of rolled pebbles gathered in the Orange River. This led to the river-diggings' on the Orange and Vaal rivers, which continue to the present time.

In 1870, at which time some ten thousand persons had gathered along the banks of the Vaa!, the news came of the discovery of diamonds at a point some fifteen miles away from the river, where the town of Kimberley now stands. These were the so-called dry diggings,' at first thought to be alluvial deposits, but now proved to be volcanic pipes of a highly interesting character. Four of these pipes or necks, all rich in diamonds, and of similar geological structure, were found close together. They have been proved to go down vertically to an unknown depth, penetrating the surrounding strata.

The diamond-bearing material at first excavated was a crumbling yellowish earth, which, at a depth of about fifty feet, became harder and darker, finally acquiring a slaty blue or dark green color and a greasy feel, resembling certain varieties of serpentine. This is the well-known 'blue ground' of the diamond miners.

It is exposed to the sun for a short time, when it readily disintegrates, and is then washed for its diamonds. This blue ground has now been penetrated to a depth of six hundred feet, and is found to become harder and more rock like as the depth increases.

Quite recently, both in the Kimberley and De Beers mines, the remarkable rock has been reached which forms the subject of the present paper. The geological structure of the district, and the mode of occurrence of the diamond, have been well described by several observers.

As Griesbach, Stow, Shaw, Rupert Jones, and others have shown, the diamond-bearing pipes penetrate strata of carboniferous and triassic age, the latter being known as the Karoo formation.

The Karoo beds contain numerous interstratified sheets of dolerite and melaphyr, also of triassic age, the whole reposing upon ancient mica schists and granites. The careful investigations of Mr. E. J. Dunn demonstrate that the diamond-bearing pipes enclose fragments of all these rocks, which fragments show signs of alteration by heat. Where the pipes adjoin the Karoo shales, the latter are bent sharply upwards, and the evidence is complete that the diamond-bearing rock is of volcanic origin and of post-triassic age.

The diamonds in each of the four pipes have distinctive characters of their own, and are remarkable for the sharpness of their crystalline form (octahedrons and dodecahedrons), and for the absence of any signs of attrition. These facts, taken in connection with the character of the blue ground, indicate, as Mr. Dunn has pointed out, that the latter is the original matrix of the diamond.

Maskelyne and Flight have studied the microscopical and chemical characters of the blue ground, and have shown that it is a serpentinic substance containing bronzite, ilmenite, garnet, diallage, and vaalite (an altered mica), and is probably an altered igneous rock, the decomposed character of the material examined preventing exact determination of its nature. They showed that the diamonds were marked by etch figures analogous to those which Prof. Gustav Rose had produced by the incipient combustion of diamonds, and that the blue ground was essentially a silicate of magnesium impregnated with carbonates.

The blue ground often contains such numerous

fragments of carbonaceous shale as to resemble a breccia. Recent excavations have shown that large quantities of this shale surround the mines, and that they are so highly carbonaceous as to be combustible, smouldering for long periods when accidentally fired. Mr. Paterson states that it is at the outer portions of the pipes where the blue ground is most heavily charged with carbonaceous shale that there is the richest yield of diamonds.

Mr. Dunn regards the blue ground as a decomposed gabbro, while Mr. Hudleston, Mr. Rupert Jones, and Mr. Davies regard it as a sort of volcanic mud. Mr. Hudleston considers that the action was hydrothermal rather than igneous, the diamonds being the result of the contact of steam and magnesian mud under pressure upon the carbonaceous shales, and likens the rock to a boiled plum-pudding.'

The earlier theories as to the origin of the diamond have, in the light of new facts, quite given way to the theory that the diamonds were formed in the matrix in which they lie, and that the matrix is in some way of volcanic origin, either in the form of mud, ashes, or lava.

The exact nature of this matrix becomes, therefore, a matter of great interest. The rocks now to be described are from the deeper portions of the De Beers mine, and were obtained through the courtesy of Mr. Hedley. They are quite fresh, and less decomposed than any previously examined. Two varieties occur, - the one a diamantiferous, the other free from diamonds, and the lithological distinction between them is suggestive. The diamantif⚫erous variety is crowded with included fragments of carbonaceous shale, while the non-diamantiferous variety is apparently free from all inclusions, and is a typical volcanic rock.

Both are dark, heavy, basic rocks, composed essentially of olivine, and belong to the group of peridotites. Both are of similar structure and composition, differing only in the presence or absence of inclusions. The rock consists mainly of olivine crystals lying porphyritically in a serpentinic ground-mass.

The olivine is remarkably fresh, and occurs in crystals which are generally rounded by subsequent corrosion. The principal accessory minerals are biotite and enstatite. The biotite is in crystals, often more or less rounded, and sometimes surrounded by a thin black rim, due to corrosion. Similar black rims surround biotite in many basalts. The biotite crystals are usually twinned according to the base. The enstatite is clear and non-pleochroic. Garnet and ilmenite also occur, the latter often partly altered to leucoxene. All these minerals lie in the serpentinic base, originally olivine. This rock appears to differ from any heretofore known, and may be described as a saxonite porphyry.

The diamond-bearing portions often contain so many inclusions of shale as to resemble a breccia, and thus the lava passes by degrees into tuff or volcanic ash, which is also rich in diamonds, and is more readily decomposable than the denser lava.

It seems evident that the diamond-bearing pipes are true volcanic necks, composed of a very basic lava associated with a volcanic breccia and with tuff, and that the diamonds are secondary minerals produced by the reaction of this lava, with heat and pressure, on the carbonaceous shales in contact with and enveloped by it.

The researches of Zirkel, Bonney, Judd, and others, have brought to light many eruptive peridotites, and

Baubree has produced artificially one variety (lherzolite) by dry fusion, but this appears to be the first clear case of a peridotite volcano with peridotite ash. Perhaps an analogous case is in Elliot county, Kentucky, where Mr. J. S. Diller has recently described an eruptive peridotite which contains the same accessory minerals as the peridotite of Kimberley, and also penetrates and encloses fragments of carboniferous shale, thus suggesting interesting possibilities. H. CARVILL LEWIS.

The eccentricity theory of the glacial period. I desire to add a supplementary note to my letter of Aug. 16, published in the issue of Science for Aug. 27.

In that letter I called attention to the contrast between the northern and the southern hemisphere in respect of glaciation, as tending to show, that, other things being equal, a climate of means (mild winters and cool summers) is more favorable to the accumulation of snow and ice than a climate of extremes (cold winters and hot summers). The bearing of this proposition upon the eccentricity theory is pointed out in my letter.

I now wish to call attention to another well-known geographical fact, which seems to confirm the conclusion that glaciation is favored by a climate of means rather than by a climate of extremes. I refer to the altitude of the snow-line in torrid, temperate, and frigid zones respectively. At the equator the snowline falls below the annual isothermal plane of 32° F.; while, as we recede from the equator, the snowline rises above the plane of 32°. So far does the snow-line rise above the isothermal plane of 32°, as we go polewards, that, while the latter plane reaches the sea-level not far from 60° latitude, it has been doubted whether in the northern hemisphere the snow-line anywhere reaches the level of the sea. According to J. D. Forbes, the mean temperature at the snow-line near the equator is 34.79; in the temperate zone it is 25.3°; in the arctic regions, about 21" (Johnston, Physical atlas of natural phenomena, Edinburgh and London, 1856, p. 33). While all such numerical statements of the temperature of the snow-line in different latitudes can sidered only rough approximations, there can be no doubt of the general law that (apart from local abnormalities) the temperature of the snow-line falls as we go from the equator towards the poles. Now, it is also true that the annual range of temperature increases from the equator to the poles. At the snowline near the equator, the extreme summer temperature is but little above the freezing-point; while at the snow line in the arctic regions, though the mean temperature for the year falls several degrees below freezing point, the extreme summer temperature rises far above it. The comparison of the zones of climate leads, accordingly, to the same conclusion as the comparison of the northern and southern hemispheres. The existence of perpetual snow is shown by both comparisons to depend less upon cold winters than upon cool summers.

be con

A very simple a priori consideration suggests the probability of the same conclusion which we have drawn from geographical facts. It seems probable, a priori, that extreme winter cold cannot greatly increase the amount of snow-fall. So long as the temperature of any place keeps, below 32", the precipitation will be all in the form of snow; and this

will be the case when the temperature is but little below 32°, as truly as when it falls far below zero. Cooling a mass of air from 32° to a lower temperature can produce but little additional precipitation, since the maximum vapor tension at 32° is very little, and the change of maximum vapor tension corresponding to changes of temperature in the lower part of the thermometric scale is very slight. The influx of warm and moist air bearing supplies of vapor is not favored by extreme winter cold, since such extreme cold tends to increase barometric pressure over the area affected. On the other hand, every degree that the summer temperature rises above 32° shows an effective increment of the melting-power of the summer sun. The inference would seem to be justified, that, in any place where the annual mean temperature is below or not much above 32°, the more nearly the extreme summer and winter temperatures approach the annual mean, the greater will be the tendency (other things being equal) to the accumulation of perpetual snow. This a priori inference seems to be in exact accord with the geographical facts referred to in this and in my former letter. WILLIAM NORTH RICE.

Wesleyan university, Oct. 8.

The theory of utility.

In connection with the suggestive article in Science of Oct. 1, on Launhardt's Mathematical economics,' I would like to offer a new theory of utility, or, rather, to discuss it from a new standpoint, and indicate what I consider to be the error in Jevons's main premise.

Utility, or usefulness, is the satisfying of desires. Desires are always in the present, though many, perhaps the most of them, have a prospective nature. Usefulness is not the capacity or capability of being useful it is the state or quality of being useful. It involves, not a possible, but an actual satisfying of desires: e.g., on a certain day a loaf of bread would have possessed utility for Robinson Crusoe in satisfying his hunger; a second loaf would have possessed utility, not in satisfying the hunger of the morrow, but in satisfying his desire to have the possible wants of the future provided for.

If utility be defined as a capacity to serve man or to satisfy his desires, and by this is meant something quite different from the actual satisfying, it serves no purpose of distinction, for with this definition, when affirming utility to be an attribute of any thing, we must always add, 'under certain circumstances;' and there is probably not a thing in existence but what, under certain circumstances, possesses this capacity.

The confusion prevailing as to the nature of utility has arisen from the fact, that, in discussions upon the subject, the provident trait in man's character has been entirely neglected; for from this trait spring desires which are, indeed, of a prospective nature, but whose satisfaction involves utility as indubitably as does the satisfaction of his physical needs.

Utility being of the present moment, time is not one of its dimensions, as the theory of final degree of utility' necessarily presupposes. When Jevons (Theory of political economy,' p. 51) declares that "utility may be treated as a quantity of two dimensions, one dimension consisting in the quantity, and another in the intensity of the effect produced upon the consumer," it is clear that the supposed dimension of quantity does not have reference to the

mass simply, but to the duration of the commodity, to the time elapsing while it is being consumed.

The theory of varying degrees of utility seems to have its origin in the fact, that, assuming the provident trait to be perfectly developed, the intensity of our desires of a prospective nature varies with our estimate of probable utility, the probability decreasing as the length of time estimated to ensue before the anticipated satisfaction increases; Jevons's chapter on the Theory of utility,' with the necessary changes in phraseology, would furnish an excellent discussion on the subject of desires of a prospective nature, which do have two dimensions, one the estimated intensity of the anticipated satisfaction, the other its probability as affected by the length of time to elapse before its estimated occurrence.

But when we enter upon discussion as to the sources of desires, and how desires may be modified, we must say, with Pascal, "C'est un cercle infini, dont le centre est partout la circonference nulle part." A. E. ROGERS.

Orono, Me., Oct. 5.

Earthquake sounds.

Does any one attempt to offer an explanation for the sound that preceded and accompanied the late earthquake, or earthquakes in general, where the sounds are noticeable? I supposed it was presumable that they were due to the commotion in the earth's crust caused by the radiating waves. But how can that be, when the earth-waves move six to eight times faster than sound-waves? If that be so, would it not appear as if the sound-waves ought in part to come up after the shock has passed? I was asleep when the first and heaviest shock first reached this place (six miles west of Greensborough, in Guilford county), so I cannot tell to what extent the sound preceded the shock. There were two subsequent shocks which were preceded by low roaring and tumbling, so that we predicted the coming of the earth-waves. I said to my wife, Now we will have another shake;' and we waited probably three seconds after I had spoken, when the house began to rock. I do not expect you to write me personally, as you will not likely have time, but, if my question should be worthy of note, perhaps some of the geologists of your company could give us a line through Science. JOSEPH MOORE.

New Garden, N.C., Oct. 6.

Unexplained noises.

Your comment on mysterious noises in Science for Oct. 1 recalls to my memory a very remarkable instance of the transmission of sound and motion.

On the 14th of February, 1862, I was working with my father in his sugar orchard ten miles west of Madison, Ind., and five miles north of the Ohio River. During the entire morning, which was warm, cloudy, and calm, we heard most distinctly the discharges of heavy artillery. The reports would often follow in quick succession. I, as most lads would have been in similar circumstances, became thoroughly alarmed. I felt quite sure that the whole confederate army was close upon us, since the source of the cannonading seemed to be no farther south than the river.

I finally prevailed upon my father to go home, where we found the inmates of the house greatly alarmed at the noises and the rattling of the windows. The shocks, as I remember them, were much like the slight earthquake disturbances experienced lately in

different parts of the country. For several miles along the river these noises were heard and the shocks felt. Nevertheless the day passed, and no invading foe appeared. The morrow brought the news of the bombardment of Fort Donelson.

When it is remembered that Fort Donelson is more than two hundred miles from the locality just described, it is certain that these concussions could not have been carried through the air.

I have been told that the limestone formation coming to the surface along the right bank of the river in Jefferson county, Ind., is the same as that on which Fort Donelson rests. The cannonading which was heard so distinctly that day by hundreds of people in Indiana occurred at Fort Donelson, and the sound-waves were conveyed entirely across Kentucky, and probably at a considerable depth below the surface, by a continuous ledge of limestone. I have thought the phenomena above described worthy of record in your columns. H. W. WILEY.

Fort Scott, Kan., Oct. 8.

How astronomers may work.

In your editorial of Sept. 24, referring to Professor Pickering's plan for making the Harvard college observatory useful to all other observatories, and to astronomers all over the world, you also notice a plan of my own, which I formulate as follows:

"We mean to put the large telescope (of the Lick observatory) at the disposition of the world by inviting its most distinguished astronomers to visit us one at a time, and by giving to them the use of the instrument during certain specific hours of the twentyfour. In this way we hope to make the gift of Mr. Lick one which is truly a gift to science, and not merely one to California and to its university." Your comment on this plan is that you suspect that Professor Holden was hard-pressed to devise it.' I trust that your impression will not be shared by Professor Young, if he remembers the discomforts of his expedition to Sherman; or by Professor Langley, if he recalls the hardships of his own to Mount Whitney; or by Dr. Huggins, when he recollects the hundreds of failures which have come in his delicate researches in spectroscopy and photography from the London climate; or by Mr. Burnham, when he remembers how many of the double stars which he discovered at Mount Hamilton with a six-inch telescope were difficult' in Chicago with one of eighteen inches. Not to mention any other names, I am sure that these astronomers will feel a sense of gratitude when the facilities of the Lick observatory and the opportunities of its climate are put at their disposition, and will attribute the offer to a generous desire to forward science, and not to a scheme to eke out a scanty income. As a matter of fact, I have directed the policy of the observatory since 1874, and it is a pleasure to me to be able in 1886 to announce a plan which has been constantly in my thoughts for more than ten years, and which seems to me to be a long step in the true direction. I trust it will also seem to be such to my fellow-astronomers. It would have been natural to have looked for the same view from the editor of Science; but, as long as the plan commands their respect and my own, it will be carried out. You will have to look to its results to see if it may not eventually command your own also.

Berkeley, Cal., Oct. 2.

EDWARD S. HOLDEN.

FRIDAY, OCTOBER 15, 1886.

WASHING TON'S SIGNATURE.

DR. PERSIFOR FRAZER recently published in the Proceedings of the American philosophical society a paper on composite photography as applied to handwriting. One of the most interesting results is that he obtained with the signature of Washington, the facsimiles of which we here reproduce. The difficulties of the process, and the peculiarities of composite signatures, were pointed out in Science of Jan. 22.

George Washington's signature was one of the first to suggest itself for the purpose, because many persons were familiar with it, and there are numerous well-authenticated documents in existence which bear it; but it has proved to possess other advantages which were not known when it was selected. As in every thing else, Washington was deliberate, painstaking, and uniform in his method of writing his signature, and the consequence is that it makes an excellent composite for illustration.

In writing his signature, Washington put pen to the paper five times. First he wrote the G W in one connected line. Second, he raised his hand and made the small o between the upper parts of the G and W, and the two dots which appear in all but signature No. 7. Third, his hand and arm were placed in position to write ashing, these six letters occupying a breadth of almost exactly 14 inches in every signature except the third, when they are extended to 113 inches. This is about as much of the arc of a circle (of which the centre is the elbow pivoted on the table) as one with a forearm of average length can cause to coincide with the tangent, or the straight line across the paper which the lower parts of the letters follow, unless unusual effort be made, and a great deal more movement be given to the fingers. The g ends in a curved flourish, of which the convex side is turned upwards below the right centre of the name. The lower loop of the g in all the signatures and in the composite was cut off in preparing the plate. Fourth, he wrote the final ton. Fifth, he added the very peculiar flourish above the right centre of the name, with the object of dotting the i and crossing the t at the same stroke.

In examining the composite, the effect of these various separate movements becomes manifest in its strengthened portions. It is hardly possible

that any one, during the period of sixteen years which these signatures represent, or from 1776 to 1792, should have so schooled his hand to write a long name that the first inch or so of the writing should always occupy the same relative position to the body of the signature. It would take at least that much action for the hand and arm and pen to be brought into normal signature-writing condition; and especially is this so when this part of the writing is accompanied by flourishes, as it is in the case we are considering. The G W, and the little o, and the dots at the top, were the prelude, after which the arm was moved into position to write the main body of the signature, or the ashing. Of course, from the manner of making the dots, and the extremely small space they cover, their re-enforcement of each other in the composite was almost impossible, and, in fact, like other subordinate characters, they disappear almost completely. This latter is the part of the name which one would have expected to exhibit the greatest amount of uniformity, as in point of fact it does, with the exception of its terminal g, which shows more variation than any of the other letters, because at this point the limit of coincidence between the tangent line of the writing and the curve, of which the right fore-arm was the radius, had been passed, and a freer movement of the fingers was compensating for the increasing divergence. It is likely that Washington sometimes raised the hand between the end of the long s and the beginning of h, but he does not appear to have moved the elbow. All but the second signature are consistent with this view, and in the first, third, and fifth it is plainly indicated. In the others, as in the flourish above the sixth signature, the pen may not have marked. The fourth separate act of the penman was the formation of the ton after a movement of the arm. The breadth of the space occupied by these three letters is from to of an inch, or considerably within the range of coincidence of the curve and straight line before referred to; and owing to this fact there is only a moderate degree of re-enforcement of the letters in the composite, because these letters might fall into the first or last parts of the 2-inch space which was the limit of movement with a fixed elbow. It is worthy of note that even in this case the middle letter of three is darker in the composite than eithe outside letters. The fifth and last m the flourish which dots the i and one stroke. This was done in