would tell us, that as their lives are more expofed than others to fudden death, they ought of all men to be the moft ferious. It is fimilar with Sailors and Coal-diggers. How ftrange! That thofe who are expos'd to the greatest dangers, are the most profane. Yet the caufe is evident.

Cuftom, like all other things, if well-ufed is a bleffing; if ill used a curfe. When it is once become cuftomary for us to gratify our evil propenfities, vice then enflaves us moft abominably. And we are apt to forget, that by even one evil action, we may render both ourselves and friends completely miferable. It is certainly true, that it is more eafy to do evil than good; and it has been remarked, that the opportunity to do hurt, happens every day, but to do good only once in 365. Let us be careful to commence a virtuous conduct, and tho' it be un, pleasant at first, yet custom will foon make it a path highly delightful to walk in.

SUNDERLAND.

E. WILSON.

To the Author of the RANDOM SHOT,

SIR,

HAVING been lately in the Neighbourhood of

Yarm, I have endeavoured to find fome authentic Defcription of it in Hiftory, but without Snccefs. I therefore am tempted to take up my Pen and celebrate this hitherto ill-defcribed Place.

It is fituated on the Southern bank of the Tees in a part which is nearly a peninfula, and has been long celebrated for the falubrity of its air and the Wholefom nefs of its Water. The Inhabitants were formerly very fubject to the Hydrophobia; but by fome

judicious

judicious alterations in their bridge, that dreadful diforder is not now fo prevalent there. The Lions,* which are so neceffary a fhew in every place are here feldom to be feen: as there is nothing but "Our October-fair of which the Inhabitants are vain,. and that happening only once a Year, its Vifitors at other Times are o to be contented with a defcription. To this is generally added, a History of our firft Flood in 53, and our great Flood in 71, with an Epifode of the Pig who floated down the Tees in a Wheelbarrow, and an interlude of the famous horfe Traveller, who was taken by his Owner into a Chamber at our firft Flood," and who nearly demolished a large looking-glafs in his attempts to fight an imaginary Rival.

The hofpitality and generofity of the Inhabitants they leave to be celebrated by other Tongues and Pens. To my Lot it has fallen to mention what the Ingratitude of other Vifitants would bury in Oblivion. Dear neglected Town! had 1 the Pen of a Sterne, I would make thy Merits defcend to future Ages! May thy Inhabitants accept the Will for the Deed! and receive this as a Teftimony of Gratitude of

Yours, &c.

VIATOR.

By the Lions, are generally underfood thofe Sights which the Inbabitants of any Place think worthy the Notice of Strangers. At London the Lions in the Tower, are a grand Object; at Grantham, the Steeple; at York, the Minfter; and at Yarm, “our October fair.

"

Queries

QUERIES ANSWERED.

с

XXXVI. Answered by Mr. W. PASSMAN, Billingham. THE ftrength of a beam of timber is caufed by the adhesion of its longitudinal fibres; and this adhesion is more or lefs, in different Sections (the Area of each Section being the fame) in proportion to the distance of the point a from AB-the point a being that where all the fibres are fuppofed to be collected. Fletcher, on page 192, in his Univerfal Measurer, or that Book Mr. Ward calls Fletcher's Mechanics, fays that the rectangle of the diftances of the centres of Gravity and Percuffion or Ofcillation from AB, or G (if the beam be fixed at one end) divided by the depth (GC) will give that point a where all the fibres being collected do act with their whole ftrength. He alfo fays that if the diftance G a be multiplied by the Area of the section, the product will be the total firength of that Section. This rule is the very fame as that which I cited from Emerson, in my fecond answer to the 18th Queftion. Now, from what has been faid it appears very evident, that, if by taking the part ECF away, the point a be removed to b; and that if the product of the diftance (Gb) and the area AEFB, exceed the product of the diftance Ga, and the area ABC, the part must be fronger than the qubele.

A

L G M B

On the 286 page of the EEE, I have proved that the diftance of the Centres of Gravity and Ofcillation, in the remaining Section AEFB,

from G, or AB is refpectively

11 b

48 b

8 b

which multiplied by 34 64088, the area of the remaining fection, gives

48, the ftrength of that fection, or of the reduced Beam; and

b

b

3

-Ga=1'29903; which multiplied by 35'0739, the Area

* Maclaurin's New fin, Pago 170.

of

of the whole section, gives 45,5605, the ftrength of the whole section, of the beam when whole-`

Having, I think, fufficiently exemplified Fletcher's, or rather Emerfon's Rule, which, I am convinced, from a strict investigation is as true as the 47. 1 of Euclid. I fhall proceed to examine Mr. Ward's Solution to his Query, and his antwer to the 18 Queftion, by it, and that invaluable Rule which Emerfon, has given on the 344 page of his Fluxions.

On the theoretic part of Mr. Ward's anfwer to his Query. I difdain to make any comment, being certain that every friend to demonftrative feience will look with proper indignation upon principles, which the Author himself tells us "Cannot be frictly taken for truth." (Biz, P. 355-) That three lines, out of more than forty, in my folutions, are fimilar to three lines in Emerfon's Fluxions, I readily allow, which I thought better to infert, prefuming the BEI might fall into fome hands that had not Emerfon's Work; and as I quoted the very page where thefe lines are, I had not the most diftant idea of being thought a Plagiary: and as finding the ftrength of a triangular fection is much eafier than that of a Trapezoid. I cannot help thinking that Mr. Ward only mentioned my having availed myself of Emerfon's example to divert the attention of his

readers.

Mr. Ward next tells us that Mr. Fletcher, in his Mechanics, give one fourth of the breadth into the fquare of the depth, &, and this made," &c.; but he omits to take any notice of the pofition of Fletcher's team. Fletcher undoubtedly makes the A total Arength of a fection, in the form of a triangle, and common parabola, respectively

2662

7

G

(ABb, and CG = b)

H

But then the vertex of the triangle and common parabola is at C, as the annexed figure reprefents; in which position the triangular "fection is thrice as ftrong as if the vertex were at G, and AB the axis of fracture, as it is in the Paradox.

To prove that Fletcher's beam is in this pofition we will try how the refult of a procefs or twe, by his Rule, mentioned before, agrees with the above quotations.

By Simpfon's Fluxions, page 205, the diftance of the Centre of Gra

26

vity of the triangle ABC from C; and, ibid, page 221, the dif

3.

tance

B

36

tance of the centre of Percuffion or Ofcillation from C

in Fletcher; alfo the fame as Emerfon makes it, vide his Fluxions, page 345, and his Mechanics, page 107. Had the vertex been at G, the ftrength

pendix; and the diftance of the centre of Ofcillation from C =

1

45

7

Let ABC be the common Parabola, AB = b, GC = b, CH⇒

and ED y; then by the nature of the Curvey b

per Emerfon's Fluxions, page 344, the Auent of

or the

the parabolic fection, when the vertex is at C, the fame as found abort. If the vertex C be at D, let HC=x, and HG =

then,

16 b ba
105

x b2 - 2 bx + x x = ---the total ftrength of the section

when the vertex is at D, precifely the fame as above.