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tion; secondly, to the variation of the friction of the same surfaces of contact under

different pressures; thirdly, to the relation

of the friction to the extent of the surface of contact; fourthly, to the relation of the amount of the friction of motion to the velocity of the motion; fifthly, to the influence of unguents on the laws of friction, and on its amount under the same circumstances of

pressure and contact. The following are the principal facts which have resulted from these experiments; they constitute the laws of friction.

"1st. That the friction of motion is subject to the same laws with the friction of quiescence, (about to be stated,) but agrees with them more accurately. That, under the same circumstances of pressure and contact, it is nevertheless different in amount.

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2ndly. That when no unguent is interposed, the friction of any two surfaces (whether of quiescence or of motion) is directly proportional to the force with which they are pressed perpendicularly together, (up to a certain limit of that pressure per square inch); so that, for any two given surfaces of contact, there is a constant ratio of the friction to the perpendicular pressure of the one surface upon the other. Whilst this ratio is thus the same for the same surfaces of contact, it is different for different surfaces of contact. The particular value of it in respect to any two given surfaces of contact is called the co-efficient of friction in respect to those surfaces. The co-efficients of friction in respect to those surfaces of contact, which for the most part form the moving surfaces in machinery, are collected in a Table.*

"3rdly. That when no unguent is interposed, the amount of the friction is, in every case, wholly independent of the extent of the surfaces of contact, so that the force with which two surfaces are pressed together being the same, and not exceeding a certain limit (per square inch) their friction is the same whatever may be the extent of their surfaces of contact.

"4thly. That the friction of motion is wholly independent of the velocity of the motion.

"5thly. That where unguents are interposed, the co-efficient of friction depends upon the nature of the unguent, and upon the greater or less abundance of the supply. In respect to the supply of the unguent, there are two extreme cases, that in which the surfaces of contact are but slightly rubbed with the unctuous matter, and that in which, by reason of the abundant supply of the unguent, its viscous consistency, and the extent of the surfaces of contact in relation

This Table we shall give at length at some future opportunity.-Ed. M. M.

to the insistent pressure, a continuous stratum of unguent remains continually interposed between the moving surfaces, and the friction is thereby diminished, as far as it is capable of being diminished, by the interposition of the particular unguent used. In this state the amount of friction is found (as might be expected) to be dependent rather upon the nature of the unguent than upon that of the surfaces of contact; accordingly M. Morin, from the comparison of a great number of results, has arrived at the following remarkable conclusion, easily fixing itself in the memory, and of great practical value; 'that with unguents, hogs' lard, and olive oil, interposed in a continuous stratum between them, surfaces of wood on metal, metal on wood, and metal on metal, (when in motion,) have all of them very nearly the same coefficient of friction, the value of that coefficient being, in all cases, included between 0.7 and 0.8.'

"For the unguent tallow, the co-efficients are the same as for the other unguents in every case, except in that of metals upon metals. This unguent appears, from the experiments of Morin, to be less suited to metallic substances than the others, and gives for the mean value of its co-efficient, under the same circumstances, 10.'"

The points which most want clearing up are these:

1. What the "certain limit," or pressure per square inch is, at which the friction of any two surfaces ceases to be in a constant ratio to the force with which they are pressed perpendicularly together.

M. Morin's experiments (from which chiefly the preceding "laws" are deduced) were made with insistent pressures of only from 14.3 to 28.6 lbs. per square inch; but the experiments of Mr. George Rennie, which were carried in some instances to as high as 5 and 7 cwt. per square inch, show that the co-efficient of the friction of quiescence increases rapidly as the pressure advances to the point at which the substances begin to abrade or destroy one another, though at what particular stage that increase begins, and in what ratio it proceeds, has yet to be ascertained. Professor Moseley thinks it probable that the coefficient of the friction of motion remains constant under a wider range of pressure than that of quiescence; but this also is a point which future experiment only can determine.

2. How far the approach to the point of abrasion or destruction is accelerated by the velocity of the moving surface (that it is accelerated to some unknown extent appears certain), and what the amount of destruction of surface, or wear of material is, which corresponds to the same space traversed under different pressures, and at different velocities.

The "limiting angle of resistance" is a very appropriate name first given by Mr. Moseley to that particular degree of inclination from the perpendicular at which one body, moving on another fixed body, will cease to be sustained by it; and its properties were also first investigated by him in a paper read before the Cambridge Philosophical Society, in December, 1833, and published in the Transactions of the following year. The results of that enquiry are here given in a condensed, but sufficiently intelligible form; besides which the author has been at the pains to calculate the value of that angle in respect of every one of the numerous surfaces contained in the Table of Friction before alluded to, as intended to be presented to our readers in extenso at some future opportunity.

The "Theory of Machines," which comes next, occupies by far the largest portion of the volume, and is beyond all doubt the most valuable, and important.

In a memoir by Mr. Moseley, "On the Theory of Machines," which was published in the Philosophical Transactions for 1841, he showed that the moving power in every machine divides itself into, First, that which overcomes the prejudicial resistances (the vis inertia); Second, that which causes the progression of the machine, or accumulates power in it; and Third, that which operates at the working point or points, and is represented by the work done by it. Mr. Moseley showed also, that between these three elements there obtains in every machine a mathematical relation which he called its modulus. Now what the learned Professor has done in the part to which we are now come of the present volume, is to determine

the particular moduli of all the ordinary elements of machinery, as the wheel and axle, cord and pulley, rack and pinion, &c. ; so that when we wish to ascertain the modulus of any machine, we have but to combine the moduli of all the elements of which it is compounded.

Of these elements, the most frequent in occurrence, as well as the most useful in application, are those which rotate about cylindrical axes; and in treating of these the author is particularly happy. We may select, for example, two passages relating to that often and still much debated question, the comparative merits of the beam and direct action steam-engines, which ought, in our humble judgment, to set that question at rest for ever.

Article 168. "A machine to which are applied any two pressures P1 and P2, and which is moveable about a cylindrical axis, is worked with the greatest economy of power, when the directions of the pressures are parallel, and when they are applied on the same side of the axis, if the weight of the machine itself be so small that its influence in increasing the friction may be neglected.

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For, representing the weight of su ha machine by W, it appears by equation (166) that the modulus is

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"261. It has already been shown (article 168) that a machine working like the beam of a steam-engine under two given pressures about a fixed axis is worked with the greatest economy of power when both these pressures are applied on the same side of the axis. This principle is manifestly violated in the beam-engine; it is observed in the engine worked by Crowther's parallel motion, (as used in the mining districts of the north of England,) and in the marine engines recently introduced by Messrs. Seaward, and known as the Gorgon engines. It is difficult indeed, to defend the use of the beam on any other legitimate ground than this; that in some degree it aids the fly-wheel to equalize the revolution of the crank arm,* an explanation which does not extend to its use in pumping engines, where, nevertheless, it retains its place; adding to the expense of construction, and by its weight greatly increasing the prejudicial resistances opposed to the motion of the engine."

*

On the subject of "wheels," the auther appears also to especial advantage. The direction of the vertical pressure of the teeth is determined by a method first applied by him to that purpose in his popular treatise, entitled "Mechanics applied to the Arts," 1834. In determining the moduli of different systems of wheels, he takes into account, not only the friction of the teeth, but that of the axes and weights of the wheels; and in the case of epicycloidal and involute teeth, the modulus assumes such a character of mathematical precision as incontrovertibly to establish the important practical conclusion (so often disputed) that the loss of power is greater before the teeth pass the line of centres, than at corresponding points afterwards; but that, nevertheless, the contict should in all cases take place partly before, and partly after the line of centres has been passed. In the case of involute teeth, the proportion in which the arc of contact

• The reader is referred to an admirable description of the equalizing power of the beam, by M. Coriolis, contained in the 13th vol. of the Journal de L'Ecole Polytechnique.

should thus be divided by the line of centres is determined by a simple formula; as are also the best dimensions of the base of the involute, with a view to the most perfect economy of power in the working of wheels. (To be continued.)

ON THE COMPARATIVE EXPENSE OF LIGHT
DERIVED FROM DIFFERENT SOURCES,
AND ON THE USE OF CHLORINE AS AN
INDICATION OF THE ILLUMINATING
POWER OF COAL GAS. BY ANDREW
FYFE, M.D., F.R.S.E., F.R.S.S.A., &c.
[From the Transactions of the Royal Scottish Society
of Arts, Session 1841-2.]

In a paper published in the Edinburgh Philosophical Journal for 1824, I recommended the condensation of the heavy hydro-carbons by chlorine, as an easy and efficacious method of ascertaining the comparative illuminating power of coal-gas, while, at the same time, it had the advantage of enabling us to compare one gas with another, though not brought directly into contrast with it, and thus, by fixing on one as a standard, to state the illuminating power numerically.

With regard to the methods now in use, I mean the specific gravity, the quantity of Oxygen necessary for combustion, and the depth of shadow, the last is the only one in which we can place any confidence. As to the specific gravity, if the gas be pure, that is, free from carbonic acid and sulphuretted hydrogen, then the heavier it is the more likely is it to be of high illuminating power; but this is not always the case: thus the specific gravity of olefiant gas and of carbonic oxide is the same, but the latter burns with a feeble blue flame, whereas the former gives forth a brilliant light. Now, suppose coalgas to contain little of the heavy hydro-carbon, and a large proportion of carbonic oxide, then the specific gravity may be such as to induce us to expect the illuminating power to be high, when in fact it is not.

The same remark is applicable to the mode of testing by the quantity of oxygen necessary for complete combustion. A gas with much olefiant will no doubt require much oxygen, this gas taking no less than thrice its own bulk; but let us suppose a variety of gases to have the same proportion of olefiant or of heavy hydro-carbons, while the proportion of the other inflammable gases varies, which, though they consume oxygen, give out little light during their combustion, and we shall find that the amount of oxygen required gives no indication whatever of the illuminating power.

DR. FYFE ON THE ILLUMINATING POWER OF COAL GAS, ETC.

Thus, suppose the composition to be

Olefiant

Carburetted hydrogen
Carbonic oxide
Hydrogen

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13 13 13

83 65 51
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14

8 28

100 100 100

the first would require 207, the second 180, the third 159, of oxygen, yet the illuminating power would be nearly the same in all. Supposing the heavy hydro-carbons to vary, and even to become considerable, yet the quantity of oxygen may not be in proportion, owing to the hydrogen and carbonic oxide, which require only half of their bulk of that gas for combustion. The mode of ascertaining the illuminating power by the shadow is one in which we may place the utmost reliance, provided we burn the gases with the same kind of burners, and pay particular attention to the circumstances affecting the appearance of the shadow; for it is well known that the colour of the shadow varies even from the same gas, when the flames from different burners are contrasted; besides, the reflection of light from surrounding objects will also occasion a difference. Great care is therefore necessary when conducting the trials in this way; and it requires nicely adjusted meters, and a regular pressure, so that the consumpt shall not vary during the performance of the experiment.

The other method which I formerly recommended is not liable to these fallacies. In the paper to which I have already alluded the results of numerous trials are given, in which the illuminating power, as shown by the chlorine test, very nearly agrees with those indicated by the photometric process; and these experiments were performed with every possible attention to the circumstances likely to affect the results, so far as they were then known. In a paper subsequently published by Drs. Christison and Turner, the accuracy of the chlorine test was called in question, partly because, when testing the gases by the photometric process, as pointed out by Rumford, due attention was not paid to the different circumstances affecting the combustion, and partly owing to the opinion expressed in the paper by the authors, that other ingre dients than olefiant exist in coal-gas, which afford light by their combustion, and which are also condensible by chlorine. As to the latter objection it is of little value, provided we find the results indicated by the chlorine test, to agree with the photometric one. With regard to the latter, it must be admitted, that in some of the trials, where two geses were compared with each other, due

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attention was not paid to the height of the flame, and to the other circumstances affecting the combustion, which, at the time that I was engaged in the enquiry, were not known to have an influence on the illuminating power. The influence of these has now been fully investigated, and made known, in the paper by Drs. Christison and Turner, and also in that which I read to the Society in 1840. Since then, I have again had my attention drawn to the subject, and have had many opportunities of putting the chlorine method to the test of experiment; and I must say that I am more and more inclined to put the most implicit confidence in it, not only as a very simple, but at the same time a correct method of ascertaining the comparative illuminating power. I trust

the results of the trials will not be devoid of interest.

In fixing the illuminating power of the gases by the shadow, two accurately adjusted meters were used, one for the one gas, the other for the other. Sometimes the gases were contrasted with cach other; in which case, similar burners, consuming the gas under the same circumstances, were employed; and with the view of securing accuracy in the results, the burners were sometimes changed from one gas to another; at other times, the light given by the gas was contrasted with that from candles. gases subjected to trial were sometimes those with which Edinburgh is at present supplied, sometimes they were prepared by myself, in a small apparatus, with the view of having the illuminating power as varied as I could possibly obtain.

The

It is well known that the quality of coalgas, even when manufactured from the same kind of coal, depends much on the mode of manufacture; when slowly prepared, and when the same charge of coal is long subjected to heat, a larger quantity of gas is given off, than when the time for the charge is shorter; but then the illuminating power is low, owing to the gas which is last evolved having very little of the heavy hydro-carbons; and hence those companies who dispose of their coke to advantage, have, besides the quantity of gas to be got, another object in view, viz., the freeing of the coke from all its gaseous ingredients, otherwise it is not considered valuable, indeed will not be purchased by those in the custom of using it. It is this which, in addition to the difference in the quality of the coal employed, makes such a difference between the quality of gas prepared in England and Scotland; for, as the coke from English caking-coal is more prized than that from parrot-coal, which is much used in Scotland, the English companies may generally be considered not only as gas

companies, but also as coke companies, indeed derive a great deal of their profit from the coke. Hence, in judging of the price of gas, we must take into account its quality; and hence, I conceive, the importance of having an easy method of ascertaining this, and of comparing different gases with each other.

In the first series of experiments, the results of which I am now to give, two gases, manufactured under different circumstances, were compared with the light afforded by a wax candle kept burning, as nearly as possible with a uniform flame; the gases being consumed in jet burners with a 5-inch flame. Taking the average of several trials, gas A gave a light as 2·16, compared to that of the wax-candle as 1; the condensation by chlorine was 15. Gas B, under similar circumstances, gave a light as 1·98; condensation by chlorine 13, and 15 13 : : 2·16: 1.86; by the shadow it was 1.98.

In another trial with other gases the light was compared with that afforded by a tallow candle (short six.) Gas C, the light was as 2.81, to that of the candle as 1; condensation by chlorine 15. Gas D, the light was 2 27, chlorine test 12,

and as 2.81: 2·27 :: 11: 8.02

and as 15: 13:: 1 : 8.00, which is a very close approximation.

Two gases were next contrasted with each other being consumed with fish-tail burners. By the shadow the light for equal consumpt was 1 to 827, by the chlorine, 14: 12, and as 14 12:1 : 857. In another trial with the same burners, but with gases prepared at another time, the average of numerous trials by the photometric process, gave the result as 1 to 945; condensation by chlorine was 12.5 and 11.5, and as 12.5 : 11.5: : : 192.

With jets and with other gases, the results were by the shadow 1 to 1.185, and by chlorine 11 to 14, and 11:14:: 1: 1272. Here the approximation is not so close as in some of the others.

The chlorine test was then tried with a gas, the illuminating power of which was inferior to that of the preceding. The trial by the shadow was made at different distances, to secure accuracy. By the one the result was as 1 to 1.347, by the other to 1.338, average 1 to 1342. The condensation by chlorine was 10 and 14, which very nearly coincides with the others.

think, be accounted for. It is well known that when the illuminating power of a gas is high, as when it is prepared by the decomposition of oil, it requires a burner with smaller apertures than those used for common coal-gas, otherwise it is not consumed to advantage. Now, in the experiment last recorded, in which the condensation by chlorine amounted to 17, a coal-gas jet was used, by which the gas would not give the same amount of light that it would have given, had a burner with smaller apertures been employed. Hence the illuminating power indicated by the shadow does not come up to what most likely it would have been with a differently constructed burner. May not this exception prove the accuracy of the proposed test?

From what has now been said with regard to the test which I have proposed, I think we are warranted in placing implicit confidence in it, as a means of indicating the illuminating power of coal-gas; indeed I have no hesitation in stating, that when the trial is properly conducted, it leads to results more satisfactory than those given by the shadow; for it has this advantage, that while it is much more easily conducted, it points out the amount of light that ought to be afforded by one gas as compared with another; whereas, unless all the different circumstances that affect the combustion of the gases are attended to, the results by the One of them, shadow will not be correct.

in particular, is the kind of burner,-for when gas is rich in matter condensible by chlorine, and a common coal-gas burner is used, the illuminating power indicated by the shadow will, most probably, be below what it really is, owing to the burner not being adapted for the combustion of that peculiar kind of gas; and hence one of the advantages of the chlorine test.

The process practised in the experiments I have detailed is, with a slight modification, the same as that formerly described. Two tubes of about half an inch in diameter, and 12 inches long, of the same calibre, and graduated to 100 parts, are employed; into the one 50 degrees of the gas under investigation are introduced, and afterwards into the other there are put 50 of chlorine; the water of the trough being heated to 50, or thereabouts. The coal-gas is then transferred into the chlorine, and the tube instantly covered with a shade, to prevent the action of the light. In the course of five minutes, the condensation is complete. Should only one graduated tube be used, the coal-gas must be measured first, and then put into another tube, after which the chlorine is measured, and the coal-gas transIn this instance the discordance may, I ferred into it; for, if otherwise, a part of the

The results above stated, very nearly agree with each other. In one trial, however, I found that they did not come so close. By the shadow they were 1 to 1.33, by the chlorine 11 to 17, now as 11: 17 :: 1 : 1.54.

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