Among the papers read at the meeting of the United States National Academy of Science, held at Northampton last month, was one by Captain Ericsson, which the author stated was an extract from an “Essay on Solar Heat “ upon which he is engaged. It appears that certain investigations relating to solar heat, undertaken chiefly with a view of ascertaining accurately how far the dynamic energy of the radiant heat of the sun can be made subservient in producing motive power, led him to consider, among other important practical manifestations of solar energy, the abrasion of the earth's surface caused by the flow of rain' water, in its course to the sea. In other words, the effect produced on the rotation of the earth by the mere change of position of the enormous masses of matter detached by the flow of rain water, irrespective of any expenditure of force called lor on account of friction in transit. It is evident, he says, that the effects resulting from the change of position of the matter abraded, are twofold as regards the earth's axial rotation. In the first place, the mat- •ter is brought nearer to the earth's center, which approach tends to increase the rotary velocity of the earth, since the weight transferred moves in a less circle at the base than at the top o"f th%hight from which it extends, consequently calling for the extinction of a certain amount ot vis viva. The increase of rotary velocity imparted to the earth from this cause is, however, almost inappreciable. Secondly, the abraded matter, besides its change of position relative to the earth's center, will, in its course towards the sea, either approach the equator or recede from it. In the former case the change will cause a retardation, while in the latter it will augment the earth's rotary motion round the axis. In order to arrive at some practical idea of the amount of retardation due to this cause, Captain Ericsson has chosen the Mississippi as his example. He has made choice of this river for the following reasons : It has been thoroughly surveyed, and it comprises in its field every variety of soil and climate, its source being among snows and lakes, frozen during a great portion of the year, while its outlet is near the tropics. How completely the Mississippi basin represents the average of the river systems of both hemispheres will be understood from . this fact, that although the rain gages at its northern extremity show only thirteen inches for twelve months, those of the southern extremity reach sixty-six inches with every possible gradation of rain-fall in the intermediate space. In addition to this important circumstance, the basin covers 21° of latitude and 85° of longitude, or 1,460 miles by 1,730 miles. It has been shown by the official reports prepared by Humphreys and Abbott in 1861 that the average quantity of earthy matter carried into the Gulf of Mexico, partly suspended in the water and partly pushed along the bottom of the river by the current, amounts for each twelve months to 903,100,000,000 of pounds. This enormous weight of matter is contributed by numerous large branches, and upwards of one thousand small tributaries. The mean distance along the streams by which the sediment is its eourse to the sea exceeds 1,500 miles; but the true mean which determines the amount of force acting to check the earth's rotation is far less. Now the center of the Mississippi basin rotates in a circle of 15,784,782 feet radius, and its velocity round the axis ot the globe is 1147 90 feet per second. The mouth of the river, on the other hand, rotates in a circle of 18,246,102 feet radius, with a circumferential' velocity of 1,826'89 feet per second. It will be seen, therefore, on comparing these velocities, that an increased circumferential velocity of very nearly 179 feet per seeond must be imparted to the sedimentary matter during its course from the center ot the basin to the mouth of the river. The question here presents itself, where is the motive energy to come from to impart the increased velocity acquired during the transit? The author states that the earth must supply the needed force. In other words, an amount of the earth's vis viva corresponding to the force required to generate the augmented speed will be extinguished. It has been stated above that the annual discharge of earthy matter at the mouth of the Mississippi is 903,100 millions of pounds. It has also been shown that there is an increase of velocity of 179 feet per second, a rate acquired by a fall through 500'6 feet. If, then, we multiply 908,100 millions by 500'6, we prove that the amount of energy to be given up by the earth in order to impart the stated increase of rotary velocity to the abraded matter exceeds four hundred and fifty-two trillions of foot pounds annually. But the formation of 30,000 square miles of delta, over which the Mississippi now runs, has required ages, during which the earth has been unceasingly deprived of vis TO»as.• The next point to be considered is whether there exists sufficient eompensatory force to make good the immense amount of dynamic energy expended. The mean rate of discharge into the Gulf of Mexico exceeds 38,600,000 pounds per second ; and, as has been already shown, there is an increase of circumferential velocity so considerable that a fall through 500'6 feet is necessary to generate the same. Therefore, the amount of vis viwa of which the earth is deprived every second by the waters of the Mississippi and its tributaries, will be 19,828,000,000 foot-pounds, or 85,188,000-horee power. What provision do we discover 'for making good this stupendous drag on the earth's rotation? The water precipitated on the Mississippi basin come chiefly from the Gulf of Mexico, raised by the heat of the sun. The gulf being situated south of the outlet of the river, the aqueous particles possess, at the commencement of the ascent, a greater circumferential velocity than the basin, and herfce tend to impart motion to the atmosphere during their northerly course. On purely dynamic considerations, that motion and the motion of the aqueous particles ought to restore to the earth the loss of vis w'va sustained, provided solar.influence be not present. But solar influence is present ; the atmospheric currents do not move altogether in accordance with static laws, but are controlled and perturbed by the heat of the sun—an outside force competent to di,ilturb and destroy terrestrial equilibrium. Hence it is found that in place of an easterly motion of the atmosphere tending to restore, by its friction against the surface of the basin, the loss under consideration, the sun is frequently expending a vast amount of mechanical energy productive of currents which, by friction in a contrary direction, augment the loss. Captain Ericsson observes that it would be futile to attempt a demonstration to prove that, owing to solar influence, the friction and other resistance called forth by the currents of air and vapor is inadequate to restore the loss of ®is viva sustained by the earth in sonsequence of the increase of rotary velocity which it must impart to the water of rivers running towards the equator. Nor would it be less futile to attempt a demonstration showing that the friction and resistance produced by such currents passing over the Mississippi basin from west to east is sufficient to restore the expended force of 35,000,000 of horse-power exerted in an opposite direction. As an example of rivers running in an op^site direction, the author makes choice of the Lena, which falls into the Arctic Ocean. In this case he shows that the force exerted in the direction of the earth's rotation very nearly balances the the retardation caused by the Mississippi. But the waters of the Lena, unlike the southern river, do not directly enter into a heated caldron, to be at once converted into vapor. The previously chilled masses of the Lena flow into the great polar refrigerator, and from thence are transferred to the evaporator in the equatorial regions. This transfer cannot be effected without a considerable retreat from the earth's axis —so considerable, indeed, that before the required evaporation takes place the waters are further from that axis than their source at the foot of the Gablonoi Mountains. There the imparted vis ®iva is more than neutralized. The author then proceeded to consider that portion of the subject which relates to the recovery of vis viva resulting from the lowering of the earth's surface by the abrasion caused by rain, and showed that the approach of the abraded matter towards' the center of the earth scarcely recovers 1-41,000,000th part of the energy parted with during the change of position in the direction of the equator. Captain Ericsson also urged as a cause of retardation the erection of towns and other edifices on the earth:' He considers that the change of position of the enormous masses of stone and earth in the form of bricks, together with the coal and other minerals from below the surface of the earth to some hight above it, cannot but be the cause of considerable retardation. He observed, in conclusion, that “ no reasonable doubt can be entertained that the earth sustains a loss of vis tia of 39,894,658 foot-pounds every second. Multiply this sum by 86,400 seconds, we learn that every succeeding day marks a diminution of the earth's vis viva of 3,446,898,451,200 footpounds, in consequence of the change of position of the abraded matter carried towards the equator.”