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From 4 to 3.
1. Faraday's researches on gold-leaf best illustrate this; but I hold that my explanation of them by masses of two degrees of complexity only is sufficient without his conclusion (Researches in Chemistry, p. 417), that they exist "of intermediate sizes or proportions.
From 3 to 2.
1. Sulphur-vapour first gives a continuous spectrum at the blue end; on heating, this breaks up into a channelled space-spectrum. 2. The new spectra of K and Na (more particularly referred to in the third note) make their appearance after the continuous absorption in the blue and red vanishes.
From 2 to 1.
1. In many metalloids the spectra, without the jar, are channelled; on throwing the jar into the circuit the line-spectrum is produced, while the cooler exterior vapour gives a channelled absorption-spectrum.
2. The new spectra of K and Na change into the line-spectrum (with thick lines which thin subsequently) as the heat is continued.
[Continued from p. 153.]
March 25th, 1874.-John Evans, Esq., F.R.S., President,
The following communications were read :—
The author described the Carboniferous district of Pictou County as showing the whole thickness of the Carboniferous system arranged in three synclinals, the easternmost consisting of the Lower series up to the Middle Coal-formation, and including all the known workable Coal-measures in the district,-the second towards the west of the middle and the lower part of the Upper Coal-formation,— and the third showing in its centre the newest beds of the latter. On the north the bounding anticlinal of the first depression brings up the New-Glasgow Conglomerate, which contains boulders 3 feet in diameter, often belonging to Lower Carboniferous rocks, and represents the upper part of the Millstone-grit or the lower part of the Middle Coal-formation. The author regards this as representing an immense bar or beach, which protected the swamps in which the Pictou main coal was formed.
The succession of the deposits above the Conglomerate was described in some detail as seen in natural sections. The Upper Coal-formation, as shown in the section west of Carribou Harbour, consists of:-1. Red and grey shales and grey, red, and brown sandstones; and 2. Shales, generally of a deep red colour, alternating
bing briefly our author's treatment of the question of multiplication, to which his third chapter is devoted. In the first place he explains, by means of two examples, Oughtred's method of contracted multiplication; but instead of leaving the last figure uncertain as is usually done, he notices that the process gives an approximation in defect, and points out that if the sum of the digits in the multiplier, which give partial products, be increased by the first unused digit of the multiplier, and by unity if there be a second unused digit in the multiplier, and then this sum be added to the product, we now have an approximation in excess; and by comparing the two we obtain a result in which a certain number of digits are known to be exact. Moreover the rule, as usually stated, directs that if, for instance, the result were required to be true for two places of decimals, the unit digit of the multiplier should be placed under the second decimal digit of the multiplicand; our author notices that it should usually be placed under the third decimal digit, and in certain circumstances under the fourth or He next enters on the question, fifth, and so on in other cases. Given that the factors are incommensurable numbers, to what degree of approximation must they be known that the first n digits of the product may be exact? He first shows that when the factors are approximate by defect, the relative error of their product is less than the sum of the relative errors of the factors; and then reasons as follows:-Suppose that there are p factors (p being less than 10), calculate each factor to n+1 digits; then the relative and consequently the sum error of each factor is less than
1 P.10n' of their relative errors will be less than
and their product will
have the first n digits exact. He also observes that if the first digit of the required product is known before hand, it is, urder certain circumstances (which he specifies), enough to calculate some of the factors to n digits.
It will be evident from this that the author is quite justified in thinking that "he has given completeness, in the present work, to methods laid down by other writers.” He states that the work was originally published as an appendix to that on curved lines noticed above, that it has been carefully revised, and contains several important additions; amongst others is a complete solution of the question, How many digits of a number must be known in order that its mth root may have its first n digits exact?
XXVII. Proceedings of Learned Societies.
[Continued from p. 151.]
June 18, 1874.-Joseph Dalton Hooker, C.B., President, in the
THE following communication was read:—
"On Coniferine, and its Conversion into the Aromatic Principle of Vanilla." By Ferd. Tiemann and Wilh. Haarmann.
The sap of the cambium of coniferous trees contains a beautiful crystalline glucoside, coniferine, which was discovered by Hartig and examined some years ago by Kubel, who arrived at the formula C12 H12O12+3aq.
A minute study of this compound leads us to represent the molecule of coniferine by the expression
the percentages of which nearly coincide with the theoretical values of Kubel's formula.
Submitted to fermentation with emulsine, coniferine splits into sugar and a splendid compound, crystallizing in prisms which fuse at 73°. This body is easily soluble in ether, less so in alcohol, almost insoluble in water; its composition is represented by the formula
Under the influence of oxidizing agents the product of fermentation undergoes a remarkable metamorphosis. On boiling it with a mixture of potassium bichromate and sulphuric acid, there passes with the vapour of water, in the first place ethylic aldehyde, and subsequently an acid compound soluble in water, from which it may be removed by ether. On evaporating the ethereal solution, crystals in stellar groups are left behind, which fuse at 81°. These crystals have the taste and odour of vanilla. An accurate comparative examination has proved them to be identical with the crystalline substance which constitutes the aroma of vanilla, and which is often seen covering the surface of vanilla-rods.
On analysis, the crystals we obtained were found to contain
This is exactly the composition which recent researches of Carles have established for the aromatic principle of vanilla. The transformation of the crystalline product of fermentation into vanilline is represented by the following equation:
To remove all doubt regarding the identity of artificial vanilline with the natural compound, we have transformed the former into
a series of salts which have the general formula
C, H, MO,
and into two substitution-products,
both of which had previously been prepared by Carles from the natural compound.
In order further to elucidate the nature of vanilline, we have submitted this body to fusion with alkali. The product of this action is a well-known acid discovered by Strecker, and described by him as protocatechuic acid,
which is thus formed
C, H, O, +40 = C, H, O, + H, 0 + CO,.
We have identified this substance by analysis, by the study of its reactions, and also by transforming it into pyrocatechine, C. H2O2
C, H, O = C H, O, + CO,.
The transformation into protocatechuic acid fixes the constitution of vanilline. This compound is the methylated aldehyde of protocatechuic acid; its composition referred to benzol is represented by the formula
Indeed, submitted under pressure to the action of hydrochloric acid, vanilline splits into chloride of methyl and protocatechuic aldehyde,
A corresponding action takes place with hydriodic acid; but in this case the aldehyde is destroyed.
An additional proof of the correctness of our view regarding the constitution of vanilline is obtained by treating this substance with acetic anhydride and benzoyl chloride.
The action does not go beyond the formation of the compounds
CHOC, H, O
showing that vanilline does not contain more than one hydroxylic group.
The constitution of vanilline being thus made out, there could be no doubt regarding the structure of the product of fermentation from which vanilline arises. This compound is the ethylic ether of vanilline,
/OCH, CH, OC, H, \COH.
That such is the constitution of the body is proved by the simultaneous formation of ethylic aldehyde when vanilline is formed. We obtained, however, an additional confirmation of this conception by submitting the product of fermentation to the action of hydriodic acid under pressure, when an alcohol iodide was formed, which we succeeded in separating into the iodides of methyl and ethyl,
CH-OC, H, + 2 HI = CH ̧I + C, H, I + C, H, OH
The experiments we have described in this note were performed in the laboratory of Professor A. W. Hofmann, to whom we are deeply indebted for the advice and assistance he has given us in the course of these researches.
June 11, 1874.-The following communications were read :— "On the alleged Expansion in Volume of various Substances in passing by Refrigeration from the state of Liquid Fusion to that of Solidification." By Robert Mallet, C.E., F.R.S.
Since the time of Réaumur it has been stated, with very various degrees of evidence, that certain metals expand in volume at or near their points of consolidation from fusion. Bismuth, cast iron, antimony, silver, copper, and gold are amongst the number, and to these have recently been added certain iron furnace-slags. Considerable physical interest attaches to this subject from the analogy of the alleged facts to the well-known one that water expands between 39° F. and 32°, at which it becomes ice; and a more extended interest has been given to it quite recently by Messrs. Nasmyth and Carpenter having made the supposed facts, more especially those relative to cast iron and to slags, the foundation of their peculiar theory of lunar volcanic action as developed in their work, The Moon as a Planet, as a World, and a Satellite' (4to, London, 1874). There is considerable ground for believing that bismuth does expand in volume at or near consolidation; but with respect to all the other substances supposed to do likewise, it is the object of this paper to show that the evidence is insufficient, and that with respect to cast iron and to the basic silicates constituting iron slags, the allegation of their expansion in volume, and therefore that their density when molten is greater than when solid, is wholly erroneous. The determination of the specific gra