a 1 to the experience of the living, to fhew that though the returning ftroke muft take place, in all thunderstorms, in fome degree or other; yet it is not of that alarming magnitude which the Author afcribes to it. If in any particular thunderftorm, a man in the open fields could be killed, at the inftant of a diftant explosion, merely by the return of his own electric fire, which had before been driven out of his body: furely numerous obfervations of perfons who had experienced the returning ftroke, in flighter degrees, would be familiar; and fcarce a great thunderstorm must have occurred, in which one perfon or another muft not, at the inftant of an explosion, have felt the effects of the returning stroke, in fome degree or other-from that of a violent concuffion, to that of a flight and almoft imperceptible pulsation. But no obfervations of this kind are known to us; nor have we ever heard of any perfons experiencing any kind of electrical commotion in a thunderstorm, except fuch as have either been directly ftruck, or have happened to be in the very near neighbourhood of the fpot where the explofion took place. The Author has been aware of this objection, which he proposes, and endeavours to remove: but his answer to it amounts to little more than what has been already quoted from him; that is, to a fimple estimate of the enormous difference between the electrical denfity, or the elaftic electrical preffure, of the atmosphere of an extenfive thundercloud, and that of a charged prime conductor. We have already obferved, that this is not the proper method of eftimating their different effects, when thefe two causes, how unequal foever in power, are confidered as exerting that power on bodies containing a limited, and comparatively small, quantity of electric matter. We have been induced to difcufs this fubject thus particularly, with a view to quiet the minds of the timorous; as the Author's extenfion of his principles, respecting the returning ftroke in artificial electricity, to what paffes in natural electricity, The Author does indeed produce a living evidence, in the cafe of a person at Vienna, who, he has been credibly informed, received an electrical shock, by having held one hand accidentally in contact with an interrupted metallic conducting rod, at the inftant that a thundercloud exploded at the distance, as was conjectured, of above half an English mile. He likewife obferves, that a very ftrong, bright, and fudden ftroke' (or fpark) of electrical fire has been seen by feveral electricians, to pass in the interval, or interruption, purpofely left in the conducting rod of a house, at the inftant of a diftant explofion; and when it was fully proved, by the sharp point of the conductor not being melted, or even tinged,' that the conductor itself had not been ftruck.-Thefe obfervations, however, do not by any means prove the magnitude, or danger, of the returning ftroke, but merely its exiflence; which we do not contest. holds holds out a new and, in our opinion, groundless subject of tere ror to those who, in the midst of their apprehenfions, have hitherto only dreaded the effects of a thunderftorm when it made near approaches to them; but who, if this doctrine were be lieved, would never think themselves in fecurity while a thundercloud appeared in fight, unless fheltered in a houfe furnished with proper conductors: -for we should not omit to remark, that a fubfequent obfervation tends to diminish their fears, by fhewing that high and pointed conductors tend to fecure both perfons and buildings, against the various effects of any returning Atroke whatever, as well as of the main ftroke. Indeed various parts of this work, befides those immediately appropriated to the subject, tend to prove the utility of high and pointed conductors, in preference to those which terminate in a ball, or rounded end. Towards the end of the performance, the Author difcuffes this matter very particularly; and enumerates the necessary requifites' in erecting them, in number eleven; to every one of which, though we have taken the liberty to differ from him on another fubject, we readily fubfcribe. As this matter is of a popular nature, and on a subject generally interefting, we fhall transcribe this lift; adding a fhort explanation to particular articles.-These requifites (fays the Author) are eleven in number: ift, That the rod be made of fuch fubftances, as are, in their nature, the best conductors of electricity.' 2dly, That the rod be uninterrupted, and perfectly continuous.” This is a very material circumftance. One intire piece of metal cannot perhaps be had: but it is not fufficient that the rods, of which the conductor confifts, be fenfibly in contact. They should be pressed into actual contact by means of nuts and fcrews; with a thin piece of sheet lead between the shoulders of the joints. 3dly, That it be of a fufficient thickness.'-A copper rod half an inch square, or an iron rod one inch fquare, or one of lead two inches fquare, are thought fully fufficient by the Author. 4thly, That it be perfectly connected with the common ftock.'-That is, it fhould be carried deep into the earth, which is frequently dry near the furface; and then continued in a horizontal direction, fo as to have the farther extremity dipped, fhould this be practicable, into water, at the diftance of 10 yards or more from the foundation. 5thly, That the upper extremity of the rod be as acutely pointed as poffible.'-This termination fhould be of copper; or rather a very fine and exceedingly acute needle of gold should be employed, which will not materially add to the expence. 6thly, That it be very finely tapered :'-fo that the upper extremity may be a cone, the diameter of the bafe of which may bear bear an extremely small proportion to its height; for instance that of one to forty. 7thly, That it be extremely prominent;'-that is, 8, 10, or 15 feet at least above the highest parts of the building. The Author lays great ftrefs on this circumftance; in confequence of the law above mentioned, deduced by him from his experiments relating to electric atmospheres. According to this law, the denfity of an electric atmofphere (the negative atmosphere, for inftance, of the roof of a houfe, &c. while a pofitively charged cloud hangs over it) diminishes in the inverfe ratio of the fquare of the diftance from the furface of the body to which that atmofphere belongs. Accordingly, if the rod project twelve feet into this atmosphere, it will reach to a part of it four times less denfe than if the rod projected only to half that distance, or fix feet; and to a part one hundred and forty four times rarer, than if it projected only one foot. 8thly, That each rod be carried, in the fhorteft convenient direction, from the point at its upper end, to the common stock.' 9thly, That there be neither large nor prominent bodies of metal upon the top of the building proposed to be fecured, but fuch as are connected with the conductor, by fome proper metallic communication.' Iothly, That there be a fufficient number of high and pointed rods.'-On edifices of great importance, especially magazines of gunpowder, the Author thinks thefe ought never to be above 40 or 50 feet asunder. 11thly, That every part of the rods be very fubftantially erected." The Author declares that he has never been able to hear of a fingle inftance, nor does he believe that any can be produced, of an high, tapering, and acutely pointed metallic conductor having ever, in any country, been struck by lightning; if it had all the neceffary requifites above mentioned, especially the fecond and fourth. One of the new principles contained in this work, and which the Author conceives to be as important as it is new, is, that it is the electricity itself, contained in an electrical atmosphere, which ferves fuddenly to conduct, to a given diftance, any given electrical charge.'-One illuftration of this principle is, that a charged prime conductor will not, for inftance, ftrike into a ball prefented to it, at its greatest ftriking distance, till it had been previously made to ftrike upon the ball at fome smaller distance: the ball being afterwards gradually removed from it, till it reached the greateft ftriking distance. He fuppofes that, in the previous fhorter explosions, the air lying in the path of the sparks being electrified by them, in their paffage through it, becomes a better a better conductor in confequence of that circumstance, and is thus enabled to convey the stroke to a greater distance. Though the experiments and principles contained in this work are totally fubverfive of those produced by Mr. Wilson; the Author does not make any particular application to these last, but intends very foon to give to the world a direct refutation of the conclufions drawn' from Mr. Wilfon's experiments. We learn with pleasure, too, that the experiments and obfervations that he has lately made upon Leyden jars, &c. will be the fubject of some future publication.-We hall only add that, as the Author does not write to Tyros, but to proficients in the fcience of electricity, we think that, by aiming at too great precifion, he has in the present work fallen into verbofity and repetition; by which his meaning is frequently rather obfcured than illuftrated; and the bulk, and consequently price, of the work unneceffarily increased. Brrrry. ART. V. The Doctrine of Annuities and Assurances on Lives and Survi vorfhips, ftated and explained. By William Morgan, Actuary to the Society for equitable Affurances on Lives and Survivorships, To which is added, an Introduction, addressed to the Society. Alfo an Effay on the prefent State of Population in England and Wales. By the Reverend Dr. Price. 8vo. 5s. fewed. Cadell. 1779. TH HIS very ingenious performance is divided into three chapters, of the contents of which, and the Author's motives for publication, we cannot give a better account than that we meet with in a very curious Introduction by the truly learned and ingenious Dr. Price. The first chapter contains an explanation of the nature of afsurances on lives and furvivorships; together with a particular account of the fociety for making such assurances, and of the methods which have been taken to determine how far it has been hitherto a gainer by the business it has transacted. • The fecond chapter contains an explanation of the doctrine of life-annuities in general, and of the principles on which their values are calculated. At the end of this chapter, an account is given of a method of expediting all calculations of the values of life-annuities, which muft, I think, be very acceptable to all who have ever employed themselves in making fuch calculations." In these two chapters Mr. Morgan has rendered the subjects of which he treats as intelligible, to perfons who are unacquainted with mathematics, as the nature of them will admit. The whole is delivered in a manner independent of algebra, and, in general, in words at length, with a clearness and perfpicuity which we do not remember to have seen elsewhere. The third chapter contains a complete account of the rules for folving all questions concerning the values (in fingle and annual payments) of all annuities, whether in poffeffion or expectation; and of all all reverfionary interefts depending on any one, two, or three lives, or on any furvivorships among them, either for terms or for perpetuity. Several of thefe queftions are incapable of being anfwered without entering into the abftrufeft parts of mathematics. Most of them have never been before answered; and yet there arifes, in many cafes, a neceffity of anfwering them, in order to determine correctly the value of reverfionary interefts depending on furvivorships; and some of them are often occurring in practice, at the office whose bufinefs Mr. Morgan tranfacts. The folutions in this chapter alfo are given in words at length, with fuitable examples; but the mathematical investigations have been thrown together into an Appendix; where every rule or direction, about which any doubt can be entertained, is particularly demonftrated. Every competent judge who will examine this chapter, and compare it with the demonftrations in the Appendix, must admire Mr. Morgan's attention and skill; and fee that it contains a valuable addition to this part of science.' Mr. Morgan's motives for this publication are next affigned. They appear to be partly of a public, and partly of a private nature, in as much as they relate more particularly to the affairs of the fociety in whofe bufinefs Mr. M. is engaged. Firft,' fays Dr. Price, in the course of the traffic of this kingdom, and particularly the law transactions of it, fuch queftions as are contained in this work are continually occurring; and, in numberlefs cafes, it is impoffible to give right decifions, or to make an equitable diftribution of property, according to the real value of the different claims and interefts, without obtaining accurate answers to them. The experience of many years has taught me, that there are great mistakes committed in anfwering thefe queftions, by which means many perfons are injured in their property. It feems, therefore, that it may be of particular ufe to the public to be informed where they may apply for folutions that may be depended on; and, at the fame time, to be furnished with fuch an account of the rules and principles of calculation, mathematically demonftrated, as may remove every doubt, and be a fufficient direction to all who may chufe to employ themselves in business of this kind.' But this reafon alone, the Doctor tells us, might not have been fufficient to induce Mr. Morgan to undertake this laborious work. There was another, which, though of a more private nature, more immediately and more forcibly influenced him. It was his employment in tranfacting the business of the fociety, which affures all kinds of reverfionary annuities, and contingent interefts, dependent on the continuance of any lives, or any survivorships of any lives beyond other lives. In carrying on this bufinefs the fociety profeffes to regulate its demands by calculations founded on ftrict mathematical principles. There is not any other fociety now exifting of the fame kind; and its business has been, for fome years, increafing so fast, that it is already become an object of vaft importance to the public, and is likely foon to become of much more importance. It feems therefore neceffary that the Public fhould be fully in 2 formed |