Faraday to Jacob Herbert   9 October 1845

Royal Institution | 9 Octr. 1845

Sir

On the receipt of your letter of the 27th August¹ I ordered two reflector Argand lamps burning sperm oil, and also two of the lamps of Messrs Wilkins & Kenwick [sic]²; and on the receipt of them & also of two reflectors, proceeded to experiment and observe; burning Sperm oil always in the Argand lamps and the refined Rape oil (or the oil which I may call so) in the other lamps. I am now prepared to report the general results & in doing so will distinguish the lamps by calling them Sperm oil or Rape oil lamps[.]

Having burnt the lamps for many days I have been much struck by the great steadiness of the Rape oil lamps: either considered alone or as compared with the Sperm oil lamps. They would burn for 12 or 14 hours at a time with little or no alteration of the light, the cottons or lamps not being touched the whole time; whereas, the sperm oil lamps would in the course of 4, 5 or 6 hours give a diminished flame from the encrustation of the charred part of the cotton retarding the flow of oil. In the rape oil lamps the coal is broken & porous & serves for wick almost as well as the fresh cotton, but, in the sperm oil lamps the coal forms a hard continuous ring which seals up the ends of the threads, & this with the more confined condition of the burner & the greater distance of the oil beneath (from intentional difference of flow in the lamp) causes the sperm oil lamp flame to fall in brightness & requires that the wick should be retrimmed. Several causes conspire to this hard condition of the charred cotton which I need not enter into here[.]

I have made many careful experiments on the proportion of light produced by the two kinds of lamps, in every case weighing the oil before & after combustion so as to know exactly the quantity burnt; & making during the experiments, above a hundred comparisons of the lights one with another. The Rape oil lamps were always more brilliant than the sperm oil lamps, except indeed in one or two rare cases;- but at the same time more oil was burnt in them. The observations were made numerous that the error in the perception of the eyes might compensate each other. In each particular experiment it was evident that the light was nearly in proportion to the oil burnt, & upon making a comparison of all the results the following conclusion was obtained. From 108 observations of the lights, taken at such times as appeared fitted to give the best mean expression of the light of the lamps compared with the oil burnt in them, the average light of the Rape oil lamp came out as one & a half; that of the Sperm oil lamp being one. This is the mean result of the light evolved by the lamps being for the same period of time. On summing up the amount of oil burnt in the same time, it gave almost exactly the same proportions; for the oil consumed in the sperm lamps being 1 that consumed in the Rape oil lamps was 1.505. I have considerable confidence in this result, the quantity of oil consumed being several gallons & the observations of the light very continuous & numerous.

As therefore the lights are equal for the same amount of oil the difference of price between the refined rape oil & the sperm oil expresses exactly the advantage in this respect obtained by the use of the rape oil.

In reference to the horizontal divergence of the beams of light from the sperm oil & rape oil lamps when placed in reflectors, I may observe, that, the sperm oil lamp gives a flame which when looked at in a horizontal direction, is, as to its bright part, nearly square; whereas the rape oil lamp gives a flame, which observed in the same direction, is narrow horizontally & long vertically:- its height being often twice its width. Hence the sperm oil lamp flame, when placed in the focus of a well made reflector, gives a beam having nearly equal horizontal & vertical divergence; but the rape oil lamp in the same reflector gives a beam having less horizontal divergence & more vertical divergence than the former; i.e. the light is thrown up & down rather than to the right & left. In a perfect reflector & arrangement the divergence depends upon the dimension of the flame, & therefore the above effect must follow. In practice the reflectors are not perfect & therefore the beams are more or less distended; but still the effect remains and on adjusting two lamps, (one with sperm oil & the other with rape oil,) in two reflectors so that the reflectors could be changed one for the other, & casting the beam on a distant wall in our darkened lecture room, it was readily seen, that, the illuminated space on the wall was of an oblong form upwards with the rape oil lamp, & that with the sperm oil lamp, it had more horizontal divergence. The rape oil lamp is adjusted in the reflector at a lower level than the sperm oil lamp, that the middle of the flame may be level with the axis of the reflector; but this does not alter the divergence so as to lessen the vertical & increase the horizontal direction: it only tends to lift the whole beam upwards, which otherwise would, as a whole, incline towards the earth or downwards.

The following are, as nearly as I can estimate them, the dimensions of the bright part of the two flames. The sperm oil lamp, with a flame rising about 1 1/4 inches above the level of the cotton, has a bright part from 7 to 8 eighths of an inch in height; and from 7 to 8 1/4 eighths of an inch in width. As the distance of the centre of the burner from the mirror is 3.3 inches these dimensions give a divergence of 15˚ to 17˚1/2 in the vertical direction & a divergence of 15˚ to 18˚ in the horizontal direction[.]

The rape oil lamp flame is not so easy to measure in its upright dimensions, because, from the height of the chimney & rapidity of the draught, it is impossible to prevent it from forking:- but estimating it as well as I could, I found that when rising from 1 4/8 to 1 5/8 inches above the level of the cotton, the bright part is from 8 to 9 or 10 eighths of an inch in height, the lower part being continuous & the upper more or less forked; and the width from 5 1/2 to 6 eighths of an inch, being a little greater below than above. As the distance is here the same as before these dimensions give a vertical divergence of 17 1/2˚, 19 1/2˚ or 22˚ degrees & a horizontal divergence of 12˚ to 13˚ degrees.

The vertical divergence may be diminished by lowering the rape oil flame more or less, but then the whole light falls in power; besides which, the horizontal dimension does not at the same time increase and the flame still remains forked at the top that being a disadvantage.

Vegetable oil is burnt in all the great central lamps of the French dioptric lights, and it there has not the disadvantage which is found to occur in a reflector lamp; because, from the construction of the lamp & its size, the horizontal & vertical dimensions of the flame remain the same, whether vegetable or sperm oil is burnt. By the use of vegetable oil therefore in such lamps a great saving in the expence of fuel is effected without any accompanying inconvenience[.]

I will now venture to suggest for consideration a proposition respecting the means of affecting the divergence of the beam of light issuing from a parabolic mirror with a lamp placed in its focus. The divergence of the beam is in the first place determined by the dimensions of the flame, and we cannot by any arrangement make it less than a certain amount; this amount being least when the flame is in the focus of the reflector. The extent of this divergence I have already given for the two flames. The vertical divergence therefore cannot be diminished; for though it may often seem, when the ray falling on a wall is observed, as if the concentration of the light generally, indicated a smaller divergence than this, such effect is produced, either, by the inevitable irregularities in the form of the mirror or by the lamp being a little out of focus, & so making a concentration in that point or plane at that distance:- in such cases when the beam is observed at a greater distance it is seen that the crossing rays open out again, and that the general effect & amount of divergence is that already described as due to the dimension of the flame.

But though we cannot diminish the divergence below a certain amount we can easily increase it. If a point of light were placed in the focus of a parabolic reflector, it would send forth from the reflector parallel rays; i.e rays having no divergence. If it were placed nearer to the reflector than the focus it would send forth diverging rays:- if placed at a distance greater than the focal distance, the rays on issuing from the reflector would first converge, then cross, and afterwards diverge. Such also is the case with the flame of a lamp; for though the luminous points of the flame which are above or below or to the right or left of the center or axis of the reflector, are not exactly in the same relation as those that are in the center, they are generally so & effectually so in practice[.]

Therefore it is in our power to increase the horizontal divergence of the rape oil lamp flame[.]

If in proceeding to obtain this end we were to put the flame out of focus, placing it rather nearer to the reflector, for instance, we should also increase the vertical divergence which is already too large, & should thus do harm; but if the reflector were made of such form and dimensions that its horizontal section should be that of a parabola having a focal distance of somewhat more than 3.3 inches, whilst its vertical section remained as it now is, then, a lamp placed at the present distance from the reflector, would have its horizontal divergence increased & its vertical divergence unaffected; and so the beam might be opened out in a horizontal direction. I have even obtained this effect practically by putting a bridle over the edge of one of the reflectors, springing the upper & lower edges together, so as to make the vertical diameter only 21 inches whilst the horizontal diameter was 21 7/8 inches, and their approaching the lamp a little towards the reflector[.]

Though we can by such an arrangement enlarge the horizontal divergence without affecting the vertical divergence, there are no means that I am aware of by which we can correct the vertical divergence of a tall flame into horizontal divergence.

There would be no difficulty in making such reflectors as those just described or converting the present into such and they might perhaps also be found useful occasionally with Sperm oil lamps. For instance where the lamps are placed so as to illuminate a considerable extent of the horizon (as at the South Foreland low light) the beams from the different reflectors could be made to overlap each other in the horizontal direction, so as to equalize the light and make it more uniform over every part of the horizon to be illuminated thus helping to remove the difference between brighter & darker parts which occur I think at present³.

I have the honor to remain | Sir | Your Very Obedient Servant | M. Faraday

Jacob Herbert Esq | Secretary | &c &c &c | Trinity House