It will be observed that no correction has been introduced for selective absorption in the substance of the prism itself, as this is absolutely negligible within the limited range of the spectrum we are discussing.

This table exhibits the relative effect upon very different eyes of a given amount of energy in the form of radiation of various wave-lengths.

Quite notable differences exist between the different observers, not only as to the absolute sensitiveness of the eye, but also as to the relative efficiency for different colors. This seems to be, to some extent, a function of the age of the observer, if we may draw any conclusion from so few comparisons, the younger eyes being much more sensitive to the rays of shorter wave-length. Beyond this, any unusual efficiency for a particular part of the spectrum is perhaps apt to be balanced by a deficiency in another part, which, if strongly pronounced, would be termed color blindness. Prof. J. Clerk-Maxwell, employing pure spectrum colors, formed white by combining 26.3 per cent of red with 30.2 per cent of green and 43.5 per cent of blue (Phil. Trans. R. Soc., 1860, p. 79) and on another occasion with a slightly different apparatus (loc. cit. p. 74) the same observer made white by mingling 21.9 per cent of red with 33.3 per cent of green and 44.8 per cent of blue. The Allegheny observers, F. W. V., B. E. L., and E. M., with whom this experiment was repeated, required from one fourth to onetenth less red and one-sixth to one-eighth more blue than Maxwell, forming white by mingling 20 per cent of red with 30 per cent of green and 50 per cent of blue. Since, in order to make white, more of that color is required for which the eye is most sensitive, we may perhaps infer that Prof. Maxwell was somewhat less sensitive to blue than these observers, although it should be remembered that the relative intensity of the blue and red in the solar spectrum is liable to undergo considerable fluctuations, so that where direct comparison of individual eyes is impossible, some uncertainty must remain.

We have selected for comparison with our results the following by Capt. Abney (using a different photometric method), which we have here reduced to the normal scale. (See "Transmission of Sunlight through the Earth's atmosphere," by Capt. W. de W. Abney, R.E., F.R.S.; Phil. Trans. R. Soc., vol. 178, (1887), A., pp. 274-276). From the mean of the observations of July 1st, July 5th and July 21st, 1886, made with an average air-mass of 1.33 atmospheres, we obtain these photometric values for the normal spectrum

The general form of this curve agrees with that of S. P. L. (curve a, fig. 4), showing a maximum sensitiveness near λ=0" 57.

The light curves of F. W. V. (curve c, fig. 4), and of E. M., (curve b, fig. 4), have their maxima respectively near λ=0"-52 and λ=0"-53.

Everything which has preceded has had reference to the relative luminous effects produced by any (moderate) constant quantity of energy. It may, however, be interesting to make the novel calculation as to the actual amount of energy either in horse power or any other unit required to make us see, and we can obtain an approximate estimate of this amount of energy as follows:

Actinometric measurements, made during the progress of the photometric observations, showed a solar radiation of 1.5 calories per square centimeter per minute. Of this amount of heat the slit (s), being 3cm.4 high by 0cm-01 wide, received the fraction 0.034. The visible spectrum from A to H, included, according to the bolometer measures, about 21 per cent of the total energy, the absorption of the lower infra-red by the great thickness of glass in the prism being large. We estimate that nearly 20 per cent had been lost by reflection before the bolometer was reached. The spectrum formed had a length of 86mm from A to H. The average energy which passed through the millimeter aperture of slit s, was therefore (within these limits and expressed as heat),

or approximately to calorie, let us say 4,000 ergs per minute.

At 1 meter from slit s,, this energy is further spread out over an illuminated area of 28 sq. cm., of which the square centimeter of fine print, being placed at an angle of 45° with the path of the ray, occupies only about. If a length of 1mm of the standard spectrum receives an average energy of 1000 calorie per minute, the actual working part of the screen, consisting of the little square of fine print, will receive at a distance of 1 meter 4000 calorie per minute. But this by no means gives the amount of energy requisite to produce vision, since the eye is able to receive a distinct visual impression in less than one-half second of time. We may say, therefore, that a luminous energy of 50000000 calorie is sufficient to give a distinct view of the small square of figures in the brightest part of the spectrum, even after the immense loss of light by absorption and diffusion in the paper, which may amount to 1% of the whole.

Even less light is needed to give the bare impression of luminosity. The sensitiveness of the human eye is indeed so extraordinary, that the chief difficulty in measuring its power is to find means for sufficiently reducing the intensity of sunlight,

which are at the same time capable of even approximate numerical estimation. Out of numerous plans tried, the following has given the most reliable result.

In front of the first slit, in the path of the rays from the siderostat, was placed a plate of glass very lightly smoked whose transmission for different kinds of light was first photometrically measured and found to be

For violet light (=0"-40) transmission 0.000210

The photometer wheel was next interposed, its aperture being sometimes reduced until only 2 per cent of the light received passed through it.

The slit was at first kept as near the standard width of 0·1mm as possible; but it was afterwards deemed best to secure the final adjustment for the minimum visibile at the slit, as it was evident on trial that the inaccuracy due to the varying loss by diffraction was small, compared with the inevitable uncertainty of the observer himself.

Finally, the larger part of the necessary reduction was secured by reducing the aperture of the collimating lens by means of a metal plate pierced by a minute aperture whose

area, 0·000159 cm was 0-000003 of the fully illuminated area

of the lens.

The aperture of the human eye, according to du Bois-Reymond's photograph (see Nature, May 3, 1888, p. 15), is about 0.789 cm, when fully expanded, or the same as that of the foreshortened disk of figures previously employed. The size of the light spot at the standard distance beyond slit s,, when the minute aperture is placed over the collimating lens, is reduced so that about two-thirds of the light enters the eye placed 1 meter behind the 1mm slit on which the spectrum is formed.

The following reductions of sunlight were needed in order to give a light which approximated to the minimum visibile, defining this to be, not the smallest light whose existence it is possible to suspect, or even to be reasonably certain of, but a light which is observed to vanish and reappear when silently occulted and restored by an assistant without the observer's knowledge.

Referred to the standard spectrum employed in the previous photometric work, the observer F. W. V. found:

Fraction of standard* violet light (λ=0".40) required for certain vision =0.00021X100 × 0·000003 0·000000,063.

*By "standard" is here meant the light in 1mm of the standard spectrum, whose length from A to H was 86mm.

t

Fraction of standard green light (λ=0"-55) required for certain vision 0.000655 × 0.033 X 0·000003=0·000000,0000655.

=

Fraction of standard scarlet, light (λ=0"-65) required for certain vision =0·00235 × 2•X 0·000003=0·000000,0141.

Fraction of standard crimson light (λ=0“.75) required for certain vision=10 X 0·000003 0.00003.

The measures were made on July 3d and 11th, the sky being a fairly good milky blue and the sun within one hour of the meridian.

Assuming that the energy per millimeter of the standard spectrum was 0·000001 calorie per half second for the wavelengths 0.55 and 0.75, we have from table I:

by means of which, we reduce each of the above values to absolute measure, obtaining for the maximum value of the

Stating these values in terms of horse power we have

The measurement of the minimum visibile is subject to variations of a much wider range than those of the photometric method and may perhaps be in error by 100 per cent.*

*The relative sensitiveness of the eye of the observer in question (F. W. V.) for the extreme red or violet, as compared with its power of detecting green light, appears to be somewhat less when determined by the method of minimum visibile than by the reading of fine print.

By the former we have