which naturally involve the mind in metaphyfical difficulties; but as the magnitudes they uniformly generate in a given finite time, fuppofing the fluent or space to be described by an uniform motion. And if the motion by which any magnitude is generated be not uniform, but accelerated or retarded, the idea of a fluxion will still be the fame: For though we cannot exprefs the fluxion by any space actually generated in a given time, as in uniform motion; yet we can readily affign the magnitude, or (as it is commonly called) the cotemporary increment, that would be uniformly generated, if the acceleration or retardation were to stop at any point in which the fluxion is required to be in vestigated.

Now, as our ideas of magnitude arife from a comparison of the propofed object with fome other of determinate dimenfions: fo, in the method of fluxions, we fix on a given magnitude, which is fuppofed to have been uniformly generated in a given time by the motion of a point, line, or plane, as a standard, wherewith to compare any other magnitude, which is fupposed to have been generated in the fame time, by an accelerated or retarded motion. Thus (for the fake of illuftration) fuppofe a ball to roll on an horizontal plane, in a straight direction, at the uniform rate of 20 feet in a minute: and also another ball to move uniformly in the fame direction, at the rate of 40 feet in the fame time; here then it will be plain, that the magnitudes generated in any given time must be in the ratio of 2 to 1; and therefore the fluxion of the latter will be double that of the former. And from hence it appears, that if the fluxion of x be, that of 2x will be 2*, 3x will be 3x, &c. and generally, that of nx will be nx. But if, while one ball moves along with an uniform velocity, the other is fuppofed to move with an accelerated motion, and that the law of accele ration is fuch, that the space described by the latter, from the commencement of motion, is always fome power of that described by the former, fuppofe the fquare of it; then, if the magnitude by which the fpace that is uniformly defcribed is increased in a given time be denoted by x, that magnitude which the accelerated motion would uniformly generate in the fame time, and commencing from the fame inftant, will be expreffed by 2xx. Thus, in the cafe propofed, if the first ball has uniformly described a space of 10 poles, the other must have run 100 poles; but the former ball moves uniformly at the rate of 20 feet in a minute, therefore the magnitude or space, which the accelerated ball would uniformly defcribe from the fame instant in one minute, will be 400 feet. The fluxions will be therefore at that point in the ratio of 400 to 20; or of 20 to 1."

Of this our author gives a demonftration; adding

"Hence it appears, that we have the moit rational notion of fluxions from the confideration of time in the generation of the increment or decrement, and that the fluxion of any variable quantity may be truly defined, The magnitude by which any flowing quantity would be increafed in a given time with the generating velocity at a given inftant, Suppofing it from thence to proceed uniformly or invariably. And with regard to the higher orders of fluxions, how much more obfcure are our notions without the idea of time in the operation of the fluent B 2 gene

generating the increment; fince by having recourfe to the firft ratio of the nafcent increment, or the laft ratio of the evanefcent increment, even to obtain only the first fluxion ot a variable quantity, we unavoidably fall into this abfurdity, That a velocity which continues for no time at all actually defcribes a space. How then can we form any conception not only of fuch a space or increment, but also of an infinite variety of magnitudes of it, generated into one and the fame point and inftant of time, in which it is well known all the orders of fluxions are confidered, when nothing, I think, can be more evident than that the magnitude or increment imagined to be generated must in fuch a cafe be purum putum nihil, or strictly and abfolutely nothing. If the doubt of the existence of an increment under fuch circumstances be deemed incredulity and a species of infidelity, I am afraid I fhall be ftigmatized with thofe appellations; for I confefs it is paft my comprehenfion how a mere point can contain in itself an infinite variety of magnitudes, and which are all at the fame time equal to one another. The unneceffary quibbles, and metaphyfical niceties, by which fome have attempted to explain the principles of fluxions, have not only rendered them quite obfcure to the learner, but also exposed them to the ridicule and severe criticifms, it is probable, were not intended to invalidate the method of fluxions (which it is evident may be strictly mathematically demonftrated) but to fhew the futility of the method they had taken to elucidate the principles; in which light it is well known the incomparable inventor never intended they should be viewed.

From what has been faid we may draw these practical obfervations. 1. That the common rule for finding the fluxion of a flowing quantity, viz. Multiply the fuxion of the root by the exponent of the power and the affixed coefficient, and the product by that power of the fame root of which the exponent is lefs by unity than the given exponent, is general, and without exceptions, being applicable to any expreffion whatever confifting of one variable quantity with a conftant exponent. 2. If the expreffion be a compound one, that is a binomial, trinomial, or any multinomial, the fluxion of each term must be found separately, and connected with their respective refulting figns; the fum arifing by fuch addition is the fluxion of the compound expreffion. 3. If the expreffion confifts of the product of two or more variable quantities, each quantity muft flow feparately, while the others are fuppofed to be conftant, or as coefficients to that variable quantity; the fum of thefe ftuxions will be that of the given expreffion. This follows from the general expreffion, nxIx. Thus, let the fluxion of be proposed to be investigated. Put y+zv, then willy2+2yx +z; hence yz= ={v2—{y2—{x2. And, from

2

what has been before fhewn, the fluxion of this will be vi-y-zż; but vy+, and +,.. by fubftitution, the fluxion of yz is yż + zy. And in the fame manner will the fluxion of xyz be found to be xxxzx; and that of uxyz=uxyx + uxzỷ + uxzx + xyzú;

&c."

See Colfon's Newton's Flux. p. 18, Preface.

Our

Our author proceeds to illuftrate these obfervations, by examples; but we have alreany extended this article to a greater length, than we ufually allow to elementary tracts of this

kind.

W.

The English Garden: a Poem. Book the First and Second. By W. Mafon, M. A. 4to. 5s. Cadell.

As it were fuperfluous, if not impertinent, to make any reflections on the poetical abilities of a writer, fo well known to the public as Mr. Mason, we shall confine ourselves, on the prefent occafion. to the giving our readers a fpecimen or two of his intimacy with the didactic mufe: in whofe placid province his talents appear well adapted to difplay themselves to advantage. In doing this, however, we hope not to incur his indignation fo far as to induce him to commence à profecution against us for piracy; as we have no intention in the leaft to injure his property by preventing the fale of his poem. The terrible threat, indeed, which he hath hung up in terrorem, by way of advertisement, oppofite the title page of the fecond book, might make us hefitate a little in our choice of fuch fpecimen, could we be perfuaded Mr. M. is fo litigious or avaricious, as he has been reprefented by a certain profecuted bookfeller. Looking upon the quotation we fhould make, as matter of property; we fhould, in order to do the least injuftice to him poffible, felect fome of the very worst paffages in his poem, as being of the leaft value. And yet, if we did this, it is ten to one if he did not complain of our doing both him and his poem injuftice. On the other hand, if we should felect the best paffages, fhould we not do him greater injustice by robbing him, as he might call it, of the most valuable part of his poem?-The matter is intricate; and we would advise Mr. M. to let his counsel make a cafe of it, and submit it to higher opinion. In the mean time noftro periculo we shall proceed impartially to felect neither the best nor the worst parts of his poem, to do as much juftice and as little injuftice both to Mr. M. and our readers as poffible.

The poet has thought no other apology for the choice of his fubject, neceffary, than the following paffage from Lord

Verulam.

"A garden is the pureft of human pleasures, it is the greatest refreshment to the spirits of man: without which, buildings and palaces

See Mr. Murray's letter to Mr. Mason, in our laft Review.

are

are but grofs handy-works. And a man fhall ever fee, that when ages grow to civility and elegancy, men come to build ftately, fooner than to garden finely as if gardening were the greater perfection."

:

The poem opens with an address to Simplicity.
"To thee, divine Simplicity! to thee,
Beft arbitress of what is good and fair,
This verse belongs. O, as it freely flows,
Give it thy powers of pleafing: elfe in vain
It strives to teach the rules, from Nature drawn,
Which all should follow, if they wish to add
To Nature's careless graces; loveliest then,
When, o'er her form, thy easy skill has taught
The robe of Spring in ampler folds to flow.
Hafte Goddess! to the woods, the lawns, the vales;
That lie in rude luxuriance, and but wait
Thy call to bloom and beauty. I meanwhile,
Attendant on thy ftate ferene, will mark
Its faery progrefs; wake th' accordant string;
And tell how far, beyond the tranfient glare
Of fickle fashion, or of formal art,

Thy flowery works with charm perennial please."

The poet then proceeds to apoftrophize the Mufes and deelare the motive of his verfe; pathetically lamenting the cause.

"Ye too, ye fifter Powers! that, at my birth,
Aufpicious fmil'd; and o'er my cradle drop'd
Those magic feeds of Fancy, which produce
A Poet's feeling, and a Painter's eye,
Come to your votary's aid. For well ye know
How foon my infant accents lifp'd the rhyme,
How foon my hands the mimic colours spread,
And vainly hop'd to snatch a double wreath
From Fame's unfading laurel: arduous aim;
Yet not inglorious; nor perchance devoid
Of fruitful ufe to this fair argument;

If fo, with lenient fmiles, ye deign to chear,
At this fad hour, my defolated foul.

*

For deem not ye that I refume the lyre

To court the world's applaufe: my years mature
Have learn'd to flight the toy. No, 'tis to footh
That agony of heart, which they alone,

Who beft have lov'd, who best have been belov'd,
Can feel, or pity; fympathy fevere !
Which the too felt, when on her pallid lip
The laft farewell hung trembling, and bespoke

This poem was begun in the year 1767, not long after the death of the

amiable perfon here mentioned.

A

A wish to linger here, and bless the arms
She left for heaven. She died, and heaven is hers!
Be mine, the penfive folitary balm

That recollection yields. Yes, Angel pure!
While Memory holds her feat, thy image ftill
Shall reign, fhall triumph there; and when, as now,
Imagination forms a Nymph divine

To lead the fluent ftrain; thy modeft blush,
Thy mild demeanor, thy unpractis'd smile
Shall grace that Nymph, and fweet Simplicity

Be drefs'd (Ah meek MARIA!) in thy charms."

On the improvements and improvers of Gardening in
England, the Poet makes the following poetical encomiums.
"O how unlike the scene my fancy forms,
Did Folly, heretofore, with Wealth confpire
To plan that formal, dull, disjointed fcene,
Which once was called a Garden. Britain ftill
Bears on her breast full many a hideous wound
Given by the cruel pair, when, borrowing aid
From geometric fkill, they vainly ftrove
By line, by plummet, and unfeeling sheers,
To form with verdure what the builder form'd
With stone. Egregious madnefs; yet purfu'd
With pains unwearied, with expence unfumm'd,
And science doating. Hence the fidelong walls
Of fhaven yew; the holly's prickly arms
Trimm'd into high arcades; the tonfile box
Wove, in mofaic mode of many a curl,
Around the figur'd carpet of the lawn.
Hence too deformities of harder cure:
The terras mound uplifted; the long line
Deep delv'd of flat canal; and all that toil,
Mifled by taftelefs fashion, could atchieve
To mar fair Nature's lineaments divine.

"Long was the night of error, nor difpell'd
By Him that rofe at learning's earliest dawn,
Prophet of unborn Science. On thy realm,
Philofophy! his fovereign luftre spread,

Yet did he deign to light with cafual glance
The wilds of tafte. Yes, fagest VERULAM,
'Twas thine to banish from the royal groves
Each childish vanity of crifped knot
And fculptor'd foliage; to the lawn restore
Its ample space, and bid it feast the fight
With verdure pure, unbroken, unabridg'd;
For green is to the eye, what to the ear
Is harmony, or to the smell the rofe.

"So taught the Sage, taught a degenerate reign
What in Eliza's golden day was tafte.
Not but the mode of that romantic age,

The