Page images
PDF
EPUB

The actual figures of the experiment were as follows:

[merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small]

That nothing should distil over below 170° is most remarkable, inasmuch as there is actually present in kerosene a liquid with a boiling-point of 78° C. The proportion of this lowboiling liquid is indeed small; but there are other volatile ingredients, and the sum total of the ingredients boiling below 170° C. amounts to more than one fifth of the total kerosene.

The 688 cub. centim. of distillate (which has just been mentioned) were submitted to redistillation, and they yielded 505 cub. centim. below 210° C. And in that manner one litre of kerosene was caused to yield 505 cub. centim. of distillate below 210° C. When it is directly distilled a litre of kerosene does not give anything like half its volume of distillate at temperatures below 210° C.

Continuing the investigation, the 505 cub. centim. of distillate were redistilled, and they began to distil at 125° C., and up to 170° C. 270 cub. centim. came over. And in that manner a litre of kerosene (which when directly distilled yields only one drop of distillate below 170° C.) may be caused to evolve 270 cub. centim. of distillate below 170° C. All this illustrates how admixture with a high-boiling liquid raises the boiling-point of low-boiling liquids.

We have carried out a most laborious investigation of kerosene, and, operating on a considerable scale, after many months of fractionation have separated 24 different liquids, which, with probably a few others, and together with about 13 per cent. of residue boiling at temperatures above 290° C., make up the complex mixture known as kerosene. As to the proportions of the different ingredients of the mixture, it is to be noted that there is no one preponderating ingredient. There appears to be a very small proportion of the two most volatile terms of the series, but for the rest the distribution is not very uneven. We doubt whether the proportion of any one ingredient exceeds 5 per cent. of the whole kerosene.

In the following table are set forth the main results of our work :

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][subsumed]
[ocr errors]

Gg

222

6.83

6.77

C1 H

28

230

Hh.

237

246

253

260

267

274

280

Z Residue a dark coloured liquid (sp. gr. about 0·880 at 15°5 C.), being a mixture of several liquids of very high boilingpoint.

The series of liquids, A to O, presents the following characters. Each liquid, when distilled separately in the wellknown fractionation-flask, begins to distil about 10 degrees higher than its predecessor begins to distil. Thus the first term A begins to distil at 77°5; the second term Az at 87°; the third term Aa at 96°; the fourth term Ab at 105°5; the fifth term B at 116°; the sixth term Bb at 127°; the seventh term Bc at 138°, and so on up to the last term 0.

Except the few highest terms the members of the series fulfil the requirement, viz. that half of the liquid shall distil without the thermometer rising more than 2 or 3 degrees, that three-quarters shall distil within 5 or 6 degrees of the starting-point, and that by the time the boiling-point of the next in the series is reached 90 per cent. shall have distilled

over.

Within the last few weeks the seven lowest terms, viz. A

to Be inclusive, have been prepared anew from fresh kerosene and fractionated with great perseverance. The first two terms A and Az have not yet been procured in sufficient quantity to admit of the very elaborate treatment to which we should like to subject them, but the five next terms, Aa to Be inclusive, have been obtained in abundance and have been exhaustively treated.

As an example we will quote the record of the final testings of Aa :

Exp. I.—Vol. of Aa employed=136 cub. centim.

[merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][ocr errors][ocr errors][merged small][merged small][ocr errors][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][ocr errors][ocr errors]

Showing that three-quarters of Aa distils over without a greater rise than 3 degrees, and that the retort becomes dry before the boiling-point of Ab is reached.

Before making the three final distillations Aa had been deprived of traces of Az (the next lower term) by the following course of procedure.

139 cub. centim. of Aa was placed in a retort and 50 cub. centim. was then distilled off. Next the 50 cub. centim. of distillate was redistilled thus:

[merged small][ocr errors][ocr errors][merged small][ocr errors][merged small][ocr errors]

Then the 16 cub. centim. of distillate was redistilled,

[merged small][ocr errors][merged small]

and 8 cub. centim. was distilled off and rejected.

As has been said, five consecutive terms, viz. Aa, Ab, B, Bb, and Bc, have been exhaustively treated, and each one has been proved to be incapable of being resolved into fractions with different boiling-points. We believe that the conclusion cannot be resisted that the kerosene series of hydrocarbons mounts by increments of 7 instead of by increments of 14, and we hold that the real atomic weight of carbon is 6 and not 12.

Laboratory, New Malden, Surrey.

14th April, 1894.

L. Notices respecting New Books.

UNIPLANAR ALGEBRA being Part I. of a Propedeutic to the Higher Mathematical Analysis. By IRVING STRINGHAM, Ph.D., Professor of Mathematics in the University of California. San Francisco, the University Press.

“THE

HE logical grounding of Algebra," writes the author in his preface," may be essentially arithmetical or geometrical. I have chosen the geometrical form of presentation and development." "The point of departure is Euclid's doctrine of proportion, the fundamental propositions of which are enunciated and proved in an Introduction (pp. 1-20) in which I have followed the method recommended by the Association for the Improvement of Geometrical Teaching."

With Chap. I. commences the explanation of the "Laws of Algebraic Operation" as affecting real, or magnitudes involving only the idea of length; imaginary, including also the idea of turning through a right angle, and complex, embodying length and rotation through any angle. The product is obtained as a fourth proportional to the unit, or "idemfactor" (Peirce), and the factors of that product; the quotient as a fourth proportional to the unit, the dividend, and the reciprocal of the divisor. Indeterminate Forms are here introduced, their evaluation being treated of lower down; combinations of signs, the Associative, Commutative, and Distributive Laws are successively treated of and proved. Logarithms are defined in Napier's manner, treated so as to introduce the conceptions of the modulus and base as well as exponential, whose Laws of Involution and the Index-are proved. The law of the interchange of indices and coefficients in Log Operations is called by the distinct name "Metathesis." To conclude the chapter, Indeterminate Exponential forms are touched on, and a useful synopsis of the matter of the chapter added.

Chap. II. contains an introduction to the circular hyperbolic and Gudermannian functions, with proofs of some fundamental limits.

Chap. III. is occupied with "Complex Quantities," represented

by vectors, of which real quantities represented by segments of the axis and "imaginary" by vectors perpendicular to that line are particular cases. Perhaps more unity would have been imparted to the terminology by the substitution of "unreal" for "imaginary;" then "real" would have expressed the complex of which the component perpendicular to the axis vanishes; "unreal," that the real component of which is zero. The abbreviation cis. 0, to be read sector of 0, is adopted for the complex cos 0+i sin 0. The associative, commutative, and distributive laws are then proved for complex magnitudes. All this has, of course, been founded on Argand's construction, which, however, is only formally explained hereafter.

In the second section of this Chap. III. the Exponentials and Logarithms of complex quantities are dealt with by means of a diagram; the theory as adopted having been the subject-matter of a paper by the author read before the New York Mathematical Society in October 1891, and subsequently published in vol. xiv. of the Am. Journ. of Math. Without the diagram, a description of this theory would be hardly intelligible. Just as the vanishing of an angle causes the complex to degenerate into a real, so in the diagram referred to the vanishing of an arbitrary angle in it changes the Exponentials and Logarithms of complex into those of ordinary magnitudes. The result of these discussions leads to the definition of "an Algebra;" viz. since the aggregate of all complexes operating howsoever on one another form a" closed group," i. e. evolve only complexes, such a group forms an Algebra. Reference is made to Peirce and Cayley.

The chapter concludes with proofs that every magnitude can be expressed, with an error less than any assignable, in terms of an assumed unit by a rational number.

Chap. IV. treats of the Cyclic and Hyperbolic Functions (direct and inverse) of complexes, defined with respect to a complex modulus (), and hence called " modo-cyclic" functions, having a period 2ikπ or iπ, and of the inverses of these.

Chap. V. explains the one to one correspondence of points on a plane and on a sphere, having its centre in the plane, through rays drawn from one end of the normal diameter, and the transformation of the planar complex into the tri-dimensional sphero-surface complex (Cayley, Klein). The rest of this chapter on "Graphical Transformation" is occupied with some particular cases of "Orthomorphosis" (Cayley). In it occurs the only misprint which has been noticed, of a symbol Bw for Bw. The typography is highly creditable to the San Francisco press-is, in fact, dainty of its kind.

In the concluding chapter, "Properties of Polynomials" with complex coefficients are proved, after a preliminary page on the evaluation of the n-nth roots of a complex quantity; this, as every other branch of the matter of the book, being illustrated by a collection of " Agenda" or Examples, on which the student may exercise himself.

66

« PreviousContinue »