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Theory of least squares applied to the problems arising in our observatory by Arthur George Smith, 1895

Theory of Least Squares Applied to the Problems Arising in our Observatory by Arthur George Smith, 1895, Page 25

[[stamped number]]15370?5or3?[[/stamped number]]
- Azimuth Screw Transit Instrument    [[page#]]21[[/page#]]
E 0 = mean error of given interval ; t = single interval ; P = weight

[[8 columns listed in reading order]]

[[columns1,2,3,4]]
===========================================
||  Interval  | [[?hr?]] |       Diff.         | delta delta |
---------------|---------|-------------------|-----------------|-
|| D1 - D2   |   1     |      19.28        |  15.9404      |
|| D2 - D3   |   1     |      18.38        |  25.5904      |
|| D3 - D4   |   1     |      19.43        |  22.5544      |
|| D4 - D5   |   1     |      19.11        |  39.0096      |
||                |          |                       |                     |
|| D5 - E1   |   2     |      35.78        |  38.9104      |
|| C5 - D1   |   2     |      36.91        |  21.2976      |
|| E1 - E3   |   2     |     39.01        |  39.8971      |
|| E3 - E5   |   2     |     37.14        |  33.6096      |
|| C1 - C3   |   2     |     37.11        |  16.6896      |
|| C3 - C5   |   2     |     37.99        |  14.4476      |
||                 |          |                      |                     |
|| E5 - F      |   4     |      74.07       |  11.4104      |
|| B - C1      |   4     |     75.38        |  18.6104      |
||                 |          |                      |                     |
|| F - A        |   6     |    113.40       |  22.3600      |
|| A - B        |   6     |    112.80       |  16.1000      |
|| B - C3      |   6     |    112.54       |    9.9796      |
|| F - E3      |   6     |    111.30       |  25.3600      |
||                 |          |                      |                     |
|| D3 - B      |   12   |    225.1         |  24.6600      |
|| C?3? - A  |   12   |    225.47       |  17.8704      |
||--------------|--------|-------------------|-----------------|---
||                 |          |                      |                     |
||--------------|--------|-------------------|-----------------|---

[[columns5,6,7,8]]
=========================================
 E 0       |       t            |  [[sqrt]]P   |      ([[sqrt]]P)(t)    ||
-----------|-----------------|---------------|-----------------------||
.133      |  19.28         |      7.7       |      148.46           ||
.169      |  18.38         |      6.0       |      110.28           ||
.158      |  19.43         |      6.3       |      122.41           ||
.208      |  19.11         |      4.8       |        91.73           ||
             |                    |                  |                            ||
.208      |  17.89         |      6.7       |      119.86           ||
.153      |  18.45         |      9.3       |      171.58           ||
.211      |  19.50         |      6.7       |      130.65           ||
.193      |  18.57         |      7.3       |      135.56           ||
.136      |  18.56         |    10.0       |      185.60           ||
.127      |  18.99         |    10.8       |      205.09           ||
             |                    |                  |                            ||
.113      |  18.52         |    18.2       |      337.06           ||
.144      |  18.84         |    14.2       |      267.53           ||
             |                    |                  |                            ||
.158      |  18.90         |    15.4       |      291.06           ||
.133      |  18.80         |    18.9       |      355.32           ||
.165      |  18.76         |    24.0       |      450.24           ||
.168      |  18.55         |    14.0       |      259.70           ||
             |                    |                  |                            ||
.165      |  18.76         |    21.5       |      403.34           ||
.141      |  18.79         |    24.8       |      465.99           ||
-----------|-----------------|---------------|-----------------------||
             |                    |  226.6       |    4251.46           ||
-----------|-----------------|---------------|-----------------------||
X 0 = weighted mean = [([[sqrt]]P)(t)]/[[[sqrt]]P] = 18.17
[[stamp]] The State UNIVERSITY OF IOWA Library [[/stamp]]

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[[stamped number]]15370?5or3?[[/stamped number]] - Azimuth Screw Transit Instrument [[page#]]21[[/page#]] E 0 = mean error of given interval ; t = single interval ; P = weight [[8 columns listed in reading order]] [[columns1,2,3,4]] =========================================== || Interval | [[?hr?]] | Diff. | delta delta | ---------------|---------|-------------------|-----------------|- || D1 - D2 | 1 | 19.28 | 15.9404 | || D2 - D3 | 1 | 18.38 | 25.5904 | || D3 - D4 | 1 | 19.43 | 22.5544 | || D4 - D5 | 1 | 19.11 | 39.0096 | || | | | | || D5 - E1 | 2 | 35.78 | 38.9104 | || C5 - D1 | 2 | 36.91 | 21.2976 | || E1 - E3 | 2 | 39.01 | 39.8971 | || E3 - E5 | 2 | 37.14 | 33.6096 | || C1 - C3 | 2 | 37.11 | 16.6896 | || C3 - C5 | 2 | 37.99 | 14.4476 | || | | | | || E5 - F | 4 | 74.07 | 11.4104 | || B - C1 | 4 | 75.38 | 18.6104 | || | | | | || F - A | 6 | 113.40 | 22.3600 | || A - B | 6 | 112.80 | 16.1000 | || B - C3 | 6 | 112.54 | 9.9796 | || F - E3 | 6 | 111.30 | 25.3600 | || | | | | || D3 - B | 12 | 225.1 | 24.6600 | || C?3? - A | 12 | 225.47 | 17.8704 | ||--------------|--------|-------------------|-----------------|--- || | | | | ||--------------|--------|-------------------|-----------------|--- [[columns5,6,7,8]] ========================================= E 0 | t | [[sqrt]]P | ([[sqrt]]P)(t) || -----------|-----------------|---------------|-----------------------|| .133 | 19.28 | 7.7 | 148.46 || .169 | 18.38 | 6.0 | 110.28 || .158 | 19.43 | 6.3 | 122.41 || .208 | 19.11 | 4.8 | 91.73 || | | | || .208 | 17.89 | 6.7 | 119.86 || .153 | 18.45 | 9.3 | 171.58 || .211 | 19.50 | 6.7 | 130.65 || .193 | 18.57 | 7.3 | 135.56 || .136 | 18.56 | 10.0 | 185.60 || .127 | 18.99 | 10.8 | 205.09 || | | | || .113 | 18.52 | 18.2 | 337.06 || .144 | 18.84 | 14.2 | 267.53 || | | | || .158 | 18.90 | 15.4 | 291.06 || .133 | 18.80 | 18.9 | 355.32 || .165 | 18.76 | 24.0 | 450.24 || .168 | 18.55 | 14.0 | 259.70 || | | | || .165 | 18.76 | 21.5 | 403.34 || .141 | 18.79 | 24.8 | 465.99 || -----------|-----------------|---------------|-----------------------|| | | 226.6 | 4251.46 || -----------|-----------------|---------------|-----------------------|| X 0 = weighted mean = [([[sqrt]]P)(t)]/[[[sqrt]]P] = 18.17 [[stamp]] The State UNIVERSITY OF IOWA Library [[/stamp]]