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Chemical Parentage of the Spectrum under discussion, That spectrum is, says Dr. Watts, the spectrum of carbon, and not of a hydrocarbon or any other compound of carbon.

This is so far very plain and distinct as an assertion, and indicates that the learned world of London, as represented by the Philosophical Magazine, is not yet advanced beyond the position it was in when I sent my first paper to the Royal Astronomical Society in May 1871, and gave then such extracts from the authorities on either side as showed, I verily thought, that the spectroscopists declaring for pure carbon, in opposition to those pronouncing for carbohydrogen, were blundering little less than the perpetual-motion men of last century.

For why? Carbon is a simple element in chemistry; and to give its spectrum at all as a luminous and discontinuous one, it must be driven off in vapour, glowing and incandescent.

This is the condition for any and every chemical element to give forth its spectrum under the prism; and some elements will send out their vapour easily enough at very moderate temperatures in any common candle-flame, while others require much more intense heat; for even in a powerful blowpipe-flame they only become hot and luminous as solid bodies, without rendering out any vapour, until the aid of oxygen or the electric spark is brought in. But carbon ! wby, that has never been volatilized yet by any contrivance or accumulation of contrivances by modern men; so that M. Lielegg in Austria, and Mr. Crookes in the Chemical Journal' in England, pronounced years ago that the merely talked about vapour of carbon was only an hypothesis, a delusion. I have, too, myself seen the full power of a 12-horse steam-engine converted by Mr. Wylde of Manchester into electric currents, and the whole directed for several minutes through a little thin pencil of carbon in a manner that would have melted and dissipated the same bulk of platinum over and over again, but with no other effect than merely to make the carbon, as a solid, white-hot, or just as I have found chloride of magnesium to go on glowing as a hot solid but nothing more (unless to show faintly the lines of calcium and sodium impurities) in an ordinary blowpipe-flame.

Hence, then, if man has never volatilized carbon, human eye has never yet knowingly seen its spectrum, and can form no idea from theory of what it will be like, except that it will be totally different in kind and species from the many-banded spectrum of ranks of closely arranged perspectives of lines which bas been so positively mistaken for it by certain parties. For as Mr. Norman Lockyer has recently shown, that kind of spectrum indicates at once a chemical compound of two or more

elements in actual chemical combination ; while, whenever the heat is raised high enough to dissociate those elements, then immediately their several spectra appear as elements; and they give spectra of fine lines only, sharp, well defined, usually far apart, and not affecting in any degree to occupy the place of the bands of the compound.

How, then, came so egregious an error to grow up in the modern world, as to mistake so very unlikely a spectrum and of the most easily volatilized compound, and at the very beginning, instead of end, of its burning, for the most refractory of all the elements ?

The history of errors is always instructive; and the following seems to have been its course in this carbon case.

The Rise of the Myth of Carbon-vapour. The Royal Society (acting unhappily through its secret committees) first patronized the mistake, by publishing in their Philosophical Transactions Mr. Atfield's paper of 1862, p. 221, wherein he examined, rather cavalierly*, what Professor Swan had previously called the carbohydrogen-spectrum, and declared it to be the spectrum of the glowing and incandescent vapour of carbon ; wherefore the earlier announced truth of the Scottish professor was extinguished, and the error of the Royal Society became so fashionable in London circles, that every one began to talk thenceforth of that particular spectrum as the undoubted spectrum of “carbon.”

* As one example :-"The yellow-green (citron) band, composed,” says Mr. Atfield (p. 222), “according to the drawing accompanying Swan's paper, of four lines, I find to contain six; the green band to have five instead of two."

From this statement any one might be led to conclude that there was a definite number of lines of equal observing importance in each band, that Professor Swan had committed a grave error in alluding to only four and two when there were really six and five, and that the new lines might be in spectrum-place either before, behind, or amongst Swan's lines in order of dispersion-entirely therefore destroying the value of his observed spectrum-places of those lines reckoned as first, second, third, &c. of each band, counting from the less-refrangible side.

Yet, in place of this, the new lines only tack on to the fainter and more. refrangible end of a vanishing series, of which Professor Swan correctly described all the components, from the first and brightest up to the last and faintest one certainly visible in his apparatus. Mr. Atfield, by an unlimited use of oxygen in place of common air, was able, in a rich London laboratory, to produce more brilliance in the light operated on by his spectroscope, and therefore could carry on the vanishing series, as night well have been expected, a little further; and since then M. Morren, in Paris, has carried it on further still. But all these additional lines are hardly equal even in collective light and importance to the last line of the series previous to them; nor do they alter the place of the brighter preceding lines in any degree, either as being the first, second, &c. of each band, or in their recorded wave-lengths.

It is also worthy of note, that there is neither a plate-view, nor a single measured-scale place of any one spectrum-line throughout the whole of Mr. Atfield's paper-an omission of all that is accurate in spectroscopy, of all that has tended to make it a high science, which can only be explained (in a memoir crowned by being printed in the Philosophical Transactions of the Royal Society of London) by its one chief burden (viz. putting pure carbon vapour for hydrocarbon) having been grateful to the then already formed prejudices of the secret committee who passed it.

Hence, too, when so admirable an observer and inimitable a spectroscopist as Dr. Huggins found the spectra of two small comets resolvable into bands somewhat similar to those of the carbohydrogen, he boldly called them the bands of the carbonspectrum; and it was approved by the secret committee of the Royal Society and printed in their Philosophical Transactions in 1868.

But Dr. Huggins, as a good practical experimenter as well as astronomical observer, knew full well the impossibility of the spectrum of carbon being seen without an almost supernatural degree of heat being applied to it; how, therefore, did he show that such heat existed in the ultra-faint comets which he had spectroscoped ?

The method is worthy of the gravest note, as showing (from its being actually printed with honour in the Philosophical Transactions) what equivocal conclusions will pass the secret committees of the Royal Society when they correspond with the prejudices of some person or persons behind the scenes there; though those unknown powers do occasionally act as very dragons in keeping out any salutary doubt expressed on a favoured topic. For this was the heat-agency announced, viz. :

That "some comets have approached the sun sufficiently near to acquire a temperature high enough to convert even carbon into vapour.”

Not the comets, be it remarked, that were actually the subject of these observations, but some other comets of a totally different form of orbit and infinitely nearer approach to the sun.

Of such totally different comets, tou, the only one that was mentioned is the unprecedented comet of 1843, which approached the sun's surface within a distance of a seventh part of the solar radius. But even there, no proof is attempted or demonstration given either of what spectrum that comet would have shown if any one had spectroscoped it (for no one did), or that its temperature was high enough to volatilize carbon efficiently for the spectroscope-only that Sir John Herschel had said that the heat the comet had experienced must have been 47,000 times as intense as what the earth receives from the sun. But as that still more eminent authority in solar spectroscopy, Professor Angström, has declared since then for there not being heat enough even in the sun itself to volatilize carbon—why, even if the small comets said, in the Philosophical Transactions, to be throwing off the incandescent vapour of carbon every night they were under observation, even in a dark and cold sky, had been taken thence and placed on the very surface of the sun itself, and had experienced there not only the heat which that other comet had experienced of earth's x 47,000, but earth's x 300,000, they could not have shown a pure carbon-spectrum.

As our sun, according to Father Secchi, ranks only among the yellow stars, and they are supposed not to be so hot as the white stars, perhaps the vapour of carbon may exist glowing and incandescent in Sirius, which is so noted a member of the latter class of stars. We may, too, perhaps be privileged to see the actual and real spectral lines of carbon there, in any good telespectroscope—but with the drawback that, however plainly the lines may appear in themselves, we cannot recognize their chemical origin and assign them their true name, because neither has man ever yet volatilized pure carbon, nor has any angel (in default of theory) ever told us the wave-lengths of carbon-lines when the carbon has been volatilized by a higher power.

Hydrocarbon compound it is given to man to volatilize and spectroscope; and he should be thankful for its many admirable uses; but as to the spectrum of the pure carbon element being seen in the base of the flame of every little candle made and set alight by human hands, it would be well if certain modern men, and the secret committee of the Royal Society in particular, were to come forward openly and confess with deep contrition in the words of ancient Job,

“I have uttered that I understood not; things too wonderful for me, wbich I knew not."

“Wherefore I abhor myself, and repent in dust and ashes."

IV. Statistics by Intercomparison, with Remarks on the Law of

Frequency of Error. By Francis Galton, F.R.S.* MY

Y object is to describe a method for obtaining simple sta

tistical results which has the merit of being applicable to a multitude of objects lying outside the present limits of statistical inquiry, and which, 1 believe, may prove of service in various branches of anthropological research. It has already been proposed (Lecture, Royal Institution, Friday evening, February 27, 1874), and in some degree acted upon (Hereditary Genius, p. 26), by myself. What I have now to offer is a more complete explanation and a considerable development of previous views.

* Communicated by the Author. Phil. Mag. S. 4. Vol. 49. No. 322. Jan. 1875.

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The process of obtaining mean values &c. now consists in measuring each individual with a standard that bears a scale of equal divisions, and afterwards in performing certain arithmetical operations upon the mass of figures derived from these numerous measurements. I wish to point out that, in order to procure a specimen having, in one sense, the mean value of the quality we are investigating, we do not require any one of the appliances just mentioned: that is, we do not require (1) independent measurements, nor (2) arithmetical operations; we are (3) able to dispense with standards of reference, in the common acceptation of the phrase, being able to create and afterwards indirectly to define them; and (4) it will be explained how a rough division of our standard into a scale of degrees may not unfrequently he effected. Therefore it is theoretically possible, in a great degree, to replace the ordinary process of obtaining statistics by another, much simpler in conception, more convenient in certain cases, and of incomparably wider applicability.

Nothing more is required for the due performance of this process than to be able to say which of two objects, placed side by side, or known by description, has the larger share of the quality we are dealing with. Whenever we possess this power of discrimination, it is clear that we can marshal a group of objects in the order in which they severally possess that quality. For example, if we are inquiring into the statistics of height, we can marshal a number of men in the order of their several heights. This I suppose to be effected wholly by intercomparison, without the aid of any external standard. The object then found to occupy the middle position of the series must possess the quality in such a degree that the number of objects in the series that have more of it is equal to that of those that have less of it. In other words, it represents the mean value of the series in at least one of the many senses in wbich that term may be used. Recurring to the previous illustration, in order to learn the mean height of the men, we have only to select the middlemost one and measure him; or if no standard of feet and inches is obtainable, we must describe his height with reference to numerous familiar objects, so as to preserve for ourselves and to convey to strangers as just an idea of it as we can. Similarly the inean speed of a number of horses would be that of the horse wbich was middlemost in the running. If we proceed a step further and desire to compare

the mean height of two populations, we have simply to compare

the

representative man contributed by each of them. Similarly, if we wish to compare the performances of boys in corresponding classes of different schools, we need only compare together the middle boys in each of those classes.

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