photogra:\imetry. 597 



neutralises the other, and the result is that even with a large 

 apertiu-e there is practically no distortion of any kind, and the 

 alteration of focal length required to give sharpness of definition 

 to an image comprising near and distant objects is only about 

 a I'm., and may be restricted to narrower limits. If the middle 

 distance be sharply focussed the greatest error of focal length will 

 usually be about -rg^n. 



In determining the focal length of a rectilinear lens by a method 

 published by Mr. Grubb, the writer recently adopted the following 

 course : — Two points about half a mile away, subtending a suitable 

 angle for full width of a picture, were focussed, and their distance 

 apart, as seen on the ground glass screen, was measured and found 

 to be 6in., i.e., .Sin. upon each side of the middle upright line. Ry 

 means of the theodolite, placed over the same spot, the true angle 

 was found to be 38*^ 56'. By solving the isosceles triangle thus 

 formed with a base of 6in., and with adjacent angles of 70° 32' 

 each, the distance from apex to base is found to be 8-|-in., which is 

 technically called the equivalent focal length. This would answer 

 sufficiently well if one were sure that the negative occupied exactly 

 the same position as the screen, but as there was reason for doubt- 

 ing whether the above result really gave the correct factor required 

 for a constant divisor or not, the following test was resorted to : — 

 A photograph of the landscape at hand was taken, and, with a 

 theodolite placed over the same spot, horizontal and vertical angles 

 were read to prominent hilltops, gables, and trees that could after- 

 wards be recognised upon the print for comparison with angles 

 scaled from the negative or proof. Two calculations were made, 

 as shown by Fig. 1 — one by reference to a chimney, which by 

 scale upon the picture was 315in. to the left of the vertical line, 

 and 0-30in. above the horizontal line ; the other by reference 

 to a jjost on the horizontal line, and 2'37in. to the right of the 

 vertical line. The angles taken with the theodolite were 19^ 45' 

 and 15° 37' respectively. In the first place by trigonometry. 



Left hand offset 315 log 2-49831 



Angle 19° 45' log. tan 9-55513 



(F +/) = 877 log 2-94318 



Then subtracting J\ = 0-30in, we have F = 8-47. In the 



P 



second case, bv trigonometry, F = 



" •' tan. A 



Right hand offset 237 log 2-37475 



Angle 15° 37' log. tan 9-44641 



F = 848 log 2-92834 



