Page images
PDF
EPUB
[ocr errors][ocr errors][ocr errors]

of Galvanism. 437 opposite wires of a battery, which are the terminating points of a broken circuit, the mechanical action resulting from their contrary forces may induce them to unite with such rapidity as to render manifest all their combustible energies. This principle of action, and the probability that the bases of the galvanic fluids partake of an oxygenous and hydrogenous nature, will enable us to form a tolerably correct idea of the combustible effects of galvanism; but the most perplexing results attending the galvanic phenomena are said to be the invisible transfer of different bodies through various fluid media.

From the view we have taken of the subject there must be at the same time a distinct fluid quitting the end of each wire that proceeds from the battery, when they are placed in an imperfect conducting fluid medium; and to keep up the evident circulation, each fluid must endeavour to gain the wire opposite to the one it bas quitted; it is therefore highly probable that the opposing forces of these contrary currents of the galvanic fluids, give rise to their powers of decomposition, rendered so manifest at the end of each conducting wire of a battery.

These general conclusions give us a new hypothetical view of the galvanic phenomena, the truth or correctness of which, will be the best ascertained by its application to explain what are termed the most perplexing results in galvanism.

In attempting to account for the invisible transfer of acid and alkaline matter through various fluid media, and the appearance of oxygen and hydrogen gases at the opposite wires of a battery, when separated by a column of water some feet in length, the correctness of this hypothesis will be put to a tolerably fair trial.

So w If we consider the characters we have attributed to the galvanic fluids, the invisible transfer of this acid and alkaline master in opposite directions appears consistent with the view we have taken of the subject; for if the base of the positive fluid partakes of an oxygen nature, this Auid will probably convey to the negative wire, by the influence of affinity, the alkaline part of any saline solution which is decomposed at the positive wire, and deposit the greater portion of this transferred matter at the negative wire, when it enters that metallic part of the circuit. We have supposed also that the base of the negativa

Auid may partake of an hydrogenous or alkaline nature, consequently this Huid may by the force of affinity convey the acid portion of any saline solution decomposed at the negative end of the battery, towards the positive wire; and there deposit this acid matter, when it enters the metallic part of the circuit; and this exchanging process most probably goes on, until the alkaline part of the solution is collected round the negative wire, and the acid portion of the same

compound is collected round the positive wire of the battery. On this principle we may account for the appearance of oxygen and liydrogen gases at the opposite wires of a battery though separated by several feet of water.

[ocr errors][ocr errors][ocr errors][ocr errors]

'

[merged small][ocr errors]

1

Omnile

[ocr errors]
[ocr errors]

When water is decomposed by the galvanic action, and two disa tinct gases appear at the opposite wires, although separated by such a body of water, one of these gases must have been transferred in an invisible manner from one wire to the other, or the water must have been decomposed at each wire, and the constituent portions which do not appear at the point of decomposition must have become so far changed and influenced by the fluids from the battery, as to have passed with them through the water in an invisible state. This latter opinion, though rather novel, is agreeable to what has been advanced, and is strongly corroborated by the transfer of other substances, as well as those just mentioned. By keeping in view the preceding illustration of galvanic effects, it will appear that the hydrogen of the water decomposed at the positive end of the battery will be transferred by the positive fluid towards the negative wire, and there liberated : and that the oxygen of that portion of water decomposed at the negative end of the battery will be transferred by the negative fluid to the positive wire, and be there liberated ; and ascend through the water in the character of oxygen and hydrogen gases.

These inferences are supported by the fact, that all the bodies collected and liberated round each wire of a battery possess such characteristic properties as are likely to be influenced by the attractive affinity of the galvanic fluids; if we admit that these fluids possess the constituent nature ascribed to them in this communication. *

The positive evidence we have that the most dense bodies can be transformed by the agency of caloric to assume so many characters, naturally suggests the idea, that a great variety of combinations may

take place by its union with the constituent parts of water, which are still unknown; and no products are more likely to be among this class than those elastic compounds which, in all probability, form the galvanic fluids; as they seem a link between well known geseous bodies and caloric, by partaking of the constitutional character of the one, and the action and subtle nature of the other. Nor is it improbable but both the electric and galvanic fluids will, at some advanced period of these sciences, be considered merely as a newly discovered class of peculiar gaseous bodies, sufficiently attenuated by various degrees of caloric to give them different electrical energies.

It is not the results mentioned in this paper only that support this mode of reasoning, for the whole series of regular galvanic

a

* In a small essay I lately published on Electricity, I have endeavoured to shew the probability that the electric fluids excited by the machine consist of a large quantity of caloric intimately united to a small portion of oxygen and nitrogen obtained from the atmosphere by the mechanical action of the cylioder and rubber. Perhaps if the machine was so constructed that the cylinder could be surt"unded and worked alternately in different kinds of gas, the electric fluids excited under these circumstances might display a variety in their chemical action that would lead to some iuteresting results ; and it is not extremely impro. bable, but that the galvanic fluids would also manifest some variety of character, if they were excited by different agents properly calculated for such a purpose,

[ocr errors]

effects, as well as several anomalies, seem to point at something of this nature; and as opinions formed agreeably to this view of the subject will account for most of the galvanic phenomena in a simple and plausible manner, without the aid of mysterious prin ciples, the subject assumes an highly interesting character, by the increasing probability, that the phenomena of galvanism are most intimately connected with many other important branches of natural philosophy.

[ocr errors]

ARTICLE VIII.

t is a

Defence of the Opinion that all Numbers have Four Imaginary

Cube Roots. By James Lockhart, Esq.

(To Dr. Thomson.). SIR, I Am much obliged to Dr. Tiarks, and to your Correspondent N. R. D., for their attention to my late communication. The disagreement of these Gentlemen in respect of the value of the imaginary quantity gives me encouragement to hope that some doubt of the error which they suppose I have made will be excited. Dr. Tiarks affirms that the quantity is nothing but a different form of a well-known root of 64; whereas N, R. D. insists that it cube root of 8, and not of 64; and thus it would appear that the quantity is the square, and the square root of itself also. If impossible expressions, only a little complicated, universally lead to such difference of sentiment, it will be wise to abandon them altogether. Nevertheless, it now becomes me to endeavour to show that I have not made a hasty assertion, and that I was duly acquainted with the nature and construction of the quantity in question; and for this purpose I resort to the following remarks and demonstration. In the general equation x-bx= 6, there are three roots,

som C, o the greater, t the middlemost, and - v the least. The rule promulgated by Cardan gives all the three values, which, however, is denied by some eminent algebraists of the present day. I shall place the cube roots in their order under Cardan's binomials; and I believe that it is the first time of their being so exhibited.

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

3

3 LIN?

- } :

By means of these roots, and 28 varieties connected with them, the cube roots of all binomials may be obtained, if such roots admit os a finite expression, even when they are irrational, and without trial or assumption,

The imaginary quantity which I introduced relates only to t, and to the second cube root in the column on the left hand, which cube root is thus demonstrated to be exact :Let It - t=

{ bt

t3 2 72 t2

[ocr errors]
[ocr errors]

o t4 6
+

4

[ocr errors]

4

63 27

[ocr errors]
[ocr errors]

16

b?

63
27

2

27

[ocr errors]

(

27

bt's 13

2

[blocks in formation]

subtracting internally to the parenthesis
-+-= (-)

:) v
or(-) v (-) = V(-)

* N 4

* * ; adding to one side of the equation, and its equal to the other side. ber! + (1 - ) xwe - tv-)

g G-) extracting the cube roots

+ VG-3)=1; + V No other value can be used in this case for the cube root of the binomial, which the algebraist may readily prove by adapting it to an irreducible equation where there is no ambiguity in respect of the square foot. Such is the equation 23 - 63 x = 162, where the binomial is 81 + N = 2700, and the cube root for ¢ is ~ 3 + V - 12.

To obtain the imaginary quantity which is the subject of consideration, I employed the reducible equation 23 - 24 x = 72, where x = 6, t = 3 + V - 3, V=3 ✓ Cardan's rule the roots of the equation are thus expressed :

V 36 + 7 784 + 36 -7 784

V and by the previous demonstration, the cube root of the binomial on the left hand connected with t is the quantity I gave; namely,

. Algebraists universally give precedency in magnitude to the binomial on the left hand; and in this they follow the old masters,

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

3

[ocr errors]
[ocr errors]
[ocr errors]
[ocr errors]

It would be strange indeed to call the first binomial 8, and the latter 64.

The binomial on the left hand being, then, by common consent and usage, equal to 36 + 28 or 64, it follows that my number is a true cube root of 64ot of 8, which your correspondent N. R. D. affirms it to be, and that I have properly, and in conformity with the practice of algebraists, taken the positive square root of 784.

I conceive, therefore, that I have now only to show that the quantity is different from the known forms of the cube roots of 64. Dr. Tiarks has divided x3

64 by x

4, and by means of the quotient he obtains 2 + N 12, which are the cube roots connected with the equation x3 – 48 * = 128, where by Cardan's

x rule the roots are represented by v 64 + N 4096 4096 +

64 4096 4096, and where, by the roots previously exhibited depending on t and v, the cube roots become - 2 +

12; but these are the cube roots of binomials in their vanishing state, in which state they have functions and connexions widely different from those deduced from binomials which are not evanescent.

The means taken by Dr. Tiarks to prove my quantity to be equal to 2 2 w 3 is by no means sufficient.

This, as well as the correctness of my assertion, may be sufficiently evidenced by the nature of vanishing fractions; and on this evidence, and not on any ambiguity of expression, I entirely rest my opinion.

If binomials are not in a vanishing state, one of the roots of the equation from which the binomials are deduced will, by a simple operation, become extinct; but all the roots will be preserved if the binomials are evanescent.

Thus let 3 as = 2
23

I !?!!
Or X m2 = 2X1
1

= x2 + x = 2 Here the roots are preserved, because the binomials connected with the given equation vanish. But

23 = 6 х x = 6

6 x or 2018 X 1

a

[ocr errors]

2 X

X

23

Let 7 x

Here the value of unity is extinct, because the binomials

[ocr errors]
[ocr errors]
« PreviousContinue »