Letter from Charles S. Peirce to his father Benjamin Peirce
(New York, 11.02.1877)

Spanish translation & annotations


New York, 1877 Feb 11


My dearest Father,

I have been on the Washington and in spite of the imbecility of Mr. Hein, have got the matter straightened out, I believe. I shall be able this week to pay the Barings about half of what is due them & I expect to make all right without troubling Jem further. I have this morning received a note from Pickering in which he proposes to consider any claim I may


have of a definite kind against the observatory (and I have such a claim) and to meet my less definite claim proposes that I apply for money to the Rumford Committee. I will send you his note tomorrow. I haven't yet considered it.

But I note this. Whatever Pickering may think, it would be greatly to his interest & that of the observatory to attach me to it, loosely. Why don't he combine that idea with his other about the Rumford Committee? I really think he thinks my photometric



observations are bad. He is thinking of the probable error of such observations in the laboratory which amounts for a single obs'n only to about 1/125 which by different contrivances may be reduced one half. For instance, by varying both sights at once, in contrary directions. Now the uncertainty of my stellar measures is 1/10 for each star. That seems large. But observe. 1st This figure is not derived from the comparison of my observations among each other, but by the comparison of different observers among each other, so as to include all sources of error. 2nd My probable error is smaller


than that of any other observer. 3rd He is after devoting himself to magnitudes for 20 years declared that it was impossible, owing to atmospheric sources of error, to express magnitudes to tenths (= nearly 1/10 of the light). Yet this I have done. 4th In the present state of our knowledge magnitudes accurate to tenths would give an important basis for conclusions about this distribution of stars 5th If magnitudes can be measured closer at all, the process must be so long as to prevent the whole heavens being gone over with it as I propose to date tenths.

Our friend Pickering don't know how to appreciate my work; that's all.

While in Washington, I met Major



Torining of the boundary survey. He impressed me a good deal by his scientific spirit, & mentioned that he had a discussion of the systematic errors of the catalogues for the declinations of stars in the zone where he used them. Now you know there was a list of latitude stars printed by the Coast Survey. Hilgard at that time had the idea of getting the Cambridge Obs'y. He accordingly took the matter into his own hands & out of Schott's & made a great mess of it. He is now going on to get out a catalogue of exact declinations. In my opinion, it is going to have a bad effect on the reputation of the survey. He has sim-


ply used the ordinary authorities employed by Schott in working up the places of single stars. But though you can't get the place of a single star any better, it seems to me that a Catalogue is quite a different thing & that it will be thought pretty ordinary work. If Hilgard wants an observatory, the less display he makes of his astronomical proficiency the better. I suggested to Patterson that before that was printed the plan of the work should be submitted to some counsellor of counsellors. Perhaps the best way would be to get Hilgard himself to see that something more will be expected.

In Washington, I asked Hilgard why


Sylvester & Co. so ignored the "Analyst." He said he didn't know, particularly as he had called their attention to it. Now Sylvester had better understand that it is necessary on every count to be civil in his relations to men who are doing something good for science, & that he is not to be arrogant to them simply because he is a stronger mathematician. I asked Hilgard to send me the Analyst & I find already a number on my return.

It contains a new formula on the relation between latitude & gravity. This formula is somewhat more complicated than Clairaut's but it has two merits. First, it applies to any body whose surface is an ellipsoid of revolution & is an equilibrium surface, no matter how great the ellipticity. Second,



the demonstration is excessively simple. The question is whether it is sound. Tell me what you say. Here it is

a= ecuatorial radius

b= polar radius

l= astronomical latitude

v= geocentric latitude

p= equatorial gravity

q= polar gravity

g= gravity and latitude l

r= radius at latitude l


By geometry,


Now, if one level surface (surface of equilibrium) is an ellipsoid, every exterior level surface is an ellipsoid. Hence, going from one surface to another,

If we make b/a and p/q very near unity, this reduces to Clairaut’s formula. But the difference between the two in the actual case is important.

Your loving son

C. S. Peirce

The author's name is R. J. Adcock, Monmouth, Ill.

Transcription by Max Fisch, revised by Sara Barrena (2016)
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:15 de noviembre 2016
Última actualización: 28 de septiembre 2021
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