THE

AMERICAN

JOURNAL OF SCIENCE AND ARTS.

[SECOND SERIES.]

ART. I.-Photometric Experiments. PART SECOND.-On the amount of light transmitted by plates of polished crown glass at a perpendicular incidence; by OGDEN N. ROOD, Professor of Physics in Columbia College.

It would seem that in the direct photometric experiments on this matter, the instrumental means employed have been more or less defective, in consequence of which the results gained, although having a certain amount of general correctness, still leave much to be desired. The main sources of error have been, first, the use of a defective mode of making the compensations, not allowing the experimenter to take full advantage of the sensitiveness of the eye, and secondly the employment of two sources of light, which always brings with it another set of unavoidable errors. Apart from this, in cases when the amount of reflected or transmitted light has been thus approximately obtained, the indices of refraction of the substances used do not seem to have been determined, so that for perpendicular incidence, slender data exist for comparing the results of theory and experiment.

It will be seen in what follows, that, to avoid the variability caused by two sources of light, I have devised a method in which only a single gas-flame is employed, the light being divided in such a way that a certain portion of it always illuminates the posterior side of the screen, while the other portion is reflected from a movable mirror, and pursues its way unobstructed to the screen, or is transmitted to it by the plate under experiment. The compensation is made by moving the mirror, AM. JOUR. SCI.-SECOND SERIES, VOL. L, No. 148.-JULY, 1870.

and when once effected of course remains undisturbed by fluctuations of the flame. In addition to this it will also be observed that a more delicate screen, constructed, however, on the general principles indicated in the first part of this paper, has been employed, and these modifications, taken in connection with certain precautions described below, have given the results an accuracy superior to that attained in the experiments on silver

mirrors.

Arrangement of the photometer with a single gas flame for experiments on the amount of light transmitted by plates of various substances.

Р

M

The source of light is a small gas flame at L, about an inch in height, the gas flowing as before from a plain circular opening. A portion of its light, LA, directly illuminates the screen S, while another portion NA is reflected on the screen by a Liebig's mirror, one protected by a coating of copper being selected: this equalizes the light on both sides of the bare "spot" in S. A third portion of the light from L falls on M, a mirror like that just mentioned, and there is reflected perpendicularly through P, the plate under examination, on G the ground glass. It will be observed that the path pursued by the light in this latter case is the distance LM+MG: by the graduation on the instrument MG is actually measured, GP is known; also PL; hence we have the means of calculating the distance ML, which is to be added to M G, giving the distance requir ed. As these calculations involve some labor, I constructed for my instrument a table by which the measured distance GM, is readily converted into the total dis

tance.

S

B

L

The photometer was the same as that described in the first part of this paper, the following changes having been introduced: the "spot" on the screen was made much smaller, being only about of an inch in horizontal diameter, with a length about three times as great; it was observed by a small telescope T, magnifying six diameters. This reduction in the size of the "spot" rendered it possible to illuminate the ground surrounding it in a manner beyond reproach.

Mode of adjusting the apparatus for experiment.

1st. The center of the flame at L, and the center of the mirror M, must be at the same height above the common base.

2nd. The screen and plates to be examined are to be made perpendicular to the axis of the instrument, by the aid of the small gas flame mentioned in the first part of this paper: the telescope T is also most readily collimated by the use of the same flame, the screen, &c., having been temporarily removed.

3rd. The mirror M evidently must be brought into such a position that it shall send the ray MP perpendicularly to P, or along the axis of the instrument when its distance is such as to effect compensation; for if the reflected ray were sent obliquely through the ground glass plate G, noticeable errors would be introduced. This adjustment, which is important if good results are expected, is best effected by making one or two compensations so as to determine approximately the correct distance of the mirror, which is then rotated on its vertical axis so that the reflected image of the flame is made to fall in the center of the field of the telescope, the screen having been previously removed. By a repetition of this operation finally the mirror is brought into its proper position, when a single series of measurements can be made, the minute differences in the individual compensations introducing no appreciable errors. When, however, the compensation point itself has been shifted by the introduction or removal of a plate of glass, the mirror will correspondingly be moved away or toward S, and of course the ray MP will be sent a little to the right or left, and it becomes necessary to devise some simple way in which this difficulty can be obviated, without in each instance removing the screen and altering the focus of the telescope.

The mirror then being actually in adjustment, this, when lost, can be recovered as follows: in the screen B about four inches above the telescope is a circular aperture of an inch in width; the reflection of the flame in the mirror is observed through it with the naked eye, and the image of the flame is seen higher up on the mirror, and is made to coincide with a short black line drawn there previously. The ray MP can always thus be made to coincide with the axis of the instrument, it not even being necessary for the observer to leave his seat or diminish the sensitiveness of the eye by exposure. I am particular in describing this precaution, having in my own case rejected the results of 1300 compensations which were made with a comparative lack of attention to this single point.

Mode of measuring the amount of light transmitted by a plate of glass, &c.

1st. The plate is placed at P and collimated by the use of the small gas flame.

2nd. A compensation is effected by moving the mirror.

3rd. The mirror is adjusted by the use of the aperture in B, and another compensation made, followed by a second adjustment of the mirror, if necessary.

4th. A series of careful compensations are now made, alternately by the approach and recession of the mirror; these are registered on the fillet of paper.

5th. The plate is removed without the experimenter changing position or exposing the eye to bright light, and a compensation is made which necessitates of course a new adjustment of the mirror by the aid of the aperture in the screen B. Finally, a series of compensations are effected with the free flame and registered.

At this point it may be well to notice an objection which might be urged to this mode of experimenting, viz: it is evident that the angles at which the light is reflected from the mirror will not be identical in the presence and absence of the plate of glass, and as the amount of light reflected by glass and silver varies with the angle of reflection, this might become a source of error and necessitate a correction. With the plates of colorless glass employed by me, however, the angle in one case was 5° 30′ and in the other 5° 18', the difference of 12' being much too small to produce an appreciable effect, as we know from the results of older experiments.

For the purpose of showing what can be effected by this method, I can perhaps do no better than give the results of five sets of experiments; each of them consisted of four sets of eight double, or sixteen single compensations, and during the progress of each trial the conditions remained the same. The experiments were made as follows: eight double compensations were effected with the photometer and registered; then everything being arranged as before, a new set of compensations were made, &c., all of which was repeated four times. The arithmetical mean of the distances of the source of light from the screen was then obtained separately for each of the four experiments, and from these four mean values of the distance, a final mean value was deduced. This last quantity was then squared and compared separately with the squares of each of the first four mean distances, which proceeding tells at once the difference of the four results from the final mean result, in per cents or fractions of a per cent, and is adapted to give an idea of the degree of accuracy to be expected in this kind of observation.

It will be observed that in the twenty experiments, only two cases occur in which the difference rises slightly above one half per cent, or above of the whole quantity of light, while in nearly all the other cases the difference falls considerably below this quantity, and the average of their differences is less than 0-2 per cent, or less than of the whole amount.

As the reliability of measurements with a photometer is evidently connected with the power of the eye in distinguishing different degrees of brightness in adjacent surfaces, it is well to review here briefly the results that have been obtained by dif ferent observers, as to the sensitiveness of the eye under favorable conditions.

The least difference which Boguer with his method, (two shadows,) was able to distinguish was of the whole; Fechner's friends using the same method were able to reduce this quantity to T. Arago remarked that where one of the illuminated surfaces was in motion smaller differences could be perceived, and was able under favorable circumstances to distinguish, while Masson, who used revolving discs, along with his friends, was able to distinguish between to of the whole quantity of light. Near a window Helmholtz was able to distinguish with certainty a difference of, and occasionally as small a quantity as, while in the middle of a room he was able to appreciate certainly only 1, seldom and uncertainly 3.

1

3

*

In all the better of the above mentioned experiments, photometers in any proper sense of the term were not employed, the best of them being made by the use of revolving discs of white paper furnished with narrow black sectors, which are calculated to discover the absolute sensitiveness of the eye under the most favorable conditions. It must not however be imagined that because a good eye can distinguish a difference of on a revolving disc, that the same eye would be able to obtain a similar result with ordinary forms of the photometer, where the conditions are far less favorable, and accordingly it seemed of interest to me to determine by a series of experiments the average sensitiveness of the eye while using the photometric method described in this paper, particularly as the plan of using

* Physiologische Optik, von H. Helmholtz, page 311.