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    Re: Possible limitaion for distance measurement
    From: Herbert Prinz
    Date: 2009 Mar 11, 14:55 -0400

    I took an interest in your question about Dunthorne's formula. Further 
    stimulated by Wolfgang's remark about the Germans having done a lot of 
    error analysis in this field, I am pursuing it.
    Karsten's Allgemeine Encyklopaedie is online at
    The relevant paragraph 221 starts at p. 774. It is a good description of 
    the methods available at the time, their historical evolution and the 
    reasoning behind them. (The presentation is in several respects superior 
    to Cotter's later attempt.) Accuracy is frequently mentioned as the 
    motive for the introduction of a new method, but to my disappointment, 
    no error analysis is provided for any of them. Nevertheless, one foot 
    note leads to another and I hoped to gain more insight from an article 
    cited on p. 784 and again on p. 801 in which Bremiker investigates the 
    error according to the principles established by Gauss in his Theoria motus..
    Bremiker, Astronomische Nachrichten 1850, Bd 30, p.311 - 318
    I could not find the publication online and got it only last Friday 
    through ILL, so I have not come very far with it. The purpose behind the 
    paper is a sales pitch for a formula of Bremiker's own that he 
    apparently presented in the Nautische Jahrbuch pro 1852. (If anybody has 
    access to that, I would like to see it.) The article is difficult 
    reading, because Bremiker presents results without showing his work. So 
    far, I am having trouble to verify his numbers. In particular, for 
    Dunthorne's formula I get half the errors that Bremiker claims. I also 
    find contradictions in the text that I cannot resolve. It's premature 
    for me to discuss it, but I thought I mention the source as one of 
    possible interest to you. I shall have more to say at a later time.
    A direct answer to your original question regarding the alleged 
    limitation of  Dunthorne's formula is not to be found in this article, 
    because Bremiker looks generally only  at the accuracy of distances in 
    the interval from 20 to 120 degrees. At least for his own formula and 
    for Dunthorne's.  Only when he gets a chance for a polemic against 
    Borda, a distance of  5 deg all of a sudden comes into play. Bremiker 
    does not reveal how his own formula does under those circumstances.
    I have posted a scan of the article (4 jpeg pages, browseable) at
    Best regards,
    Herbert Prinz
    KENT AE NORDSTR�M wrote:
     > Again thanks for your views regarding possible limitations in lunar 
    distances. I have gone through almost a dozen old manuals and I have not 
    found any stated limitation such as in the German manual from 1906. I 
    didn�t expect to find anything either. The only limitation I have found 
    in e.g. Tables Requisite from 1766 is about very short lunar distances, 
    which should require 6 fig logarithms and not 5 fig as usually used. The 
    limitation is in this context of no interest because distances less than 
    about 30 degrees were not taken because short distances were not 
    tabulated in old NA�s. But there might be of interest to check the 
    background to the German manual with an other approach. On the pages 
    Wolgang K�rberer kindly provided there is a foot note down on page 385 
    saying (my translation) that a comprehensive explaination for these 
    methods can be found in �Allgemeinen Encyklopadie der Physik� issued by 
    G. Karsten, in the chapter about �time and finding positions�, this 
    chapter written by G.D.E. Weyer. I have tried to find this reference on 
    the internet without success. I am going to alert my collegue about this 
    hoping for an answer. But perhaps somebody else has the above 
    encyklopedie available and would like to check.
     > Kent N
     >  >
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