RETROGRESSION

, or Retrocession. The same with Retrogradation.

RETURNING Stroke, in Electricity, is an expression used by lord Mahon (now earl Stanhope) to denote the effect produced by the return of the electric fire into a body from which, in certain circumstances, it has been expelled.

To understand properly the meaning of these terms, it must be premised that, according to the noble author's experiments, an insulated smooth body, immerged within the electrical atmosphere, but beyond the striking distance of another body, charged positively, is at the same time in a state of threefold electricity. The end next to the charged body acquires negative electricity, the farther end is positively electrified; while a certain part of the body, somewhere between its two extremes, is in a natural, unelectrified, or neutral state; so that the two contrary electricities balance each other. It may farther be added, that if the body be not insulated, but have a communication with the earth, the whole of it will be in a negative state. Suppose then a brass ball, which may be called A, to be constantly placed at the striking distance of a prime conductor; so that the conductor, the instant when it becomes fully charged, explodes into it. Let another large or second conductor be suspended, in a perfectly insulated state, farther from the prime conductor than the striking distance, but within its electrical atmosphere: let a person standing on an insulated stool touch this second conductor very lightly with a finger of his right hand; while, with a finger of his left hand, he communicates with the earth, by touching very lightly a second brass ball fixed at the top of a metallic stand, on the floor, which may be called B. Now while the prime conductor is receiving its electricity, sparks pass (at least if the distance between the two conductors is not too great) from the second conductor to the right hand of the insulated person; while similar and simultaneous sparks pass out from the finger of his left hand into the second metallic ball B, communicating with the earth. At length however the prime conductor, having acquired its full charge, suddenly strikes into the ball A, of the first metallic stand, placed for that purpose at the striking distance. The explosion being made, and the prime conductor suddenly robbed of its elastic atmosphere, its pressure or action on the second conductor, and on the insulated person, as suddenly ceases; and the latter instantly feels a smart Returning Stroke, though he has no direct or visible communication (except by the floor) with either of the two bodies, and is placed at the distance of 5 or 6 feet from both of them. This Returning Stroke is evidently occasioned by the sudden re-entrance of the electric fire naturally belonging to his body and to the second conductor, which had before been expelled from them by the action of the charged prime conductor upon them; and which returns to its former place in the instant when that action or elastic pressure ceases. When the second conductor and the insulated person are placed in the densest part of the electrical atmo- sphere of the prime conductor, or just beyond the striking distance, the effects are still more considerable; the Returning Stroke being extremely severe and pungent, and appearing considerably sharper than even the main stroke itself, received directly from the prime conductor. Lord Mahon observes, that persons and animals may be destroyed, and particular parts of buildings may be much damaged, by an electrical Returning Stroke, occasioned even by some very distant explosion from a thunder cloud; possibly at the distance of a mile or more. It is certainly not difficult to conceive that a charged extensive thunder cloud must be productive of effects similar to those produced by the prime conductor; but perhaps the effects are not so great, nor the danger so terrible, as it seems have been apprehended. If the quantity of electric fluid naturally contained, for example, in the body of a man, were immense or indefinite, then the estimate between the effects producible by a cloud, and those caused by a prime conductor, might be admitted; but surely no electrical cloud can expel from a body more than the natural quantity of electricity which this contains. On the sudden removal therefore of the pressure by which this natural quantity had been expelled, in consequence of the explosion of the cloud into the earth, no more (at the utmost) than his whole natural stock of electricity can re-enter his body, provided it be so situated, that the returning fire of other bodies must necessarily pass through his body. But perhaps we have no reason to suppose that this quantity is so great, as that its sudden re-entrance into his body should destroy or injure him.

Allowing therefore the existence of the Returning Stroke, as sufficiently ascertained, and well illustrated, in a variety of circumstances, by the author's experiments, the magnitude and danger of it do not seem to be so alarming as he apprehends. See Lord Mahon's Principles of Electricity, &c. 4to. 1779, pa. 76, 113, and 131. Also Monthly Review, vol. 62, pa. 436.

REVERSION of Series, in Algebra, is the finding the value of the root, or unknown quantity, whose powers enter the terms of an infinite series, by means of another infinite series in which it is not contained. As, in the infinite series &c; then if there be found &c, that series is inverted, or its root x is found in an infinite series of other terms.

This was one of Newton's improvements in analysis, the first specimen of which was given in his Analysis per Æquationes Numero Terminorum Infinitas; and it is of great use in resolving many problems in various parts of the mathematics.

The most usual and general way of Reversion, is to assume a series, of a proper form, for the value of the required unknown quantity; then substitute the powers of this value, instead of those of that quantity into the given series; lastly compare the resulting terms with the said given series, and the values of the assumed coefficients will thus be obtained. So, to revert the series , &c, or to find the value of x in terms of z; assume it thus, | &c; then by involving this series, for the several powers of x, and multiplying the corresponding powers by a, b, c, &c, there results

z = aAz	+	aBz2	+	aCz3	+	aDz4,	&c.
	+	bA2z2	+	2bABz3	+	2bACz4
					+	bB2z4
			+	cA3z3	+	3cA2Bz4
					+	dA4z4

Then by comparing the corresponding terms of this last series, or making their coefficients equal, there are obtained these equations, viz, , &c, which give these values of the assumed coefficients, viz, ; &c. and consequently &c; which is therefore a general formula or theorem for every series of the same kind, as to the powers of the quantity x. Thus, for

Ex. Suppose it were required to revert the series , &c.

Here a = 1, b = -1, c = 1, a = -1, &c; which values of these letters being substituted in the theorem, there results , &c, which is that series reverted, or the value of x in it.

In the same way it will be found that the theorem for reverting the series .

Various methods of Reversion may be seen as given by De Moivre in the Philos. Trans. number 240; or Maclaurin's Algebra pa. 263; or Stuart's Explanation of Newton's Analysis, &c. pa. 455; or Coulson's Comment on Newton's Flux. pa. 219; or Horsley's ed. of Newton's works vol. <*>1, pa. 291; or Simpson's Flux. vol. 2, pa. 302: or most authors on Algebra.