of four experiments. The load in every case was 40 lbs. The inclinations of the plane were as follows: No. 1 15° 6', No. 2 =16° 9', No. 3 =17° 5′, No. 4 =18° 9'.

Table A shows the accelerations corresponding to different velocities in the four experiments. The units used are the To of an inch and the of a second.

Table B shows the coefficients of friction in each experiment, deduced by substituting the observed accelerations given in Table A in the formula given above. The observed accelerations were of course reduced to feet in a second.

From the tables it will be observed: 1st. That with a given

inclination of the plane, the coefficient of friction decreases as

would trace upon the smoked glass a waved line, which would be a perfect autographic register of the experiment. The time of sliding, the velocity at any point, the distance passed over in any unit of time, could all be measured or counted directly from the smoked glass.

The graphical method of working up the experiment was employed, as follows: The bottom of a sheet of section paper was made a "time line" (5 of a sec.= a unit). At various points on this line the corresponding velocities were erected as ordinates. The equation of a line connecting the upper extremities of these ordinates would express the law of the motion studied.

It is evident that this line would have been straight if the acceleration of the slide had been uniform, like that of a body falling in vacuo. If, however, a variable resistance be opposed to the motion of the slide, the acceleration will no longer be uniform, and the line will become curved, concave toward the axis of abscissas, if the resistance is increasing, convex if the resistance diminishes. The acceleration of such a motion at any time will be proportional to the tangent of the angle which the direction of the curve at that point makes with the time line. It is also evident that such acceleration may at once be measured from the paper, since it is the difference between the velocities for two successive units of time. The curve constructed as above, from every experiment made, was decidedly convex toward the time line, showing a constantly decreasing resistance to the motion of the slide as the velocity increased. If we assume that this increase in acceleration was due to a diminished coefficient of friction, the value of the coefficient for any time may be found in the following manner:

Let a, b, and h the altitude, base, and length of the inclined plane.

W= weight of the slide and contents.

W'= normal pressure on the plane,

b

= W.

h

g= acceleration of a body falling freely.

a

g' theoretical acceleration of the slide =g..

g" the observed acceleration at any time.

=

W

Then the resistance of friction = F= (g'-g'), and the co

The following tables give the results obtained from a series

of four experiments. The load in every case was 40 lbs. The inclinations of the plane were as follows: No. 1 =15° 6', No. 2=16° 9', No. 3 17° 5', No. 4 =18° 9'.

Table A shows the accelerations corresponding to different velocities in the four experiments. The units used are the T' of an inch and the of a second.

Table B shows the coefficients of friction in each experiment, deduced by substituting the observed accelerations given in Table A in the formula given above. The observed accelerations were of course reduced to feet in a second.

From the tables it will be observed: 1st. That with a given

inclination of the plane, the coefficient of friction decreases as

the velocity increases, rapidly at first but more slowly afterward. 2d. With the same velocity, the coefficient of friction is greater the greater the inclination of the plane, within the limits of the experiments. 3d. The coefficient of friction in each experiment tends toward a constant quantity. 4th. This constant seems to be the same in each experiment.

No simple expression which will show the variations in the coefficient of friction has yet been found; indeed, I have not thought best to attempt to formulate the work till certain errors, which will be referred to, have been corrected. It was found impossible to procure a plank with a perfectly uniform surface. The one used in the experiments given showed at the same inclination and velocity à coefficient which slightly but regularly increased from one end to the other. The end which gave the lower coefficient was placed uppermost. The obvious result of this was to make the coefficients in Table B at high velocities greater than they otherwise would have been. This fact also explains the apparent anomaly in columns 3 and 4 of the same table, where the coefficients at high velocities are seen to fall below the corresponding coefficients in col

umn 2.

In experiment 4 the slide had the velocity 120 at a distance of 40 inches from the upper end of the plane; in experiment 2 it did not acquire that velocity until it had passed over a distance of 60 inches, and consequently was on a rougher portion of the plane. The uniformity of the plane was tested by starting the slide at different points along its length, and comparing the curves on the smoked glass. These experiments have not been corrected for the resistance of the atmosphere. The effect of such correction would be to diminish still more the coefficients at high velocities.

As the inclination of the plane increases the normal pressure decreases. Thinking that this change of pressure might explain a part of the difference due to a change of inclinations, we made three experiments at the same inclination, with weights of 18, 80 and 140 lbs., in the box. At the end of one second we found the velocities in the three cases to be as 1, 1.18 and 1.32, showing a less resistance in the case of the greater load, and corresponding to a decrease of about 21 per cent in the coefficient of friction. This seems to be insufficient to explain the change in the coefficient when the inclination of the plane is changed. But it is interesting as showing that in the case of pine on pine friction is not strictly proportional to the normal pressure.

As soon as possible we propose to repeat these experiments, extending the range of velocities, also to try the effect of a change of pressure, with a view to formulate deviations from

the received laws, if simple expressions can be found. We have also designed a modification of apparatus to test our results when a uniform motion is given to the slide.

The experiments in the series (nearly 100 in number) and a greater part of the computations have been very carefully made by Messrs. Butterfield and Wilson, students in the department of Physics.

ART. XXIII.-On the constitutional formulæ of Urea, Uric Acid, and their derivatives; by Professor J. W. MALLET, University of Virginia.

FEW classes of organic compounds have given rise to more difference of opinion amongst chemists than that which includes urea and its conjugates.

The remarkable number of such compounds, their complicated relationships, the varied circumstances of their production and decomposition, and their variety of chemical character, have led to nearly every one of them being viewed in several different lights, and represented by several different formulæ, by those who have given the subject special attention.

The structure of the simple molecule of urea itself is by no means settled. The arguments of Heintz* and Kolbet in favor of the view that urea is identical with carbamide (H,N-CO -NH,) have been opposed by the observation of Wanklyn and Gamgeet as to the behavior of urea (unlike that of admitted amides) when oxidized by an alkaline solution of potassium per-manganate. The latter chemists proposed the formula ((NH)"

CNH,, but, as Watts remarks in his Dictionary of ChemOH

istry, without assigning specific reasons (other than the difference of behavior just noted) for adopting this instead of the carbamide formula which they reject. Wolcott Gibbs | independently put forward the same view, but did give some of the grounds upon which it was adopted by him. It has also been proposed to represent urea as O=C=NH,-NH,, in which formula one of the nitrogen atoms is pentad. Most recent writers of text-books, however, as Fittig and Naquet,** seem to have fallen back upon the view that urea is simply carb* Ann. der Chem. u. Pharm., cxl, 276; cl, 73. Zeitschr. für Chem., II, iii, 50. Jour. Chem. Soc., Jan., 1868, 31. § 1st Suppl., 1115.

Amer. Jour. Sci., II, xlvi, 290, Nov., 1868. TWöhler's Grundriss der org. Chem., 8te. Aufl., 206.

** Principes de Chimie, troisème éd., t. ii, 532-533.

AM. JOUR. SCI.-THIRD SERIES, VOL. XI, No. 63.-MARCH, 1876.