The arc ha´c´e´ is extended from the horizontal to the vertical beneath in the same manner as above by steps of 30° with centers O, b´, and d´, and radii Or´, OS´ and Ot´ respectively. The curve ecarr´a´c´e´ is now continuous and complete. A vertical line QQ´ is drawn through the convenient point H and the points e c a a´ c´ e´ are projected upon the same. The length HQ, is the upper hemispherical intensity and the length HQ´ the lower hemispherical intensity. Their arithmetical mean is the mean spherical intensity. Since in this case the upper and lower hemispheres are symmetrical HQ = HQ´ = QQ´/2 = mean spherical intensity. By measurement this half length is found to be 3.125 inches and from the scale used this corresponds to 9.67 candle power. The spherical reduction factor for these lamps is, then
9.67/12.4 = 78%
Fig IV
Kennelly’s Diagram for Spherical C. P.
V. PHENOMENA OF “OVERSHOOTING”.
The singular property of the tungsten lamp to “overshoot” or to give temporarily a higher initial than normal candle power, was first discovered by John B. Taylor and is explained in the following manner:—The filament of the carbon incandescent lamp possesses a negative temperature coefficient; that is to say, a rise in voltage causes a more than corresponding rise in current and when the lamp is connected to a source of constant potential, the current starts at a comparatively small value and increases to a maximum when the lamp has attained full candle power.
In the case of the tungsten lamp, the situation is just the reverse, since tungsten has a positive temperature coefficient. When the lamp is connected to a constant potential supply the current is a maximum when the lamp is cold and decreases to a final value when the lamp reaches full brilliancy. The most important difference between the two lamps due to these different characteristics is that while a tungsten lamp reaches full candle power the instant the current is turned on a carbon incandescent lamp comes up to full candle power only after a perceptible period of time.
The apparent temporary increase in the candle power of a tungsten lamp was observed early after the lamp was invented but it was generally ascribed to some possible physiological action due to the slow contraction of the pupil of the eye.
The following curve was obtained by means of the oscillograph and shows clearly the rush of current for the first instant after the lamp is turned on. The break in the curve is due to an imperfection in one of the operating switches and has nothing to do with any characteristic of the lamp. The cycle wave was put on merely to obtain the time.
