Faults in this direction are discovered at once by examination of definition, whereas in determining the other constants they are less noticeable. In comparing the definition of any two instruments it is ordinarily necessary only to scan distant objects and observe to what extent details may be distinguished.
The following test may also be used: Focus on printed matter at a distance just beyond that at which perfect clearness is given and gradually approach until the letters are distinctly defined. The instrument with which the print can be read at the greatest distance has the best definition.
To express definition as an absolute measure, use instead of printed matter, a white sheet of paper upon which a series of heavy lines are drawn at intervals equivalent to their thickness. Focus upon this and gradually approach from a point where the impression of a uniform gray field ceases and the black lines and white intervals begin to appear distinct and defined.
Let the distance thus found be 20 yards and the thickness of the lines and intervals between them one-tenth inch. The circumference of a circle with a radius of 20 yards or 7,200 tenths inches is 14,400 by 3.1416 or 45,240 tenth inches; but a circumference equals 360° or (360 by 60 by 60) 1,296,000[''].
If, therefore, 45,240 tenths inches correspond to 1,296,000[''], then 1 tenth inch equals 1,296,000 divided by 45,240, or 28.6['']. The definition is therefore 28.6[''], or practically half a minute.
The capabilities of glasses, including telescopes, in a general way, lie between the following limits:
(2) Light may be 0.01 to 200 times that of the unaided eye.
(3) Field measures in most favorable case, 10°; in the most unfavorable, .01°.
(4) Definition varies between 40[''] and 0.1[''].
Thus, as a maximum, an object may be seen by means of a telescope, magnified 1,000 times, 200 times brighter and 400 times sharper than with the naked eye.
If these advantages could be fully utilized for military purposes the use of glasses would be extraordinary, a power of 1,000 practically effecting the same purpose as the approach of the observed object to one-thousandth of the distance. A hostile command 10 miles distant could be seen theoretically as well as if they were only 53 feet away, and the slightest movement of each single man would become visible. Of course no such wonderful effect is physically practicable, and the limiting conditions increase greatly in proportion as either one or the other of the qualities, power, field, etc., is especially sought.