quent fi, au lieu de 28, qui eft le nombre des piés cubiques contenus dans les deux cubes, on n'avoit, par example, que 3 piés et, on devroit encore avoir une folution poffible. Cette folu. tion donneroit pour le nombre des piés cubiques contenus dans un des cubes 27, et dans l'autre ; or, pour que ce résultat qu'on appelle poffible eut un fens raisonnable, il faudroit fuppofer qu'un des deux cubes fût un vide fait dans l'autre, c'est-à-dire, qu'il faudroit fuppofer un cube de 27 pouces cubiques contenant un vide de de pouce cubique. Mais cette folution est toute semblable à celle qu'ont fournie les racines imaginaires de l'equation du probleme précédent. Les deux folutions ont donc la même espèce de polibilité, quoique l'une foit donnée par un refultat imaginaire et l'autre par un résultat qui ne l'est pas."

on

IV. Chemical Experiments en Guaiacum. By Mr. William Brande.

The more obvious properties of guaiacum are a green external hue, a. flight degree of tranfparency, and a vitreous fracture when broken. If pulverized its colour is grey, but the action of the ambient air foon renders it greenish. K melts when heated, and diffuses a pungent aromatic odour. It has, when in powder, a pleasant balfamic fmell, but scarcely any tafte, although, when fwallowed, it excites a very powerful burning fenfation in the throat. Its fpecific gravity is

1,2289.

In order to investigate the nature of this fubftance, Mr. B. fucceffively expofed it to the action of diverfe folvents, fuch as water, alcohol, the acids, and the alkalies; he carefully examined each folution, precipitation, &c. and noted the refults, which are ftated in the prefent paper. He then expofed 100 grains of very pure guaiacum in powder to the action of heat in a glass retort, furnished with the usua! apparatus. This diftillation produced an acidulated water, a thick brown oil, a thin empyreumatic oil, and fome mixed gaffes, coufifting chiefly of carbonic acid and carbonated hydrogen; leaving a coaly refiduum in the retort. The refult of the whole examination is contained in the following paragraphs.

"From the action," this author fays, "of different folvents on guaiacum, it appears, that although this fubftance poffeffes many properties in common with refinous bodies, it nevertheless differs from them in the following particulars :

"1. By affording a portion of vegetable extract.

"2. By the curious alterations which it undergoes when fubjected to the action of bodies, which readily communicate oxygen,

fuch

fuch as nitric and oxy-muriatic acids; and the rapidity with which it diffolves in the former.

"3. By being converted into a more perfect refin; in which refpect guaiacum bears fome resemblance to the green refin which conftitutes the colouring matter of the leaves of trees, &c.,

4. By yielding oxalic acid.

5. By the quantity of charcoal and lime which are obtained from it when fubjected to deftructive distillation.

"From the whole, therefore, of the abovementioned properties, it evidently appears that guaiacum is a fubftance very different from thofe which are denominated refins, and that it is alfo different from all thofe which are enumerated amongst the balfams, gum-refins, gums, and extracts; moft probably it is a fubftance diftinct in its nature from any of the above, in confequence of certain peculiarities in the proportions, and chemical combination of its conftituent elementary principles; but as this opinion may be thought not fufficiently fupported by the facts which have been adduced, we may for the prefent be allowed to regard guaiacum as compofed of a refin modified by the vegetable extractive principle, and as fuch, perhaps the definition of it by the term of an Extracto-Refin may be adopted with out impropriety." P. 26.

V. On the Direction of the Radicle and Germen during the Vegetation of Seeds. By Thomas Andrew Knight, Efq. F.R.S.

The very fingular property which the feeds of plants have been obferved to have in their germination; namely, the effort of forcing the radicle downwards, while the elongated germen takes a direction precifely oppofite, and that in whatever pofition the feeds may be placed, has long puzzled the minds of naturalifts, It has indeed been fufpected by fome, that gravitation was likely to be the cause of that fingular effect; but their hypothefis was not fupported by the evidence of actual experiments. Mr. Knight therefore thought proper to inftitute a series of experiments for the exprefs purpofe of elucidating this fubje&t, and the refult has corroborated the above-mentioned hypothesis.

If gravitation be the real caufe of the defcent of the radicle, and of the afcent of the elongated germen, Mr. K. naturally concluded that by fufpending that action, the directions of the radicle, and of the elongated germen would be altered accordingly. With this view he faftened certain nearly germinating feeds round the circumference of a wheel which was kept conftantly turning in a vertical direction, by the action of a stream of water.

"In a few days," he fays, "the feeds began to germinate, and as the truth of fome of the opinions I had communicated to you, and of many others which I had long entertained, depended on the refult of the experiment, I watched its progrefs with fome anxiety, though not with much apprehenfion; and I had foon the pleafure to fee that the radicles, in whatever direction they were protruded from the pofition of the feed, turned their points outwards from the circumference of the wheel, and in their fub. fequent growth receded nearly at right angles from its axis. The germens, on the contrary, took the oppofite direction, and in a few days their points all met in the centre of the wheel. Three of thefe plants were fuffered to remain on the wheel, and were fecured to its fpokes to prevent their being fhaken off by its mo tion. The stems of thefe plants foon extended beyond the centre of the wheel but the fame caufe which firft occafioned them to approach its axis, ftill operating, their points returned and met again at its centre." P. 101.

Befides the above-mentioned conftruction, Mr. K. alfo faftened the feeds round the circumference of a wheel that moved in an horizontal direction, and which might be caused to move with different velocities; he then says,

"But I conceive myself to have fully proved that the radicles of germinating feeds are made to defcend, and their germens to afcend, by fome external caufe, and not by any power inherent in vegetable life and I fee little reafon to doubt that gravita tion is the principal, if not the only agent employed, in this cafe, by nature. I fhall therefore endeavour to point out the means by which I conceive the fame agent may produce effects fo diametrically oppofite to each other." P. 103.

Mr. K. then proceeds to explain his idea of the mechanical part of this operation of nature, and adduces inftances to illuftrate his explanation. But for these we must refer our readers to the paper itself.

VI. A third Series of Experiments on an artificial SubStance, which poffeffes the principal characteristic Properties of Tannin; with Jome Remarks on Coal. By Charles Hatchett, Efq. F.R.S.

In purfuance of the investigation of the fame fubject, of which accounts are inferted in the preceding volumes of the Philofophical Tranfactions; namely, the properties of the tanning principle, &c. the prefent paper contains the ftate ment of the effects produced by the action of the fulphuric acid upon a great many refins, balfams, gun-refins, and

gums.

gums. The process in these is the fame as was used in the former experiments, and the general effects are concisely expreffed in the following lines.

"The fulphuric acid almoft immediately diffolved the refins, and formed tranfparent brown folutions, which progreffively be

came black."

"The fame effect was produced on most of the other fub. ftances, but the folutions of the balfams and of guaiacum were at firft of a deep crimfon, flightly inclining to brown.

"Caoutchouc and elaftic bitumen were not diffolved, but after having been digefted for more than two months, were only fuperficially carbonized."

"The gums and the faccharine fubftances required many evaporations and filtrations before the whole of their carbonaceous refidua could be obtained.

"Thefe were the principal effects obferved during the experiments, and I have ftated them in this manner, that tedious and ufelefs repetitions may be avoided.

"Turpentine, common refin, elemi, tacamahac, maftich, copaiba, copal, camphor, benzoin, balfam of Tolu, balfam of Peru, afafoetida, and amber, yielded an abundance of the tanning fubftance.

Oil of turpentine alfo afforded much of it; asphaltum yielded a small portion; fome slight traces of it were even obtained from gum arabic and tragacanth; but none was produced by guaiacum, dragon's blood, myrrh, gum-ammoniac, olibanum, gamboge, caoutchouc, elaftic bitumen, liquorice, and manI am perfuaded, however, that many of these would have afforded the tanning substance had not the digeftion been of too long a duration.

na.

"Olive oil was partly converted into the abovementioned fubstance, and alfo linfeed-oil, wax, and animal fat; but the three laft appear to merit fome attention." P. 110.

After defcribing the particular effects which the fulphuric acid produced upon the three laft-mentioned fubitances, Mr. H. obferves, with respect to the tanning fubftance yielded by the aforementioned articles, that from whatever fubftance it is obtained, its nature feems to be exactly the fame.

Subfequent to this Mr. H. defcribes a feries of experiments made upon a variety of vegetable fubftances previoufly roafted, and then digefted in water. The very remarkable refult of this series of experiments is as follows:

"The whole," this author fays, "of the artificial tanning fubftance was extracted by different portions of water, and the remainder

N n

remainder of the bark thus exhaufted, was again treated in the manner above defcribed, and again afforded a confiderable quantity of the tanning fubftance, fo that thefe proceffes evidently might have been continued until the whole of the bark had been converted into it.

"This might alfo have been accomplished, if in the first inftance, the exhaufted bark had been converted into charcoal, and digefted in nitric acid, as defcribed in my firft paper; but then, the effects would have been more flowly produced, and much more nitric acid would have been confumed. I am now, therefore, fully convinced, not only by the refults of the experiments related in this paper, but alfo by many others which it would have been fuperfluous to have ftated, that the most speedy and moft economical of all the proceffes which I have described, is that of treating roafted vegetable fubftances in the way which has been mentioned, and confidering that all refufe vegetable matter may be thus converted into a tanning fubftance by means the moft fimple, and without any expenfive apparatus, I cannot help entertaining much hope, that, eventually, this discovery will be productive of fome real public advantage." P. 125.

In the feventh fection this author gives a lift of the proportional quantities of coal that remained after having extracted the tanning principle, and other products, from the refins, balfams, &c. And he remarks, that the coal thus. obtained by the humid way from many of the refins, was fhining, hard, and iridefcent; while few of the coals obtained from the fame bodies by fire, had any of thofe pro perties.

In the 8th fection, which is the laft of this valuable paper, the author endeavours to inveftigate a problem in natural hiftory, which has always proved difficult and perplexing; but to the elucidation of which his experiments contribute in a confiderable degree. The queftion is, whence does pit-coal derive its origin ?--It being not in our power to follow the philofopher's reafoning fiep by flep, we fhall only mention his concluding obfervation; which is, that pit-coal feems to have been formed in the humid way, principally from vegetable bodies, and moft probably by the agency of fulphuric acid; allowing that animal fubftances may allo have contributed to their production.

VII. The Application of a Method of Differences to the Species of Series whoje Sums are obtained by Mr. Landen, by the Help of Impible Quantities. By Mr. Benjamin Gompertz.

The