A NEW interest seems now to be taken in Ocean Currents, and much is being said and written upon the subject. In the investigation of this subject it is very important that we should understand well all the forces and agencies concerned in the production and maintenance of the currents, and that we should consider well all the principles, and theories based upon hypothetical forces, which have come down to us from preceding generations, however plausible and however much sanctioned by high authority they appear to be. As in the case of the winds, so also in ocean currents, the modifying force arising from the earth's rotation has a very important bearing, and should be well understood. There are certain erroneous views in connection with this force, which have come down to us from preceding generations, and which are contained in text-books, and are being taught in colleges and schools, which are liable to have, and do have, a mischievous bearing upon this subject. These are the more dangerous because they appear to have received at least the tacit sanction of past ages, so that almost any one is liable to adopt them without much consideration. Prof. Colding has in this way been unsuspectingly let into error in his recent paper on ocean currents. We are all familiar with the usual explanation of the trade-winds contained in text-books, which assuming that a particle of air at the equator, at rest relatively to the earth, and consequently having a lineal velocity in space of about 1,000 miles per hour, is forced to move toward the pole, it will, on arriving at the parallel of latitude where the earth's surface has a velocity of only 900 miles, still have its velocity of 1,000 miles per hour in the case of no friction, and consequently have a relative velocity of 100 miles per hour, and on arriving at the parallel of 60°, will still have its initial velocity of 1,000 miles, and consequently have a relative velocity of 500 miles per hour. But this is at variance with a fundamental and well-established principle in mechanics. The force in this case is a central force, or at least the compound perpendicular to the earth's axis can be neglected, since it can have nothing to do with any east or west motion. This being the case, the principle of the preservation of areas must be satisfied, and consequently the particle of air, when it arrives at the parallel where the earth's surface has a velocity of 900 miles, must have a velocity of more than 1,000 miles, and a relative velocity of more than 200 miles per hour, and on arriving at the parallel of 60°, where the earth's surface has a velocity of 500 miles, it must have a velocity of 2,000 miles, and consequently a relative velocity of 1,500 miles, instead of 500 miles per hour. Adopting thoughtlessly, and very naturally, the erroneous principle which is usually taught, that a particle of air or of water in moving toward or from the pole, tends to keep its initial lineal velocity relative to space, Prof. Colding estimates the amount of deflecting force due to the earth's rotation, eastward when the particle is moving towards the pole, and westward when moving from the pole, and the result is, that his force is just one half of what it really is. Consequently, all the results based upon his estimated amount of this force should be doubled. Prof. Colding has also entirely neglected one component of the force due to the earth's rotation. It has been shown by Prof. Everett, and also by the writer, that when a body moves east or west, there is also a similar deflecting force due to the earth's rotation, exactly equal to the former. Prof. Colding has, therefore, taken into account only the one-fourth part of the whole force. If he had taken in this latter component of the force also, and resolved it in the direction of the line of motion and perpendicular to it, as he did the former, he would have found that the parts in the direction of motion, arising from both components, exactly cancel one another in all cases, and that the resultant of both components is a force perpendicular to the direction of motion. This force then tends only to change the direction of the motion, and never to accelerate or retard it, in whatever direction it may be. Prof. Colding's result, therefore, that the velocity of the current is accelerated by the earth's rotation, when moving in certain directions, and retarded in others, is erroneous.