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 73

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 73

The Coast Survey Report for 1880 gives the following table of weights of observations taken with small instruments, as far as the weights depend upon the declinations of the stars, the weight of an equatorial star being unity:
[table]
δ | p | square root of p
0° | 1.00 | 1.00
10 | 0.98 | 1.00
20 | 0.92 | 0.96
30 | 0.83 | 0.91
40 | 0.70 | 0.83
50 | 0.53 | 0.73
55° | 0.94 | 0.66
60 | 0.34 | 0.59
65 | 0.26 | 0.51
70 | 0.18 | 0.42
75 | 0.10 | 0.32
80 | 0.05 | 0.22
[/table]
In case some of the wires are missed, the weight is diminished. The weight for an incomplete transit is pP , where, as found by Schott of the Coast Survey, P=((1 + (2/N))/(1 + (2/n))) for small instruments, N being the total number of wires and n the number of wires observed.
The reticle of transit instrument Wu"rdemann No.26 contains 19 wires, so in this case N=19 and P=(21/19) (n/(n+2)) . For our ten observations we have the following values of n and the corresponding values of P.
[table]
Star | n | P
(1) | 15 | 0.98
(2) | 19 | 1.00
(3) | 19 | 1.00
(4) | 17 | 0.99
(5) | 15 | 0.98
(6) | 15 | 0.98
(7) | 7 | 0.86
(8) | 11 | 0.94
(9) | 3 | 0.66
(10) | 15 | 0.98
[/table]

The Coast Survey Report for 1880 gives the following table of weights of observations taken with small instruments, as far as the weights depend upon the declinations of the stars, the weight of an equatorial star being unity:
[table]
δ | p | square root of p
0° | 1.00 | 1.00
10 | 0.98 | 1.00
20 | 0.92 | 0.96
30 | 0.83 | 0.91
40 | 0.70 | 0.83
50 | 0.53 | 0.73
55° | 0.94 | 0.66
60 | 0.34 | 0.59
65 | 0.26 | 0.51
70 | 0.18 | 0.42
75 | 0.10 | 0.32
80 | 0.05 | 0.22
[/table]
In case some of the wires are missed, the weight is diminished. The weight for an incomplete transit is pP , where, as found by Schott of the Coast Survey, P=((1 + (2/N))/(1 + (2/n))) for small instruments, N being the total number of wires and n the number of wires observed.
The reticle of transit instrument Wu"rdemann No.26 contains 19 wires, so in this case N=19 and P=(21/19) (n/(n+2)) . For our ten observations we have the following values of n and the corresponding values of P.
[table]
Star | n | P
(1) | 15 | 0.98
(2) | 19 | 1.00
(3) | 19 | 1.00
(4) | 17 | 0.99
(5) | 15 | 0.98
(6) | 15 | 0.98
(7) | 7 | 0.86
(8) | 11 | 0.94
(9) | 3 | 0.66
(10) | 15 | 0.98
[/table]