DIY History | Transcribe | Scholarship at Iowa | Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no.26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903 | Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no. 26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903, Page 75

Transcribe
Translate

Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no.26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903

Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no. 26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903, Page 75

   The general form of these equations of condition is
   a[subscript]1[/subscript]a[superscript]s[/superscript] + c[subscript]1[/subscript]c[superscript]s[/superscript] + d[subscript]1[/subscript]x[superscript]s[/superscript] = n[subscript]1[/subscript][superscript]s[/superscript] .

   Using Ganes's symbols of summation the general form of the normal equations is 

[aa] a + [ac] c + [ad] x = [an]
[ac] a + [cc] c + [cd] x = [cn]
[ad] a + [cd] c + [dd] x = [dn] .

   Let s[subscript]1[/subscript] = a[subscript]1[/subscript] + c[subscript]1[/subscript] + d[subscript]1[/subscript] - n[subscript]1[/subscript] ,

   Let s[subscript]2[/subscript] = a[subscript]2[/subscript] + c[subscript]2[/subscript] + d[subscript]2[/subscript] - n[subscript]2[/subscript] ,

   etc.

   Then the check equations will be

[aa] + [ac] + [ad] - [an] = [as]
[ac] + [cc] + [cd] - [cn] = [cs]
[ad] + [cd] + [dd] - [dn] = [ds].

therefore the quantities to be computed are:

[aa], [ac], [ad], [an], [as]
         [cc], [cd], [cn], [cs]
                 [dd], [dn], [ds].

   We compute also [nn] and [ns]. Following are the computations:

Saving...

The general form of these equations of condition is a[subscript]1[/subscript]a[superscript]s[/superscript] + c[subscript]1[/subscript]c[superscript]s[/superscript] + d[subscript]1[/subscript]x[superscript]s[/superscript] = n[subscript]1[/subscript][superscript]s[/superscript] . Using Ganes's symbols of summation the general form of the normal equations is [aa] a + [ac] c + [ad] x = [an] [ac] a + [cc] c + [cd] x = [cn] [ad] a + [cd] c + [dd] x = [dn] . Let s[subscript]1[/subscript] = a[subscript]1[/subscript] + c[subscript]1[/subscript] + d[subscript]1[/subscript] - n[subscript]1[/subscript] , Let s[subscript]2[/subscript] = a[subscript]2[/subscript] + c[subscript]2[/subscript] + d[subscript]2[/subscript] - n[subscript]2[/subscript] , etc. Then the check equations will be [aa] + [ac] + [ad] - [an] = [as] [ac] + [cc] + [cd] - [cn] = [cs] [ad] + [cd] + [dd] - [dn] = [ds]. therefore the quantities to be computed are: [aa], [ac], [ad], [an], [as] [cc], [cd], [cn], [cs] [dd], [dn], [ds]. We compute also [nn] and [ns]. Following are the computations: