lamp, but it does receive light from the candle. Since the former shadow is not so dark as the latter, and both sources of light are at the same distance, we arrive at the conclusion that the lamp emits more light than the candle. Now move the lamp farther away until the shadows appear of the same depth. In order to see this effect plainly the lamp should be placed in such a position that the two shadows are formed side by side, as in the figure. Now measure off by means of a rule, the distances from the screen to the candle, and from the screen to the lamp, and we will sup FIG. 38. pose for the purpose of illustration that these distances are 1 foot and 2 feet respectively when the shadows are of equal depth. It will consequently follow that the illuminating power of the lamp is to that of the candle as (2)2 is to 1, or as 4 is to 1. In connection with the shadow photometer it is necessary to recollect that although the comparison is made by judging of the comparative depths of two shadows, what are really being compared are the intensities of illumination on two adjacent portions of the screen, and adjusting these to equality; also that the illuminating powers of the two sources of light are directly proportional to the squares of their distances from the screen. If the distances had been 1 foot and 3 feet (instead of 1 foot and 2 feet), the illuminating powers would have been 1 to 9, and so on. In other words, in order to obtain the relative illuminating powers of two sources of light when tested by means of the shadow photometer, the rule is to square the distances of the two sources of light, and divide the one into the other. For example, suppose a gas flame is fixed at 100 inches from the screen, and it is found that the shadows are equal when the candle is 25 inches from the screen, then the gas would give 16 times the light of the candle, or would be what is known as 16-candle gas, for 100 inches 25 × 4, and 42 16, or 25: 1 :: 1002 : x. .. 625 x = 10.000 10,000 .*. x = 625 = 16 The photometers employed at the present day, however, are all based on a method suggested by Bunsen. The principle consists in saturating a piece of white paper with melted spermaceti, leaving a portion in the centre untouched. Now when a piece of paper so treated is held between the observer and a source of light, the portion which has been saturated with sperm, by reason of its being more transparent than the central portion, which has not been so acted upon, will appear light, while the central or untouched portion will appear dark. If, however, the disc be illuminated from the same side as the observer, the converse effect will be produced, the central portion appear ing bright, and the outer or transparent portion comparatively dark. This effect arises from the fact that the most opaque portion of the disc effects the greatest amount of reflection of light, and consequently appears the brightest, while the light which falls on the more transparent portion is more transmitted and less reflected: if the disc is placed between two sources of light of the same intensity the disc will appear equally bright on each side, consequently no distinction will be apparent between the opaque and the transparent portion; but should one of the sources of light be greater than the other in relation to the position of the disc, the central portion of the latter will appear darkest on the side of the weakest light, caused by the reflection of light on the one side being less than the light transmitted from the other. The opposite side of the disc shows a contrary effect, the opaque portion in this case appearing brighter than the surrounding portion, owing to the reflection of the light being greater than its transmission. As previously stated, Professor Bunsen employed this device for the purposes of practical photometry. A piece of paper prepared as above described was placed between the two lights to be compared, and moved until it was equally illuminated on both sides, the equality of illumination being indicated by both sides of the paper appearing alike. The distance of each light from the paper was measured and squared, and the value of one light was thus obtained in terms of the other. "As soon as the Bunsen disc came to be used for accurately measuring the illuminating value of different sources of light, various forms of photometers began to be introduced. The instrument first consisted of an open bar, 100 inches in length, with the Bunsen disc fixed on a frame, which rolled on the bar, and could be moved backwards and forwards. At one end of this the standard burner was arranged; and at the other end, the candle which was to be used as a unit of light. This was afterwards improved by Dr. Letheby, who fitted the disc in a small box open at each end to the two sources of light, and sliding as before upon the bar. In the front of the box was an opening through which the observer looked, and across which, at right angles, came the edge of the disc. This sighting-box was fitted with two small mirrors at such an angle that the reflection of the two sides of the disc could be simultaneously seen by the observer standing in front of the box. A still greater improvement was also made by replacing the one candle-flame by two flames emitted by two halves of the same candle. The candles used for testing gas are mould candles, and are therefore slightly taper, in order to admit of their easy removal from the mould in which they are cast; and if one candle only be employed, the quantity of sperm melted during its consumption will be continuously altering. The great improvement consists in cutting the candle in half, and lighting in the middle, so that while one half burns down to the thick end, the other burns down to the thinner end. These candles are arranged upon a small balance, so that the amount of sperm consumed during the period of testing can be accurately determined; and, under existing regulations, only those candles that burn more than 114 or less than 126 grains of sperm per hour are considered to comply with the term 'standard candles.' Dr. Letheby also reduced the length of the bar from 100 to 60 inches. This may or may not be an advantage, according to the state of the atmosphere. On the open 100-inch bar, the travel of the disc for an alteration of illumination was considerably larger than on the 60-inch bar; and for this reason the 100-inch bar was an advantage. But if the atmosphere contains fog or any large quantities of suspended matter, it is manifest that the longer the bar, the greater will be the interference of the atmosphere with the amount of light falling upon the disc. If, however, the time should arrive when the standard and the light to be tested are of nearly the same value, this interference will disappear, and increase in accuracy will be obtained by returning to the 100-inch bar." The graduations on the photometer bar indicate direct the value of the strongest light in multiples of the weakest, thus saving time and trouble in making calculations, and also avoiding the liability of errors. As all the photometers in actual use at the present time possess the common feature of having a graduated bar, and as it is of the first importance that these graduations should be correct, it will be advisable, before describing the construction of a photometer in detail, to explain how to graduate photometer bars of various lengths as ordinarily met with. We will first take a bar 100 inches long. Let a equal the distance from the candle of the point in the bar where the mark is to be made to represent a given number of candles, and let n equal that number, then the number of candles n, multiplied by a2, is equal to (100 – x)2, or n = (100 – æ). From this equation the value of x is found to be: 300 15 20 inches. That, therefore, is the place where the mark on the bar is = = |