instance, where a thousand clerks were employed, it would greatly facilitate the operations of calculation and book-keeping. Thus, discarding millits, (for bankers now excluded the subdivisions of a penny in their accounts,) the sum of 177. 3 Victorines, 7 cents would be represented at once by 17.37; only two places of decimals, instead of as now in pounds, shillings, and pence. It was shown how the principle was applicable, with still greater advantage, in cases of weights and measures, where the scale was now most anomalous and absurd. Suppose the rental or value to be required, and that the land cost 697. 3 Victorines, 4 cents an acre; the reduction in common arithmetic was one of very considerable labour, difficulty, and time. Indeed, if this decimal system were adopted, the labour of teaching arithmetic to school-boys would be reduced nearly one-half. But by this plan, (as the rev. author showed,) the result might be obtained in five lines of decimals, containing only twenty-one figures. The most extensive change in weights recommended by the Committee would be to introduce the uniform weight of 101b. to the stone. instead of the varieties of 8lb. in some, and 14lb. or 16lb. in other parts of the kingdom; the hundred-weight to be called centua, a German term. These were all the changes proposed in weights.

As to the measure of length, the Commission thought it too violent a change to alter all the milestones; but there would be no difficulty, (with reference to the standing order of Parliament in railway matters, &c.) to introduce the measure of 1000 yards, and call it a milyard.

ON WAVES.

MR. SCOTT RUSSELL has communicated to the British Association, the results of Experiments recently made by him, which he wished to present as a Supplement to the former Report of a Committee on Waves. (See Year-Book, 1841, p. 106; 1842, p. 96.) On former occasions he had submitted observations that were principally directed to the examination of one kind of wave, but his present communication referred to new and beautiful phenomena of a different class.

Much of the difficulty in attaining clear conceptions of the phenomena and mechanism of waves is to be attributed to confounding with each other, under the general name of wave motion, a variety of phenomena essentially different in their origin, their form, and their laws; and he had now matured this classification. Of waves there seem to be three great orders, obeying very different laws:-1, Wave of the first order, the wave of translation,-is solitary, progressive, depending chiefly on the depth of the fluid: has two species, positive and negative. 2, The waves of the second order,-the oscillatory waves,-are gregarious; the time of oscillation depending on the amplitude of the wave of two species, progressive and stationary. 3, The waves of the third order,-capillary waves; gregarious: the oscillations of the superficial film of a fluid, under the influence of the capillary forces, extending to a very minute depth: short in duration: of two species, free, and constrained. To the last of these classes he wished to draw attention, as amongst the phenomena which we most frequently

see, and have yet failed to examine. He believed them to be the minute waves or dents indicated by the theory of Poisson: he had, therefore, thought it his duty to examine them. The waves of the third order were observed by Mr. Scott Russell in the following manner :— a slender brass wire was inserted vertically into a still fluid, and drawn in that position slowly along its surface. When the velocity is one foot per second, the surface of the water exhibits a group of waves of great beauty and regularity, extending forward before the exciting point, and spreading on both sides of it in the form of a con-focal group of hyperbolas; the focal distance of each hyperbola, and its asymptotes, being determined by the velocity of the motion. Although the exciting point was no more than one-sixteenth of an inch in diameter, these waves extend over several feet, and the diagrams exhibited the phenomena as having great regularity and beauty. Numerical results, showing the number of these waves in an inch of distance from the exciting point, are nearly as follows :

These waves were examples of capillary waves, not in free but constrained motion. He had generated them in a different manner, so as to examine them in free motion, uninfluenced by the generating point; and found that the capillary waves, when moving freely, have a constant velocity of 8 inches per second-that their duration is short, becoming insensible in about twelve seconds after describing a path not longer than eight or nine feet; in the free state, their breadth is very small at first, gradually increases, and just before vanishing attains an amplitude of nearly an inch. The capillary waves are among the phenomena we most frequently observe. It is in generating them that a gentle breeze forming over the surface of a smooth lake destroys the translucent and reflective power of the surface; they are also to be observed in all cases of primary and secondary wave motion, when the superficial film is by any cause compressed, so as to produce corrugation, and they always disappear in about twelve seconds after the exciting cause is removed. The second order of waves had also been made the subject of careful observation. A mode had been discovered of generating these waves in large groups, so that instead of observing single waves, the length of one could be deduced from the measured length of a number, thus getting the advantage of repetition of the quantity observed. It had thus been finally determined, that these oscillating waves follow Newton's law in so far that the velocities of transmission are as the square roots of the amplitudes; but the absolute velocity differs from that of Newton, so that, instead of having

the wave whose period is a second of an amplitude=3.26, it is found to be 3.57. The velocities determined are as follows:

Mr. Russell had also completed some further examinations of the wave of the first order, and could now present the subject in a tolerably complete form.-Athenæum, No. 766.

At the late meeting of the British Association, was read a communication from Mr. Walker, (of Plymouth,) who found that waves near the breakwater, in 36 feet water, moved faster, and were further apart, than those in 24 feet water and nearer the pier-head; but all those waves moving shoreward had their velocities diminished as they approached the shore. He found, in one instance, waves traversed 46 feet per second, and were 460 feet apart, breaking in five fathoms water; others had a velocity of 42 feet per second, and were 442 feet apart; the height of the unbroken waves was 27 feet above the surfacelevel, and they broke in five and six fathoms. Others, again, had a velocity of 46 feet per second, the distance between them was 345 feet, and the height of the unbroken wave only five feet.

THE STEAM-WAVE.

On Feb. 3, was read to the Royal Society, an abstract of a paper "On the Steam-wave," by the Rev. Thomas Boys. The term Steamwave is employed by the author to denote that peculiar kind of wave which is generated during the motion of steam-vessels on the water; and which, he shows, results from the combination of two separate sets of waves; namely, those occasioned simply by the progressive advance of the vessel, and which consequently recede from it on each side, nearly at right angles to its course; and those arising from the impulses given to the water by the action of the paddles, and proceeding in the same direction as the vessel itself. He ascribes the cumulative force acquired by the waves at the parts where they cross one another, to the extraordinay violence of effect with which they strike against all obstacles opposed to their progress, and which renders them so formidable to boats and other small vessels exposed to the encounter.

OIL UPON WAVES.

ON June 27, was read to the Academy of Sciences, at Paris, a paper on the effect of Oil in calming the Waves of the sea, by M. Van Beck. M. Van Beck thinks, with Franklin, that the phenomenon

may be explained by admitting that there exists between air and water a certain natural affinity or adhesion. Water, he says, takes in with avidity the air with which it comes in contact, so that it is with difficulty expelled. It results that, whilst a current of air passes over the surface of the water, the air attaches itself to the liquid, and creates small waves, which, as the wind increases, become large and dangerous. As soon as these waves are covered with a membrane of oil, the adhesion of the air upon the water ceases to exist, and the surface is no longer disturbed.

"MOUNTAIN-HIGH" WAVES.

SOME writers have asserted that the height of the Waves of the ocean, from the trough to the crest, reaches often 40 and 50 feet. But Dr. Arnott, in his Elements of Physics, affirms that "no wave rises more than 10 feet above the ordinary sea level, which, with the 10 feet that its surface afterwards descends below this, gives twenty feet for the whole height, from the bottom of any water valley to the adjoining summit." From observations subsequently made with great care in the midst of the Pacific Ocean, by the French Exploratory Expedition, it appears that Dr. Arnott was very nearly right. The maximum height was then found to be 22 feet.-Mechanics' Magazine.

46

TIDES OF THE FRITH OF FORTH.

MR. SCOTT RUSSELL has presented to the British Association, a Report on the Abnormal Tides of the Frith of Forth," supplemental to a former Report on the same subject. (See Year-Book of Facts, 1841, p. 106.) He had on a former occasion presented the result of tidal observations on the Frith of Forth. These observations brought to light the existence of certain very remarkable tidal phenomena, proving the occurrence, on some parts of that Frith, of double tides, or rather perhaps of quadruple tides; being four high waters in each day, instead of only two, as usual. When this subject was formerly discussed, Mr. Russell attributed those anomalies to the great southern tide wave entering the Frith at a different period from the northern tide wave, to which the periods of high and low water on the east coast of Britain are principally due. But other explanations had also been suggested in quarters so high as to entitle them to great respect. For the purpose of settling this question, and, if possible, reducing these anomalous tides to some law, Mr. Russell had recently instituted a second series of observations on the Tides of the Frith of the Forth, conducted under very careful observers; the height of the tide being observed simultaneously by different observers, at the different stations, who recorded their observations every five minutes, and continued them unceasingly night and day. They had only as yet extended over a few weeks, but already there had come out of them results of a decided character, so as to set at rest the question of the origin of these tides, and to illustrate some curious points in the history of littoral tides. The tides already

observed had, he thought, proved the accuracy of the theory he had formerly advanced on this subject.

Mr. Russell's theory is this: that the tidal wave is a compound wave of the first order; that its phenomena are correctly represented by the wave which he has called the great wave of translation-that this tide's motion along our shores is correctly represented by this type. Now, the wave of translation in ascending a channel whose breadth and depth vary, exhibits the following phenomena :-First, a velocity varying as the square root of the depth of the channel; second, an increase of height with the diminution in breadth and in depth of the channel; third, a dislocation of the centre, which is transferred forwards in the direction of transmission according to a simple and wellestablished law. And these changes exactly correspond to the epoch of high water, the law of rise and fall, and the exaggeration of range in the Frith of Forth. Of the four successive high waters of each day, he has ascertained the latter tide of each pair to be normal, and the earlier the abnormal tide. It is well known that the tide which brings high water to the east coast of Britain, as far at least as the Thames, comes round the north of Britain, bringing high water to Aberdeen about noon, Leith about two, and London about twelve o'clock at spring tides. This wave is the same which brings to the whole of the Frith of Forth the normal high water, and of the double tides the later of each pair corresponds exactly with the time as predicted by the excellent tables of Mr. Lubbock. But if we conceive the great southern wave, which comes up the English Channel, to continue its course northward in the opposite direction to the normal tide, it would enter the Forth at ten o'clock, being two hours previous to the normal tide, due to the succeeding transit of the moon; or the tide E at Leith will consist of the normal tide due to transit B and the abnormal tide due to transit A. Now, the double tides are in exact correspondence with these conditions, the abnormal tide being generally about two hours in advance of the normal tide. But the circumstance which most perfectly fixes the identity of the tides, as due to the successive transits A and B, is found in the character of their diurnal irregularities. If the theory adduced be correct, the normal and the abnormal tides will have opposite inequalities. The observations made exactly correspond with this view; and, so far as they go, establish the soundness of the view which has been adduced for their explanation. Another remarkable confirmation of this view is derived from the examination of the diurnal inequality of places on opposite coasts at the mouth of the Forth; the diurnal inequality on the south side being that due to the northern or normal tide, and that on the northern coast being that due to the abnormal or southern tide wave. At Leith, both waves, meet; whilst, the inequalities nearly neutralize each other, and give only the difference of the inequalities. By the same process, using the wave of translation as a type of the tide wave, some further anomalies of the tide wave were illustrated; and the absence of all tide frequently observed on opposite and adjacent coasts, as at the north of Scotland, and the opposite coast of Norway. These are