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red sandstone to appear at the water's edge ; but about the whirlpool, and especially opposite the Old Mill, the brown, black, grey, and red stripes in the mural precipice point out, in a clear manner, the size and relative position of its component strata. They are also well seen on the east side of Queenston Gorge, where, particularly, the saliferous shale comes into view, and supports the villages of Queenston and Lewiston, in abraded banks, eighty feet high.
The grey sandstone is a grey or greyish white aggregate of uncemented grains of quartz, here and there spotted with ironrust. It is in very thick strata, and is best seen in the face of the heights close to Queenston, where it is quarried. Mr. Eaton found it to be fourteen feet thick here, and in the river Genesee. It contains no fossils.
This rock is hard, breaking into thick, shapeless, or squared blocks. “ In some places, it alternates with the red rock below; but generally they are separated by a continuous layer, or extensive bed of argillaceous iron ore,” (Survey, p. 120,) as at Niagara, according to Mr. Eaton. The red argillaceous sandstone beneath this rock is very shaly. It is often soft and almost homogeneous; but frequently, in the contiguous layers, it is harsh and granular. It is about twentythree feet thick, (Survey, p. 121 ;) its colour is principally red, variegated in clouds, spots, and circlets, with green and blue colours, which occasionally occupy considerable thicknesses of the shale. It is extremely ferruginous, both as disseminated generally, and in bluish-black knots, with a semi-metallie lustre. It contains terebratulæ, both large and small; and a fossil which resembles somewhat the orthocera annulata of Sowerby; but it varies from it in being much more narrow, in having its sides compressed into a quadrilateral form, and in being traversed by minute and numerous ridges. Casts of shells, apparently unios, in red sandstone, are common. The calcareo-argillaceous sandstone, occurring next, evidently belongs to the saliferous formation, like a similar stratum at Runcorn and Manley, in Cheshire.--Geol. of England, Coneyb, and Phill., p. 280. It is here a moderately hard granular rock, chiefly of quartzose materials. It is white, chequered with flakes of green. It is thin, but is continuous
on the east for 200 to 250 miles. It is only eight feet thick. here. It contains exquisitely fine lingulæ mytiloides, in which the original shell is beautifully preserved. There also are many thick white casts of shells, of the unio family. The variety of orthocera, above noticed, is also found here in white. casts. The two latter, and the terebratulæ of the red sandstone, are found near Grimsby.
The red saliferous rock, principally argillaceous, occupies the lower seventy or eighty feet of the Gorge of Queenston, and extends a considerable distance into the expanded river below. Its mineralogical characters are quite the same as at Salina, on the south of Ontario; and as at St. Catharine's and at Saltfleet, near the head of that lake. At all these!' places, its geological relations are the same. At the two latter, it appears at the foot of the “ Parallel Ridge,” which is · composed of the same materials as in the chasm.
This rock presents no peculiar characters on the river: Niagara. It has been most fully studied by Mr. Eaton on the borders of Lake Ontario. I therefore refer the reader to its description in the paper on Lake Ontario, where the Saltworks of St. Catharine’s and Saltfleet will be more appropriately introduced than here,
JOHN J. BIGSBY,
On the Relation between the Density, Pressure, and Tema
perature of Air ; and on Experiments regarding the Theory of Clouds, Rain, &c.; with a Conjecture about Thunder and Lightning. By Henry Meikle, Esq.
[Communicated by the Author.] Few things, I presume, would tend more to facilitate and promote the study of pneumatical and meteorological science than an acquaintance with the relation between the density, pressure, and temperature of air. Preparatory, therefore, to entering on the consideration of some meteorological phenomena, I submit the following attempt towards investigating that relation.
1. It was inferred from Boyle's experiments, and subse.
quently confirmed by others, that, under the same temperature, the elasticity or pressure of air is as its density, or inversely as its volume ; and, consequently, while air undergoes the same change of temperature, its volume varies under a constant pressure, precisely in the same proportion as the pressure would do, were the air confined in an inextensible vessel.
2. Mr. Dalton, M. Gay Lussac, &c. have ascertained, that on heating air, under a constant pressure, from 32. F. to 2129 its bulk acquires an increase of three-eighths. Such increase in the air-thermometer is divided into 180 equal parts, or degrees, for Fahrenheit's scale; and the like divisions, corresponding to equal variations of bulk, are continued both above 2129 and below 32o. Now, as three-eighths to 180°, so is the whole bulk at the freezing point to 480°; and, therefore, there cannot be more than 480 degrees below 32° on the Fahrenheit scale of an air-thermometer; for by taking 480 such equal parts from the bulk, the whole would be exhausted *.
3. The freezing point being marked 32°, it is obvious that 480° below this will be at — 448°. The bulk of a given mass of air, therefore, under a constant pressure, varies as its temperature reckoned from -448°, according to the common graduation ; that is, as 448° +t. The degree indicated on Fahrenheit's scale being t. Hence, by art. 1, the pressure of air confined in an inextensible vessel likewise varies as 448° +t.
4. It has been more recently found, that, whilst air undergoes the same alteration of temperature, the change in its quantity of heat is one-third greater under a constant pressure than if confined in an inextensible vesselt; also, when the
* Hence, unless we make the incomprehensible supposition, that air may contract by cooling, till its volume be less than nothing, the absolute zero, if such a thing exist, cannot be lower than-448° F., with reference to the common graduation of an air thermometer; no matter what relation the degrees bear to true ones. But however clear this may be to most people, Mr. Ivory's new law of condensation and rarefaction, to be shortly noticed, recognises no such limitation; but readily produces a cold of thousands of degrees below the impassable limit of that very scale which he maintains to be the true one. In short, his law is fraught with contradiction, view it which way we may. This shews the propriety of examining and trying the consistency of everything, even though it should have issued from an oracle.
oft Omitting this property, all that is contained in the first six articles would hold, without regard to the nature of heat, provided the experiments, especially those to be after noticed, be correct.
density of air suffers a minute and sudden change, such variation of density is to the whole density as three-fourths of the accompanying variation of pressure to the whole pressure; or, p being the density and
р 3 Consequently, one-fourth of the minute variation of pressure must be due to change of temperature; for (art. 1) when the temperature is constant, the pressure varies exactly as the density; and hence because (art. 3) p varies as 448° +t for temperature, we have
448° + 4p 3p 5. The equation
P P evidently expresses the relation between the fluxions of the logarithms of the pressure and density of air, when its quantity of heat is constant. The fluent is
3 log: p=4 log: p+C; and if p' and ø be put for the initial values of p and
Po C=3 log: p'-4 log. p, and
3 log. ?=4 log:,; or
3 = which is the relation between the pressure and density of air, when its quantity of heat is invariable ; viz., that the cube of the pressure varies as the fourth power of the density. 6. Also, by integrating the equation
445°+t 3p and putting ť for the initial temperature, we get 448°+t
; or, t-ť=( 448° +ť 448° + t'
for the change of temperature on the common scale solely due to change of density *. Neither this conclusion, nor that
In the seventh Number of the Quarterly Journal of Science, 1 adduced a few examples to shew what an incoherent rule Mr. Ivory had given for estimating the change of temperature in air due to a change of
which terminates article 5, necessarily depend on any theory of heat,
7. If the areas which the curves ABC and DEF intercept from the straight line GH, between the same perpendiculars to GH, be everywhere to each other as 4 to 3; and, G being a fixed point, if every three perpendiculars ADH, BEI, CFK,
GI which make
likewise make area BIHA=
GH FKHD, the curves are hyperbolas.
For if not, with G as a centre, and GH as an asymptote, describe two rectangular hyperbolas, abc, dEf, cutting AH and CK in a, d, c, f. Then all the ordinates of either hyperbola being, as is well known, inversely proportional to their distances from G, the corresponding ordinates of the two hyperbolas are everywhere to each other as BI: EI :: 4:3;
its density, and how directly it is opposed to observation. This I instanced, both so far as regards the inconsistency of the results when we revert the process, and likewise when we compare the change of temperature computed at one operation with what it would be, if computed by the same rule, supposing the whole change of density to take place by successive steps. At present, I only beg to call the reader's particular notice to the circumstance, that the smaller these successive variations of density are assumed, the nearer will the aggregate results or changes of temperature, obtained by the continued application of Mr. Ivory's theorem, approach to perfect consisteney ; whether among themselves, or when we retrace our steps by reversing the proeess. Now such continued summation of minute variations of temperature being similar to integration, shews that Mr. Ivory's error consists in his using the fluxion of the time as its fluent; or at least in assuming the fluent to be proportional to, or a mere multiple of the fluxion. Thus t-t being the change of temperature caused by e- the change of density, if we take these changes as differentials, Mr. Ivory's theorem, viz.
$-s', becomes tt= 4480+x
dt 3 de
448o+t which, with the exception of the constant for }, is just the fluxion we had in art. 6; and therefore the integration gives
- 1 a self-consistent result, but as different from Mr. Ivory's new law of condensation as light from darkness. The notation in my paper
above quoted only differs from this, in that I there used i and unit, in place of tết and;' here