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inclusive, and those tending to depress it, for the other six months, from September to February inclusive." By referring to the preceding curve representing the variation of mean level at Key West, it is seen that these winds cannot cause the corrected variation of mean level, since the argument of variation of the former does not at all correspond with that of the latter, and hence there must be still some other cause affecting the mean level of the sea at Key West also.

From what has been stated, it is evident that the effect of the winds at Brest must be to decrease the amount of variation, and to cause the maximum and minimum to happen a little later in the season of the year. On the other hand, their effect at Key West must increase the variation and cause the maximum and minimum to happen earlier in the season of the year. If, therefore, the variations of mean level at Brest and Key West were corrected for the effect of the winds, the arguments of the variations at both ports would probably be the same, making the maxima and minima of the variations about October and April. This indicates that the cause or causes of the variation of mean level which we have yet to seek are not local, but more general, affecting both ports simultaneously. There have been no researches to show that the argument of the corrected variation of mean level would be about the same at other ports of the Atlantic ocean also.

There is still another cause affecting the mean level of the ocean at different seasons, which is much more effective than either of those which have been stated, and which, I think, satisfactorily accounts for the remaining and greater part of the observed variation, which has not been explained. This is a tangential force arising from the motions of the ocean combined with the motion of the earth's rotation. It was first brought out in its most general form in my paper on the “ Motions of Fluids and Solids relative to the Earth's Surface, published in the Mathematical Monthly, and also in an abridged form in Silliman's Journal (Second Series, Vol. XXXI.), and expressed in the following language: In whatever direction a body moves on the surface of the earth, there is a force arising from the earth's rotation which deflects it to the right in the northern hemisphere, but to the left in the southern hemisphere. From this force there must arise a change in the level of the sea wherever its waters have a motion of any kind, and as these motions depend, for the most part, upon the difference of temperature of the ocean between the equator and the poles, and consequently upon the change of seasons, there must be a change in the mean level of the sea at most ports corresponding with the change of seasons. The principal motion of the water of the Atlantic Ocean affecting its level is the motion by which it is supposed to complete a gyration in about three years. In the paper already referred to it was shown that the force arising from this gyration would cause the middle of the gyrating mass of the water to stand about five feet higher than the exterior part on the coast of Europe and America. Now as the greatest difference of temperature in the ocean between the equator and the poles must be in the latter part of winter, a little later than the time of the greatest difference in the atmosphere between the equator and the poles, the greatest gyratory motion of the water of the Atlantic Ocean, on account of the inertia of the water, must happen still a little later, say in April, and then the surface of the water must stand highest in the centre of the gyrating part, and lowest at the exterior part, and consequently at the ports of Brest and Key West. On the contrary, in October, when the gyratory motion is the least, the surface must fall a little in the middle and rise a little at its exterior part, and consequently stand at its maximum height at the ports of Brest and Key West. The position of the gyrating mass also changes with the seasons, being farthest north in the fall, and nearest the equator in the spring, as must necessarily be the case, and as the vibrating motion of the northern part of the Gulf Stream indicates. The surface of the gyrating water being a little convex, this circumstance must also affect the mean level slightly at some ports.

The difference between the maximum and minimum mean height of the sea at Brest is about six inches, which, when corrected for the effect of the winds and other causes, would probably be a little more. The difference at Key West, corrected in like manner, would probably be about the same. A decrease, therefore, of less than one half in the gyratory velocity of the ocean from April to October would be sufficient to cause a variation of that amount in the mean level of the sea at Brest and Key West ; and as the argument of the variation of the gyratory motion of the Atlantic Ocean, as we have seen, must very nearly or quite correspond with the argument of the variation of mean level unaccounted for by other causes, we have reason to think that the variation of the gyratory motion of the Atlantic Ocean is the cause of this part of the change of mean level.

Five hundred and Afty-seventh Meeting.

November 8, 1865. — STATUTE MEETING.
The PRESIDENT in the chair.
Mr. Safford presented the following paper:-

On the Right-Ascensions observed at Harvard College Ob

servatory in the Years 1862-1865. By T. H. SAFFORD.

It is part of every astronomer's duty to assure himself in some way of the accuracy of the elements upon which the reduction of his observations depend. If he is a meridian observer, he must make sure that the right-ascensions of the clock- and polar-stars which he employs are correct; and the most thorough means of so doing is to determine them by his own observations.

It is true that this process requires much time and patience; that we, in America, are tempted to think that it has all been so excellently done abroad, that anything we can do will not add to the accuracy of the determinations we derive from foreign sources. I think this notion is somewhat ill-founded. The quantities in question are, as above stated, the right-ascensions of standard stars; they must be predicted, and are so predicted for many years in advance; and the simple formula by which this prediction has to be made,

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shows that not only do the errors of the modern observations come in with more than their full amount, but are somewhat increased by a part of those of the ancient ones.

It ought also to be considered that the observations made with any meridian instrument are liable to errors of obscure origin, which make it somewhat better to use its own results to reduce other observations obtained with it; and that, on the other hand, each good instrument well used, and each well-trained observer, contributes something to the general foundations of the science which no other observer or instrument can do.

The eminent German, English, Russian, and French astronomers have followed this plan within the present century.

Admirable fundamental catalogues have appeared from the observatories of Königsberg, Åbo, Dorpat, Cambridge (Eng.), Greenwich, Edinburgh, and Paris ; and two from Pulkova and one from Leiden are to appear within a few years.

I wish to call the attention of American observers to this subject, and will give a short sketch of the process, and enumerate the systematic errors which must be guarded against, and their sources.

First, it is assumed that an approximate catalogue of time-stars is at hand; the first object is to obtain a correct right-ascension of Polaris, peculiar it may be in some degree to observer and instrument, and this is done by opposite culminations, at all seasons; or at two opposite seasons, as spring and autumn. If the values for spring and for autumn differ by any sensible amount, the instrument is ill-mounted, but a constant difference of three seconds of time here did not prevent Bessel from obtaining a value accurate to 08.3. In our Cambridge observations of Polaris, this difference has been much less ; in fact hardly sensible.

The next step is to derive the right-ascensions of other polar stars from that of Polaris; and it is here necessary to observe at two opposite seasons of the year, or, which is the same thing, at two opposite culminations.

Now comes the comparison of time stars among themselves, and the best method, and the method which must in all cases form the ultimate test, is to begin by comparing at two opposite seasons the stars Castor, Procyon, and Pollux with the stars y, a, B Aquilæ ; and, finally, to compare the remaining fundamental stars (Maskelyne's 36, for example) with both these groups, though oftener with the nearest one. But this is a method which requires a very perfect clock, especially with perfect compensation, or else not exposed to changes of temperature. In case it is not practicable, we may content ourselves for a time with the more ordinary process of assuming the freedom from constant error of large groups of stars, and thus getting the individual errors of the assumed fundamental catalogue ; and the only objection which I know to it is, that being almost universally employed, and Bessel's Fundamenta being the old Catalogue always used for proper motion, we may in this way accumulate dangerous errors, sensibly identical, in nearly all modern observations. It is, therefore, desirable that this point, too, should be tested oftener than it is.

At the Observatory of Harvard College, a fundamental catalogue of about three hundred and twenty stars is now in process of reduction, which depends on nearly ten thousand observations made since 1862. The instrument has shown a stability of mounting sufficient for an independent and accurate determination of thirty-five polar stars, while it has also proved itself capable of being used for exact right-ascensions of time-stars by the excellence of its pivots, and its general stiffness.

The catalogue will be, if I am not mistaken, the first American Fundamental Catalogue of Right-Ascensions ; I can venture to call it 80, although the still unfinished normal clock, and the lack of a good circle for solar observations, compel some reliance upon the general accuracy of other determinations. But with the requisite apparatus, about one thousand more observations would free us from even this necessity.

Mr. Oliver presented the following paper:

On some Focal Properties of Quadrics. By J. E. OLIVER.

I. Any two quadrics have one, and usually but one, common autopolar tetrahedron, T. Referred to this their equations become

U= aw? + bx? + cya + dz=0,

Y= a 2 + B x + xyz + 8z = 0, whether in tangential or in point-coördinates. Using tangential coördinates, all the quadrics

Utar= (a + 2a) w* +.....=0 (1) have a common enveloping developable ; and the entire system is determined by any two of its quadrics (or by any eight of its developable’s planes which are not specially related].

The four quadrics that correspond to

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are plane conies in the respective planes of reference.

Deforming T and (1) together till T has one plane at infinity and the other three mutually orthogonal, and then lengthening in suitable proportions the three sets of principal axes, the rectangular pointequation of the system becomes

2 2 , ya Annet Bath + 0212=1, .. (2)

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