Letter from Charles S. Peirce to Carlile P. Patterson
(New York, 06.09.1877)



 
Spanish translation & annotations
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New York, 6 de septiembre de 1877


Dear sir,

You ask me to send you "the whole paper proposed to be submitted" to the International Geodetical Union. You have already had the paper submitted to you, and I think I shall answer your desire now best by sending a full abstract of it, as I cannot get the whole thing copied inside of several days.

The paper opens with a strict mathematical analysis of the problem of the oscillation of a pendulum on a slightly flexible stand. I will send a copy of this part as soon as possible; meantime I may mention that the result of the investigation is that the length of the seconds pendulum as determined by a reversible pendulum on a flexible stand requires a correction of

+MS /l


where m is the mass of the pendulum, s is the hori-

 

zontal deflection perpendicular to the knife-edge of the middle of the support of the knife-edge under the influence of a force in the same direction equal to the unit of weight; the length of the seconds pendulum; and l is the distance between the knife-edges of the pendulum used.

The second part of the memoir is experimental. The first series of experiments described are direct determinations of s. The general plan of these experiments is as follows. The tripod being set up ready for the pendulum, it is first ballasted by a weight of some 10 kilogrammes on its lower part. A cord is then attached to the middle of the support of the pendulum. This cord is stretched out horizontally and sideways (i.e. perpendicular to the direction of the knife-edge). At a convenient distance from the stand, it passes over 1/4 of the circumference of a pulley wheel, so as to turn from a horizontal to a vertical direction and to its extremity a kilogramme is alternately attached and detached. This attachment and detachment of the weight causes

Puede verse debajo la página siguiente de acuerdo con la encuadernación de la correspondencia en los National Archives. Se pierde la continuidad de la redacción, probablemente porque entregó una sección de la carta a un copista. Quizá se trata de las páginas manuscritas de Charles S. Peirce que se reproducen debajo de esta, de acuerdo con la propuesta de Max Fisch:

 

I can write no more of this today but will send the rest so you can have it by Monday morning.

In writing out this abstract I have enlarged somewhat the precautions to be taken; which are not given in such detail in the paper sent; but they are in that paper given quite fully enough for the understanding of the gentlemen addressed.

I have engaged a stateroom on the Steamer Suevia which sails for Hamburg on Thursday next, & am strongly in hopes of having leave to go. It would be well for me to have an official passport, if not too much trouble. If I am to go it would be convenient to know by Tuesday morning, but I shall not consider Thursday morning as too late. Later than that would compel me to sail for Liverpool thus adding to the expense.

Yours very respectfully,

C. S. Peirce

 

C. P. Patterson Esq.
Supt. U. S. Coast Survey
Washington DC.

 

 

En el volumen de cartas de Charles S. Peirce a Carlile P. Patterson hay otras páginas encuadernadas que pueden ser —tal como sugiere Max Fisch en su transcripción— las que faltan en esta carta del 6 de septiembre.
horizontal deflections of the support of the knife-edge owing to the elasticity of the brass of which the stand is composed. The horizontal deflection is measured as follows. Attached to the support of the knife-edge is a micrometer scale, the plane of it so that the direction of the knife-edge is perpendicular to it; and with its lines vertical, so as to be suitably placed for measuring the horizontal sideways deflection. In front of this scale and looking at it, is a filar micrometer microscope at the focal distance and with the moveable wires vertical. This microscope rests on a stand entirely separate from the pendulum-tripod. When the weight is put on or taken off, an observer looking through the microscope sees a deflection one way or the other and can measure it with the filar micrometer. The deflection so observed would be s if the micrometer scale were in the middle of the support of the pendulum. But the scale obviously cannot be placed there but must be either
forward or backward of, or above or below that position. Now the deflection produced is in this special case in the direction of the force, but the deflection is a rotation of the support of the knife-edge around an axis. It is therefore necessary to discover the position of that axis and then from the relative distances of the scale and of the middle of the support of the knife-edge from that axis to calculate the value of s. To discover the position of the axis I place the scale 1st at three different positions in the direction of the knife-edge (it being always firmly attached to the support) and also 2nd at three different heights in the vertical of the end of the knife-edge, and in each of these five or six positions the deflection is roughly measured, a specially accurate set of experiments being made with the scale as near the middle of the knife-edge as is convenient.

The memoir gives in detail the method of conducting the experiments; the following points

 

1. In setting up the tripod, pains must be taken to see that the parts which come together are clean and free from grease or other yielding substance and the nuts must be screwed up very tight. Also the feet must have a solid support & the binding screws of the feet must be tight.

2. To ballast the tripod, one block of wood is placed in front of the scale at the lower part and another behind, and the 10 kilogramme weight rests upon them.

3. Thick silk braided cord has always been used.

4. The manner of attaching the cord requires notice. In the middle of the tongue supporting the knife-edge on its upper side is a semicircular notch, crossing from side to side. This notch marks the middle of the knife-edge. The cord is wound tightly round and round the tongue so that it fills up the notch until the middle of the cord is on the level of the support of the knife-edge. It must be arranged that when this level is reached the cord

 
is precisely in the centre of the notch. Then is the moment for the winding to stop and it must be stretched out horizontally.

5. Pains must be taken to see that the cord is horizontal. In Berlin it was not quite so, and the inclination was measured and taken account of.

6. Pains must also be taken to see that the cord is precisely perpendicular to the knife-edge.

7. For the pulley-wheel the wheel of an Atwood machine is recommended.

In Geneva and Paris wheels belonging to instrument shops were used. That at Paris had considerable friction, as was shown by relieving the cord for a moment with the weight on and the pulling the other way for a moment when it was seen that the deflection had a constant difference under these circumstances.

In Berlin and Hoboken, Atwood machine pulleys were used, and no such phenomenon of friction could be detected. In Berlin the axle of the wheel rested on friction-wheels of considerable diameter. The wheel belonged to the Royal


 



 

 
Institute of Technology and was kindly lent me by Professor Paalzow. The wheel used at Hoboken was a fine one constructed in the workshop of the Stevens Institute and belonging to that institution.

8. There may be a friction of the cord on the wheel or a stiffness of the cord acting as a resistance. This should be tested by the method just mentioned.

9. The pulley should have its supports at an angle of 45º to the horizon and should therefore rest on a desk-like stand.

10. The pulley should be accurately placed

a. With the top of it at the height of the knife-edge.
b. With its plane perpendicular to the knife-edge.
c. Opposite the middle of the support of the knife-edge.

11. The whole theory of the subject rest on the assumption that the deflection of the stand is owing to any ricketiness of it but is a

 
true elastic flexure. The test of this is to see that on taking off the force it always and instantly returns to its original position. This is an important part of the observations.

That a considerable elastic flexure must exist can easily be seen by some calculations from the coefficient of elasticity of brass.

12. The best sort of micrometer scales are the ruled on glass. These were used at Hoboken, where a German silver scale was used, the value of which was determined in the Berlin office of weights and measures.

13. Care must be taken that the micrometer scale is

a perpendicular to the direction of the knife-edge

b has its lines vertical. This should be carefully determined, and looking at the lines with one eye and a plumb line with the other is a worthless method of doing this. The lines should be made parallel to the micrometer [il.] & the micrometer screw should be made horizontal to the spirit-level.

 

The microscope should have a magnifying power about 50 diameters.

Care should be taken that the optical axis of the microscope is parallel to the direction of the knife-edge.

The support for the microscope is a matter of study. It must be made as stiff as possible and it is not to be expected that it can be so stiff as not to be moved in turning the micrometer screw unless the latter is handled with the highest possible hand.

Wooden supports are objectionable because they are continually in a state of spontaneous movement, quite surprizing. A wooden stand strongly stiffened by taut iron wires has proved the worst of all supports. A long table will answer pretty well. But I was best satisfied with a support used in Hoboken made entirely of stalk. Into a cast-iron foot was screwed a gas pipe of some 10 centimetres diameter and of the requisite height. Upon the top was a rather

 
heavy brass cap fixed by set-screws. This cap is a table top with clamps upon it for fixing the support of the microscope.

17. The method of observing the deflection employed by me depended on the kind of stand for the microscope which was used. In Berlin, the stand was of wood and owing to its movements, it was important to make the experiments as quickly as possible. I therefore made single readings of the micrometer with the weight on and off alternately, making 11 readings one way and 10 the other so that the mean time of both should be the same. In Hoboken, on the other hand, I read on two micrometer lines each time, and an equal number of readings each way.

18. In measuring the deflection care must taken not to shift the weight of the body from one leg to the other, as scarcely any floor even of the most solid masonry is sufficiently unyielding not to allow great errors to be introduced in that way.

19. That the deflection produced is really in the direction of the force, when the latter is horizontal and perpendicular to the knife-edge, may be induced [?]

 
from the symmetry of the tripod. This symmetry is therefore an important property and it should not be disturbed.

20. In order to place the scale in different positions, a piece of lath is fastened to the tongue on which the knife-edge rests, either vertically or horizontally and the scale is placed at the end of the lath. The force applied undoubtedly bends the tongue more or less, but this cannot affect that pent between the point of application of the force and the extremity of the force. In attaching the lath, therefore, it should be fastened to this part only. It may be fastened by a wooden clamp [il.]. When the scale is at different heights, of course different supports for the microscope has to be used.

These are the chief precautions which are generally necessary in conducting these experiments. A number of others have to be observed under especial circumstances but the skillful manipulator will discover them for himself, and certainly no other person should undertake this sort of work.

 

 

The memoir next proceeds to give the detailed results of the various experiments  which have been made.

First, experiments, as described above, to determine the position of the instantaneous axis.

A. Experiments at the level of the knife-edge. Hoboken, 1877 March 10, Temp. 13º C.
Distance of the scale
in front of the end of the tongue
Deflection in revolutions
of the micrometer screw
Observed/Calculated
-0.m496
+0r211
+0.209
0.053
+0.356
+0.358
+0.318
+0.436
+0.431

The quantities in the last column are calculated on the assumption that the axis cuts the level of the knife-edge at a distance of 1.m355 behind the front of the tongue.

B. Experiments in the vertical of the front of the tongue. Hoboken, 1877 March 12. Temp. 14º C.

Distance of the scale
below the knife-edge
Deflection in revolutions
of the micrometer screw
Observed/Calculated
-0.m441
+0r196
+0.196
0.000
+0.340
+0.332
+0.395
+0.446
+0.454

 

 

 

Transcription by Max Fisch, revised by Sara Barrena (2017)
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 "La correspondencia del tercer viaje europeo de Charles S. Peirce (septiembre-noviembre 1877)"

Fecha del documento: 5 de octubre 2017
Última actualización: 21 de noviembre 2017
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