DIY History | Transcribe | Scholarship at Iowa | 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 67

[page]62[/page]
III
The determination of the focal length of the transit instrument.
The value in arc of an equatorial wire interval of the transit instrument evidently depends upon the focal length of the objective lens: or having the value in inches of this wire interval the focal length of the instrument may be determined as from the following figure.
[image/sketch of measurements surrounding the focal point of central lens: two lines drawn in wide sideways X form go through the focal point, left side has endpoints labeled D' and C' and has arrow pointing up, right side has endpoints labeled c and D and has arrow pointing down (right side also has a straight line bisecting its angle to focal point and it has endpoint labeled with [?symbol?])]
Let C'D' be the object observed and CD its image as formed by the lens AB ; then CD is the apparent angular magnitude of C'D' . Now suppose CD = i to be the distance between

[page]62[/page]
III
The determination of the focal length of the transit instrument.
The value in arc of an equatorial wire interval of the transit instrument evidently depends upon the focal length of the objective lens: or having the value in inches of this wire interval the focal length of the instrument may be determined as from the following figure.
[image/sketch of measurements surrounding the focal point of central lens: two lines drawn in wide sideways X form go through the focal point, left side has endpoints labeled D' and C' and has arrow pointing up, right side has endpoints labeled c and D and has arrow pointing down (right side also has a straight line bisecting its angle to focal point and it has endpoint labeled with [?symbol?])]
Let C'D' be the object observed and CD its image as formed by the lens AB ; then CD is the apparent angular magnitude of C'D' . Now suppose CD = i to be the distance between