Letter from Charles S. Peirce to his mother Sarah Mills
(Geneva, 07.08.1875)

Spanish translation & annotations


Geneva, 1875 Aug 7


My dearest Mother,

I got your letter today & I suppose I ought to reply at once to what you say about the observatory. In the first place, I haven’t the face to set myself up in opposition either to Newcomb or Gould both of whom have infinitely more claim to it than I. I think Gould the most, though Newcomb is much the strongest man. Gould has been punished enough for his bad temper. Besides many great astronomers are bad tempered. The great Bairy (Beary) & Leverrier are both famous for it & Newton, Flamsteed & a lot of ‘em. Late work perhaps is bad for the temper. Then I don't think the




position very agreeable. The place has too much apparatus with an altogether insufficient personnel. Thus it becomes impossible to get any researches made there because the Director is overwhelmed with details. Then you have to live in that house which is a wretched hole & altogether it is not agreeable even leaving the hideous fact that one would have to do business with Eliot out of the question. For my part I hope Gould will get it. Two men as singularly disagreeable as he & Eliot ought to be fastened together by their tails & flung over a clothes line. If he should get it & they should quarrel & the whirligig of time should place me in a position in which I could aid either, it should be the weaker one, so as to prolong the con-




test as long as possible. There are only two reasons why I should like the place. One is I think Zina might like it & the other is that I could bring the apparatus & means there to bear on the solution of a problem on which I am deeply interested that of the form of the cluster of stars in which we are & which includes pretty much all the stars we see. It is certainly a noble problem, which appeals grandly to the imagination & in ten years or so I could pretty much resolve it. I see precisely how, & so make quite a figure in the history of discovery. Brilliant results would soon come & the nagging at all sides from which Winlock suffered & which really killed him would cease. But then I could










not abandon my C. S. Work, to which I am fully committed & which I am now pretty well au fait at & am thus usefully employed although it seems to me a low kind of activity rather.

My photometric work is to be printed in Leipzig by Engelmann, the first scientific publisher in the world. It is to be part of a volume of Annals of the H. C. Observatory of which the other part is to be printed at home. Engelmann desired to purchase 150 copies with leave to prefix a title page & push it on his list of books published by him, an arrangement highly favorable to the interests of astronomers, to the observatory (which would so sell 150 copies of which it now wont sell one) and to me. But Eliot would none of it. Whatever his reasons were they must have been petty ones. When I get up





a microscopical society I’ll have him an honorary member, -a flea couldn’t be more charming to a lover of the infinitely little.

You needn't show father all this about Eliot as he esteems him & would not like what I say. He has certainly done well in taking some interest in providing for Mrs. Winlock. I am very sorry that I cannot possibly subscribe to that at present but a small sum would be worse than none as an expression of my sentiments. I felt & do feel his death most strongly & when I pass from thinking of Eliot to thinking of Winlock it is as cheering as possible. I did not




write either for the day I heard of it I was taken ill, partly caused by that, for I am weak & emotions affect me physically, & I had to go to bed for several days, & meantime Zina wrote. But the result is that my sentiments on the subject haven't got expressed; but if it should ever be in my power to do as much for Willie as his father did for me I will try to imitate the generous honorable gentleman like and large conduct which made Winlock's life a matter of satisfaction even to people not interested personally in it, just as the opposite qualities in the man who nagged him so would make his death a relief all round.

Well, I will try to drop that subject.


Now here comes a passage for father. Suppose

r is the distance of a star

i its real intrinsic light

L its apparent light

Then (neglecting any possible extinction of light)

L= i/r2

Farther suppose L.dL is the proportionate number of stars whose light is between L and L + dL; which proportion I will suppose is the same throughout space. Let Φr be the total number of stars in a unit of space at the distance r. Let Fl.dl be the number of stars whose apparent light is between l and l+dl. (Of course Φr and Fl have different values in different directions). We have then

Photometry combined with counts of stars give us Fl in each part of the heavens and


the problem is from this to determine Φr.

Express Fl in the form

Fl=Al-a + Bl-b+ etc.

Where a0 b1 etc. have such values that Fl cannot be expressed with equal accuracy with a smaller number of terms. Then we want to find Φr or the constants a b etc. in the expression

Substituting the developed forms in the formula we have

Substituting again L=lr2 and writing [Ln] for the mean value of Ln, we find, on comparing the first & last members

so that


This will hold good about within the limits defined by r=√l/[L] where the smallest and largest values of l are to be substituted.

Now to find [La-i] etc. I would propose to take the brightest 200 stars which are accurately measured photometrically, & whose proper motions, e, are also known. If their real motions in space were all equal, then e would be inversely proportional to r and we should have L=l/E2 and [La-i]=L=[(l/E2)a-i]. Since their real motions in space undoubtedly vary very much, the results obtained for L by this formula would be too much scattered. In default of any investigation into the distribution of the real motions we may suppose it to be similar to (but independant of) the distribution of the real light that is one may take (if I am not mistaken)





In this way I think we shall get a good enough value for Φr in every direction in order to find the general form of the surfaces of equal star density and the position of the sun in the cluster.

I have divided the heavens into 32 equal regions. Six in the milky way, two zones of six each, on each side of the milky way, & two regions at the two poles of the milky way. I am now counting the stars in these down to the 6n. 3 magnitude. It will probably not show where the density begins to fall off in the milky way but it will show if the milky way is a ring and also how near we are to one side of it. A count of the Durchmusterung down to the 10hmag if I could get it done would tell a great story. Ten years photometric star gauging would do still more.



I can see what the chief results are although I haven't yet completed my work with the stars visible to the naked eye.

1. The inner surfaces of equal density form a ring

2. This ring is very irregular but its section is two not very flat ovals

3. The radius of the densest ring is not far from the distance of a third magnitude star. Consequently we see out through the densest surfaces of the milky way with our naked eye. In fact the universe is such a wretched little place that I feel quite cramped in it ever since I found out how small it was.

4. The sun is distant from the centre of this ring by about ¼ its radius.

5. The sun is also a little out of the plane of the ring on the Coma Beronices side.



I have taken up so much space with all that that I have none left for the humanities. The fact is that I have been shut up in my room all day working at this business for some time. Consequently I have seen nothing. In fact since Zina separated from me, I have seen nothing but scientific things. I was in Munich a week without entering a gallery or going anywhere except to Seidel Steinheil & Merz. It makes me sick to think of her going home but she evidently wants to go. I couldn’t persuade her to come to Switzerland with me. I might as well not have a wife. I don't speak to a soul here. In desperation I made the waiter seat me at dinner yesterday next a rather bright looking Englishwoman whom I observed to be alone & that was almost the first word I have spoken. But I must rouse myself & force myself to go to Chamounix tomorrow. I had a lovely trip laid out but Zina would not fall in with it. I believe she is enjoying very much the society of Tom Burgess in Berlin. I often think how I should like to be back in your house once more. I think of you all very much although I don't write much.




Transcription by Max Fisch (Peirce Edition Project), revised by Sara Barrena. We are grateful to André de Tienne for some corrections
Una de las ventajas de los textos en formato electr?nico respecto de los textos impresos es que pueden corregirse con gran facilidad mediante la colaboraci?n activa de los lectores que adviertan erratas, errores o simplemente mejores transcripciones. En este sentido agradecer?amos 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: 12 de febrero 2013
Última actualización: 18 de septiembre 2019
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