his pendulum at the southern end of the hall where the difficulty of measuring the temperature was very great, compared with what it is at the north end where I have swung.

Before making my experiments I measured the flexure of my stand but having neglected to identify the particular division of the scale which I made use of I was obliged to repeat my experiments on this subject after finishing my work of swinging. Both sets of experiments were made with the same microscope and micrometer and the value of the screw ought not to be very different for the two. In both cases a weight of one kilogram was applied horizontally to the stand by means of a pulley. The first set consisted of four experiments which gave the following results (assuming a certain value of the micrometer screw thread)

mean           0.03748 (símbolo) 0.00004


So this has to be applied a correction for the friction the pulley and this was not so well determined. Ten measures of the double of it gave the following results


Mean                   0.0024 (símbolo) 0.00013

Applying the friction we have 0.0387 mm (símbolo) 0.0001 mm. To this is to be added another correction the precise value of which I cannot give at this moment, my things being packed up, but it cannot differ but very little from .02 of the quantity. It depends on the scale being a little below the fulcrum. This brings up the value to 0.0394 mm. The second series of experiments were not so accordant. The deflection produced by the weight (assuming the same value of the screw) was in five experiments


0.0360 (símbolo) 0.00017

Five determinations of double the friction gave


0.0070 (símbolo) 0.00019

which gives as the result 0.0395 mm (símbolo) 0.0002

I may mention that the temperature during the first set of experiments was 1º.2 C and during the second 8º.0 C.

Thus the two sets of


¿? as well as could be desired. The correction to the length of the seconds pendulum is about 6 ¼ times the flexure produced by one kilogram and therefore the probable error of this correction will be only 0.0013 mm which is satisfactory. The value of the correction is about 0.25 mm which is about what the comparison of Albrecht’s and Bessel’s values of the Seconds’ pendulum would lead me to suppose. For Albreght’s value requires a correction of 0.18 mm to bring it to Bessel’s and it is reasonable to suppose that the flexure of Bessel’s apparatus was a third of the other. The latter flexure has been measured by Dr. Peters of Altona, but I am not informed as to the result.

Every possible precaution was taken in my experiments here, except that I committed almost throughout a fault which I did not recognize till it was too late. In commencing the experiments I took the pendulum out of its box an put it on its stand with thickly gloved hands and allowed it a quarter of an hour to take its temperature. This time I was determined by experiments made for the purpose. But I overlooked the circumstance that the temperature in the box was perceptibly different from that of the stand and therefore more time ought to have been allowed. But as in practice a considerably greater time generally elapsed before beginning to swing, I don’t think the oversight can possibly have had any serious effect.

My bond chronograph was found to work badly, and I therefore


used an instrument constructed on the Hipp principle by Breguet. This leads me to say that my experience has generally been that the Bond chronograph does not bear transportation well. Observations of transits of a pendulum have a high degree of precision, the probable error of a single transit being only about 0s. 02. Of course I am naturally led by this to being very particular about my chronograph running perfectly. Now the Bond chronograph when in perfect order divides the second as accurately as the sheet can possibly be read when the finest attainable line is marked. In fact, when the large wheel  which turns with moderate rapidity appears to the eye to move without the slightest hitch, nothing more is to be desired. But I have found it difficult and sometimes impossible to secure this state of things in travelling about. I have therefore purchased of Breguet a Hipp machine, as a second string to my bow or a second anchor, if you please.

I have also promised Breguet to order of him a printing chronograph and he is now at work upon the designs for it. I have ventured to do this notwithstanding the economy which I suppose will be forced upon you during the next year, on account of the very great importance of obtaining a practical instrument of that sort, and the great advantage of getting such a man as Breguet interested in it. Mr. Breguet has executed several gravity governors upon a plan invented by Mr. Villarceau. The accuracy with which these work is really marvellous. For a few hours they will rival a chronometer. And what distinguishes them from the Foucault go



vernors is that they take their velocity almost immediately. Another very pretty thing about them is that the axis of rotation can be set at any angle with the vertical so as greatly to increase the velocity if desired. One principal reason of their working so well is the exquisite workmanship and the pains that has been taken, by the use of wheels to avoid friction. Mr. Breguet is so in love with them that he wished to make the printing chronograph depend on such a regulator, but that I could not consent to for an instant. This would imply trusting to the uniformity of the movement of the regulator during considerable intervals, five minutes or so, and when I reflect that a very little dust or the smallest particle of rust will put the machine all out of condition, I cannot consent to that. On the other hand, Breguet thinks it wrong to abuse the principle of electricity, and I am not sure that he would not wish almost to expunge it from the chronograph. Certainly his opinion carries weight, considering his great experience with electric contrivances. And the ordnance officers in America have I believe abandoned electricity in their apparatus for measuring initial velocities. But what I propose is to have a Villarceau governor and then  if that don’t suffice incline the axis a little so as to make its velocity a little too great and bring it up with an escapement worked electrically by the chronometer or clock with the intervention of a bond spring-governor.

I have been greatly impressed with the instrument-making establishments here of every kind, and of the immense advantage Paris has over every other place on that account for the prosecution of all physical researches.

When my experiments here were all but finished, I received word



from Turretini of Geneva that my vacuum apparatus was ready. I sent on to him to pump it out and report how much the manometer rose in four days. He sent me word 2 millimetres. Assuming this to be true, it is very good. One wonders a little at a chamber leaking so little and not being absolutely stanch. On receipt of this news I had to decide what my course would be. I have come to a decision which I hope will meet your approval. In view of the short time now before me, and the probabilities of complications and delays in the use of a new apparatus, I think it is better to continue with the present one during my experiments in Europe, trusting to a subsequent study of the difference, if any, in the results obtained in vacuo. I shall thus be limiting my ambition to something comparatively easy, namely to determine the force of gravity at the four cities Geneva, Paris, Berlin, and London to about 3 millionths. I confess that I feel that the difficulties multiply so immensely as the limit of error is sought to be diminished that I feel as if long months might elapse before they were all conquered, if I attempt much more, although I cannot foresee what they would be. I shall therefore go to Berlin immediately and to Geneva afterwards to inspect the apparatus.

I have not yet got leave to swing in England, although I feel that there are several ways in which I can certainly cut the knot when the time comes. Mr. Lockyer begged me to permit him to take up the cudgels for me but I wouldn’t. He would raise a row, you know. I don’t think that is at all necessary. I think Gassiot could arrange it very easily as he really owns the Kew observatory.

Yours very truly and respectfully

C. S. Peirce




Transcription by Max Fisch, revised by Sara Barrena (2014)
Una de las ventajas de los textos en formato electrónico respecto de los textos impresos es que pueden corregirse con gran facilidad mediante la colaboración activa de los lectores que adviertan erratas, errores o simplemente mejores transcripciones. En este sentido agradeceríamos que se enviaran todas las sugerencias y correcciones a sbarrena@unav.es
Proyecto de investigación "Charles S. Peirce en Europa (1875-76): comunidad científica y correspondencia" (MCI: FFI2011-24340)

Fecha del documento: 18 de marzo 2014
Última actualización: 21 de marzo 2014

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