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· indication of imbecility; the “embrace" Haires's system, which, to any person

of thein by Mr. Morgan, an example of conversant with the science, must, at the effect of dutage; the “assene” to one view, appear unfocoded, if I did them by Mr. Baily, a manifestation of not think it essential that there should good-natured credulity; and, finally, the not be two opinions on so important a • conviction of the fallacy of their doc- subject; as, you must be aware of the trine, by Mr. Hawes bimself, a splendid great extent of business that is daily and memorable instance of the ettica. transacted in this metropolis upon the cious power of watere when properly principles that it is Mr. Hawes's object consulted.

to overturn. . I cannot conclude, Mr, Editor, with. Mr. Rawes has very sedulously kept out observing that, in the “ objections us in the dark, as to the foundation of Mr. Hawes, the name of Dir. Baily upon which his superstructure is raised; holds a conspicuous place. Why this and the only effectual mode of showing gentleman's pame should have been so its folly will be, by contrasting it with frequently mentioned, I cannot con- the simplicity and clearness of the doc. ceive, unless with a view to depreciate trine laid down by Dr. Halley, and the the value of his works; permit me there other authors named. He asserts, (te fore, Sir, to state, that I have read and use his own words,) that the subject of studied the greater part of Mr. Baily's che present investigation is that of time, work, on the “Doctrine of Life Annue that is, its component and fractional ities and Assurances," and that I have parts:" now it appears to me evident, no hesitation in declaring it to be by far that not “ time," which is made up of the most excellent performance which divisions fixed, and not subject to mu. we have on this subject. In the the- tation, but the probability of a given oretical part of this work, by his great event happening, or not happening, in skill in analysis, and by a niore happy any one, or more, of those divisions of notation, the author bas demonstrated which time is composed, is the point in the principles of the doctrine of annu. question; and that given event being ities, in a manner which delights, no less death, we can only determine the pro. by its elegance, than by irs scientific bability of its happening, or not, by a accuracy; and in the practical part, the reference to those tables, that show very extensive and appropriate list of the progression in which given numbers exainples, and the valuable collection of bave died off, from birth, to the latest tables, while they display the unwearied probable period of human existence. exertion of the author for the perfection The fraction that gives the proba. of his work, renderlis book of the higliest bility of a person being in existence utility, not only to all the Assurance at the end of any terin, as expressed Companies in the kingdom, but also to by every author who has treated on the every individual who has any interest in subject, is this, the denominator shews annuities of every kind, or in the re- the number taken from a table of more newal of leases.

tality, living at the age of the persen Norwich,

R. Saint. and the numerator, the number living April 17, 1811.

at an age older than the given age by

the term stated: the reason of this may To the Editor of the Monthly Magazine, he given in few words; in any table of Sir,

mortality the nuinber, tlierein stated to IN your last Number I observe a letter be alive at a given age, shows the num.

1 signed by Nathaniel IIawes, in which ber of chances for a person of that die asseris the incorrectness of the age, buth living and dying, in any term; present mode of determining the proe the number alive at an age older, by babilities of life. Your correspondent, that term, than the given age, shews instead of demonstrating ihat the eini- the number of chances for liring to ment authors whom he names, have pur- the end of the term; and the difference sued a wrong principle, ofiers a mode between these two numbers, shows the of his own intention, and appears to number of persons that die in the conclude that, because the results pro- terin, or the chances for not living so duced by the two methods disagree, long. This will be made perfectly fa. his own must be correct, and that the miliar by an example; lee it be required other must necessarily be founded in to find the probability that a person, error.

aged 20, shall live 30 years, (as in the I should hardly think it necessary to first example quoted by Mr. Hawes) attempt to show the futility of Mr. and also ihe probability that he shall

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not live 30 years;-the number living one of them shall live to the end of at the age of 20, in Mr. Baily's third the same term. In his first example table is 814, and at the age of fity 581- of his own method, he makes the chance the fraction is thereforo, expresses of a person, aged twenty, being alive at the probability that the person in ques. the end of thirty years 45:6688 years : tion will be alive at the end of that that a person, aged forty, shall be alive terin, and the fraction 211 shews the at the end of thirty years, 33:4:5+ years, probability of dying in that time: both and the probability that both shall conihonse fractions added together or fitx tinue in being ingether to the end of ** will be equal to unity, as it is cer- the same terin 44:6588!!!.The same lain that the party will be either alive result is produceu in every example he or dead at the end of the terin.

bas given. I should bave been at a loss to dis. It is now almost time for me to leave cover in what way, Mr. Hawes obtains Mr. Hawes, whose futile attempts will his numerators, if I had not observed avail little, in opposition to the doc. that in those examples, where he makes trine laid down by such men as Hailey, the term for which the probability is De Moivre, Simpson, and other emin to be found, equal to the difference be. nent authors, and so ably treated by tween the age given and the oldest age Mr. llawes's contemporary Mr. Baily. in the table of mortality, from which the who has certainly combined in his va: calculation is to be made, the nume. luable treatise on the subject nearly rator is the same number that is given all the inforination to be found in prein the table of expectntions deduced ceding authors, in addition to his own from the same table of mortality; as, improvements, althought it is to be wishia for example, he inakes the probability ed that he had blended with his talent that a person, aged fifteen, shall live some greater portion of liberality. "I eighty years, 43:5638 the nuinerator of would however, before I close, inquire which fraction is the number given in of Mr. Hawes in what way writers on Mr. Baily's third Table, as the expecta. this branch of science, have overstep, Lion of a life of fifteen; and from leuce ped the bounds of probability; and I conclude, that the mode which lie so why their principles are not correct. confidently offers as a substitution for Mr. Hawes sceins by his 'sneers, at the present, is nothing more, than in what he calls the “mnihematical faiite the case of single lives, the making the ful," to suppo:e chat the science may number of years, for which the pro- be made independent of the mathemaa bability is to be calculated, the denoini. tics; to that I shall observe, that had nator, and the expectation of life for he been able to investigace the subthat terin the numerator. By the expec- ject mathematically, five of your co. tation of life, I mean the share of life, lumns would not have been occupied which, according to any table of obe with the tissue of absurdities, we have servation, belongs to any individual of seen from his pen; nor would he have a given age, or in other words the ave asked so many unmeaning questions, rage number of years which they will, which have no other tendency ihan to one with another, enjoy.

perplex his readers and to involve the Mr. Hawes has forgotten, that by at. question in obiscurity. By what jina. tempting to overturn the present mode ginary law of Nature does Mr. Hawes of estimating the probabilities of life, make his deductions froni registers of he tries to overturn the way by which lite and death? Can he suppose that his own nuinerators are calculated, a system laid down by the authors be which are nothing more than the sunis has mentioned, will yield to his insig. of the fractions expressing the chances nificant attack, which is unsupported of living one, two, three, &c. years, by either reason or argument? Had to the end of the term named. In the your correspondent stated his objeccase of joint lives, I need not under. tions, with becoming inodesty, and de. take any investigation, but shall con- ference to acknowledged talent; and tent myself with observing that he has offered his system in a manner free been guilty of a palpable error, which from arrogance, he might have been at once shews his whole system to be considered ingenious, or at the worst founded in absurdity, and maintained have passed unnoticed; but his style by ignorance. I mean, his making the is such as cannot fail of exciting emoprobability that two lives shall continue tions of contempt for his vanity, and together in existence to the end of a pity for his ignorance. term, greater than the probability that

Punto MATHEMATICUS,

To

To the Editor of the Monthly Magazine. of general interest in the minds of society, SIR,

beyond the conduct of private life. Its MTOTWITHSTANDING any differ. vious are too varrow for a proper poli.

I ence of opinion which may exist in tical topic in any other relation : and it the minds of nien, respecting the justifia- suminons into energetic action, prejubleness of war, and necessay of military dices, errors, and absurdities, of various establishments, those who interest them kinds.

PUBLICOLA. selves in the welfare of their fellowcreatures, whatever their seniiinents may To the Editor of the Monthly Magazine, be as to those points, must greatly re SIR, joice at seeing a most severe sort of THE writer of « Critical Remarks on military discipline abolished. For the T Shakespeare,” in your last Nuinber, information of your readers, the injo (page 210, vol. 31) sides with Dr. Johnsertion of the following extract from son in his observations on the word the London Chronicle is requested, “ming." I ain no commentator, and provided you thiuk it worthy a place profess to have but an accidental acw it.

quaintance with the illustration (excuse U MILITARY PUNISHMENTS." the vanity of such an expression) which « We see with infinite gratification I take the liberty of sending yon. the new clause introduced into the “Ming" is à terin frequently used in mutiny bill, granting to court niartials Norfolk, and is applied in the same sense the discretion of cominuting the pu- as “to mix,” or “mingle." Our bakers pishinent of flogging for imprisonment, and economical house wires have it in This is a salutary concession to the constant use; and the ingredients for spirit of humanity, which the enlight. bread and duinplinys are said to be coing press has aroused and spread “ming'd," or, in some instances, "nurig," through all the civilized world. This when by klieading they are formed into is as much as could be expecied per- dough. haps from government in the first in- During the scarcity nine or ten years dance, and we inay safely leave it to ayo, when a mixture of grain was recomthe feelings of the British officers them. mended for bread, the discontented used selves to do the rest. We know that to call out “No barley mung !" Dr. the service is an enemy to this shocking Warburton's therefore appears to me to practice."

be the true reading. Take the sentence, A CoxsTANT READER, “ The composition that your valour Lordox Céron. 1+15 March, 1811.

and fear make in you, is a virtue of

- good ming.) to the Editor of the Monthly Mugazine. a good unisture, } and I like the SIR,

(or) excellent mingle, J M HE numerous subscriptions which wear well." The word « composition,"

1 issue froin Lloyd's, for patriotic too, favours this sense, which seems also purposes, are known to every body. to be that of the lines from the translaPermit me, through your Miscellany, to tions of Horace and Lucan. suggest a subject (in my opinion, noble "He bears the bell in all respects, who good indeed) for ample support. It is the extension of the Lancastrian education

with sweet doth ming 7.

mingles throughout Irelanı, tıgether with ocher

us Which never mings with other methods, adapted to encourage civiliza. "" a mingless stream tion in particular. Some wpiers have Norwich,

S. S. C. ascribed ihe fall of the Roman empire to April 2, 1811. the religious disputes, which occupied P.S. Since writing the above, I introduced solely the minds of the inhabitants, when the subject while in conversation with a ollier subjects should always be the most theatrical friend, who, unacquainted with its buayant in society. Accursed pole local use, conjectured “ming" to be as mics, and an invincible itch to sellle the abbreviation of " mingle:" and, further, I affairs of God Almighty and unknown consulted my boy and maid servant, whose worlds, have been atiended with national

definitions exactly correspond with my own injuries of the most serious kind, though

and, as they cannot read, I consider them to

be in this case very high authority. I have by no means considered with a proper

detained this so long in the vain bope of leisense of their importance. A wise poljo

gore, (being much occupied,) for perusing the tician will ever feel regret when any reli- whole of the play, that I might find the gious subject, whatever, becomes a point quotation, since it does not appear in my

copy1

1

copy, (the booksellers' edition, 1803, 10 cffluvia passing through it in different die vols. with Johnson's and Steevens's notes,) rections, as well as from the regions in the place referred to by your correspondents above, together with the fresh water colle April 181h.

stantly fowing into it, tend to preserve

the aqueous, parts of our globe from the To the Editor of the Monthly Magazine. putrefaction which would otherwise take SIR,

place, and render the surface of our I REMARKED in your extensive and earth not habitable: thus we enjoy an inI useful Miscellany of Marcia 1, an calculable advantage in this action of the observation of Copernicus, jun. with no011. The advantage we receive from respect to the earth and moon, as well the tides in other respects, are numerous, as other priinaries, with their seconda- The titles we should receive from the ries--that “ Our earth's different bce action of the sun alone, would not promispheres successively receive the benefit duce this effect; but when conjoined with of the inoon's retlected light; whereas one the moon, or when she is in quadrature of the moon's hemispheres receives no in part opposed by those of the sun, do; reciprocal advantage from the reflected upon the whole, produce the most benea light from the earth. We may be confi- ficial etfects. dent (says he) that the wisdom and good. With respect to the moon, without en. ness of the Creator, had some inportant tering upon a dispute whether she is ina end in view, whereby these globes are, habited or not, it may be remarked that upon the whole, greatly benefited by the the observations made by Dr. Herschel, manner in which they are arranged. prove that she has an atmosphere, and is Not having inet with any opinion or conta mountainous siinilar to our earth, anut jecture formed upon this subject, I therefore may be inhabited. The adDerefore beg to propose as a query: vantages received from this inountainous What benefit of consequence is attained, structure, as formerly stated, render it or (which is the same) what important unnecessary to be adduced as an arguinconvenience is avoided by the secondo ment in proof of her being inhabited. , dary planets, froin their having always the From the similarity of the moon to our sanie hemisphere turned toward their globe, we may suppose that she is, like it, primaries ?"

composed of land and water. Our globe, In answer to this query, I beg leave to so far as is known of its surface, is in four observe, that the moon's hemisphere, parts of five covered with water, and only which is turned constantly to the earıh, one part is solid land. If we may, from appears to consist inostly of solid matter, her similarity in other respects, suppose. and to be mountainous. By this moun- the greatest part of the moon's heinis tainous condition of the moon's surface, sphere, which is not exposed to our view, the reflected light becomes more equably to be covered with water: we know that distributed than it would be were the our tides, which are exposed to the inoon, surface a smooth one. This equal discri- are greater than our opposite tides, there bution of light is one great benefit which fore the earth being a body so much the inhabitants of the earth receive from greater in magnitude than the moon, that nature of the moon's surface, which must make greater tides in the inoon than is turned toward it. The solid part of the she can make upon the earth, but the moon being always turned toward the tides upon her opposite hemisphere, must earth, may perhaps act more powerfully be less than they wouid be upon her upon it in point of gravitation, than it it direct hemisphere. Again suppose that were aqueous, and thus our tidęs are the moon revolved about her axis once in kept io stronger agitation; by these tides twenty-four hours, her rides in that case agitating the water to an huudred fæ- would be forty times greater than ours: thoms depth, the nauseous particles occa- bodies acting upon one another, recipro sioned by the excrements of its numerous cally as their quantities of matter: 'but inhabitants, and putrid matter arising her revolutionary inotion is near thirty froin other causes, are diffused from its times less than that of the earth, and her surface to that depth, which ocherwise tides are considered to be upon her uppoa would glut as a thick crust upon that sure site hernisphere, and not direct rides as face; this agitation, with other circuin- those she gives to the earth; thus circum. stances, such as the fresh air ceceived by stanced, her tides will not exceed ours in the water, from its incursions into the point of elevation, but the agitation land; its communication with the atmo. would he too slow to preserve the salu. Ephere by the aërial sides; the electric brity of the waters; but when we bring

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her other motions into account, we may the query proposed by Coperniens, jun. find that this is corrected; for example, 'Without such queries and conjectures her quick motion in acceding to the suni, upon them, when demonstration cannie to a considerable degi ce nearer than be brouglit directly forward, advance in what the earth approaches, and again arts, science, or literature, cannot be receding to a greater distauce ; by the expected. Although advances in either one, the sun will produce a greater effect of these are not to be formed upon con. upon her rides than upon the terrestrial jecture, at the sanie tiine, queries and tides, and by the other a less, from which conjectures may be so improved, as to her spring and neap-udes will arise, but produce al last a demonstration; or such Loth will tend to encrease the agitation a degree of certaimy, as by natural con. of hier waters, which, together with her sequence may be considered not to fall other motions, commonly designed irre. short of it.

OBSERVATOR. gularities, will regulate the motion of her waters so as to be similarly equal to the For the Monthly Magozine. .. effects produced by the terrestrial lides; A VINDICATION of the PROPOSAL to and thus the primaries and their secon REPEAL the act of UNIFORMITY, daries are mutually beneficial to one V OUR Correspondent H. at p. 29, another.

1 prosesses to examine a paper consBut as Copernicus, jun. very pro- cerning the value of uniformity in reperly observes, that, a great part of the ligious opinion. Full of his own premoon's surface does not receive the be- conceptions, and inattentive to the ar. Defit of light reflected from the earth; to gument advanced, after talking about compensate this, that part of her surface to eration, which is not the topic bane is screened froin the powerful effect of dled, he decides against the enquirer's the tides, whicis would be caused by the proposal to repeal the Act of Unifor. direct attraction of the earth upon the inity, as intolerant toward the members waters of the moon, except at change, of the establishment. and which the other motions of the Toward what members of the esta. moon, particularly in her spring rides, blishment? . would cause to be so much accelerated, Is it intolerant to the clerical order, as to render her coast not babitable for who would thereby be set at liberty to some miles from shore; her high tides read prayers and to preach sermons, making so great incursions upon her exactly consonant with their own inlaud.

dividual sentiments? Without fear of But what the opposite disk of the deposition by the consistorial court, moon is composed of, can only be the Alr. Stune might then deny the persosubject of conjecture, taken from the pality of the Holy Ghost, or Dr. George supposed similarity she may have to our Somers Clarke, the existence of proearth in that respect.

phecy; Mr. Overton night preach his It is observable, that so soon after calvinism, and the bishop of Lincoln change, as a small part of herilluminated bis arminianism, unrebuked. Clerical disk comes in view, the disk oppo. opinion would no longer be amenable site to the sun, and turned to the earth, before any inquisitorial ecclesiastic ju. likewise appears; and, under some cir- risdiction. cumstances, is rendered very discernible: Is it intolerant to the laity? Less so if at such times that disk, and such parts at least than the present system. By of her opposiie disk as are turned to the allowing the priest to accommodate his earch by her libration, be attentively ob- liturgic and homiletic addresses to the serred, in order to discover whether it surrounding state of public belief, the be serrated like the other parts of her risk of discordance between the parson disk, or whether any parts of it are more and the parishioners must evidently be smootb; and a comparison made between diminished. Something would be done its appearance, and the appearance of to meet the wish of the neighbourhood. the suriace of water at night; if such ob- Ecclesiastics of a compromising spirit, servation and comparison be carefully are more numerous in the proportion made, we might perba ps form a preity of ten to one, than ecclesiastics ambie 'true idea of the composition of the op- tious of proclaiming that they think fac posite hemisphere of the moon. I have themselves. Where an autonomous no doubt that Doctor Herschel Would mind 'exists, it is mostly attended with readily undertake these observations. a spirit of proselytism, which slowly I bare thus risked, a conjecture upon makes converts. Thus, wherever

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