Owing to the absence of an integrating photometer, the mean spherical candle power has been found by Kennelley’s graphical method. This method is very simple as compared with Rousseau’s and has the advantage of yielding the mean spherical intensity as a one dimensional quantity. This dispenses with the use of a planimeter or equivalent measuring surface device. It consists essentially in determining graphically from the given polar curve an evolute and the involute of the same and then projecting this involute upon a vertical line. Half the length of the projection is equal to the mean spherical intensity to the same scale as the original polar curve.

Figure IV shows the method and is explained thus: The polar curve OAHB corresponds to the distribution of intensity from an inverted incandescent lamp having its base at V and tip at V´. This is not precisely true but the only variation to speak of is that the tip candle power does not fall off so much as the curve between B and O. This variation is slight, however. The mean horizontal intensity is OH, the diameter of the circle, and in this case is equal to 12.4 candle power. In the diagram the construction is adapted to zones of 30° and the radii of the midzones found i.e. at +75°, +45°, +15°, -15°, -45° -75°. These are marked by dotted lines Ot, Os, Or, Or´, Os´, Ot´ respectively.

With radius Or and center O, the arc hra is described through an angle of 30°. The radius Oa is drawn at the end of the arc. A distance Ab is measured from a along a O equal to Os, the second midzone radius. With a center b and radius Os, the arc ac is described through an angle of 30° so that bc makes an angle of 60° with the horizontal OH. The line bc is drawn at the end of this arc. From c towards b, a distance cd is marked off equal to Ot, the third midzone radius. With center d and radius Ot, the arc ce is described through an angle of 30° so that de makes an angle of 90° with the horizontal OH. The line de is drawn.

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 ecaa´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