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Meteot Reaumur at the same time sinking only 10:6. The se- watery store, the moisture precipitated would cover the

ology. okupio cond observation, it should be remarked, was made in the surface of the earth only to the small depth of 7} midst of the glacier of Hautema, and it is therefore pro- inches, and in the mean parallel of 45° only about 3}

Depth of bable the ice and snow with which it was covered sup- inches. Supposing the whole atmosphere, from a water if si by sure" plied this extraordinary humidity. And this opinion is state of absolute dampness, were to discharge its entire atmosphere confirmed by another observation which he made on a watery store, it would only form an uniform sheet of were to dis

charge its projecting rock seven toises less elevated, and where about 44 inches in depth. To furnish a sufficient supply he found the humidity 14°7 less than at the lowest of rain therefore, as Leslie remarks, it was necessary the

watery station, agreeing, therefore, with the general principle air should undergo very frequent changes from dryness store. before advanced. In another observation, however, to humidity in the course of the year. Supposing the Saussure is not disposed to attribute all this difference mean quantity of water existing in a state of vapour in to the ice. Another example is also given by the same an atmospheric column, having a square inch for its indefatigable and accurate observer. In the middle of base, to amount to about 4 cubic inches, we may infer, the glacier of Miage, his hygrometer indicated a hu- that the quantity actually existing in the whole atmomidity of 81o.1, but on the Col de la Seigne, 186 toises sphere amounts to about 12,500 cubic miles. above the glacier, it indicated 100°, though the decre- (455.) Such results, however, must be truly regarded Such con

ment of temperature 30.3 according to Saussure's table, as approximations, and adopted only to enable us to clusions, Tiger ought to have indicated only a humidity of 89°.9. It catch a glimpse of the mysterious phenomena of Na- however, set.bas sometimes happens, therefore, that vapour is more ture. We know too little of the humidity of the lower

truly remert abu-abundant on the summit of a hill than in the valleys at regions of the atmosphere, to speak with certainty of garded as act on the

its base; but as the exceptions are not numerous, and any of the phenomena connected with the higher. We approximen in the may be explained by the influence of peculiar loca- know too little of the phenomena which may be said to mations. zig ben lities, we may in general conclude, that the absolute be continually within our grasp, to permit us, without

quantity of vapour in the air diminishes as we ascend. the exercise of the greatest caution, to apply them even It should be borne in mind in considering this part of as humble approximations to those lofty regions of the the subject, that the anomalies we have before proved to air, which as yet have defied the aspiring

ambition of exist in the temperature of the air at different elevations, Of this, however, we are certain, that the higher must necessarily impart a like irregularity to its humi- regions of the atmosphere are comparatively drier than dity.

those below. Colonel Beaufoy, in his interesting ascent (454.) It would be possible to compute approxima- of Mont Blanc, remarks, “ that the air itself was thirsty, a tiem tively the actual weight of vapour contained in any of its extreme dryness," said he,“ had robbed my body of

the atmospheric columns, and if necessary the whole its moisture." und quantity of moisture contained in the atmosphere. The (456.) The vapour actually existing at any time in Moisture stre com experiments of Biot and Arago have determined that the air is far however from being equally distributed in not equally 23, and the weights of equal volumes of vapour and air at the those volumes of it which possess the same degree of


in volumes temperature of the boiling point, and when both are temperature. A given volume of it, at the temperature of same subject to the same pressure of .76 metres, are as of 50°, in a portion of the atmospheric column reared

tempera-589481 to .9454476, or as 5 to 8 nearly; and since above Plymouth, may possess a very different degree of ture. both are affected in their bulk in the same manner, by humidity from a volume of a like temperature above Case of every alteration of temperature and pressure, the same Prague. The former, from its peculiar locality, may be Plymouth invariable relation may be supposed to be preserved, in a state of high saturation, whereas the other, in the and Prague. so long as the vapour retains its elastic form. In heart of a great continent, and governed by a wind from some inquiries of this sort it has been assumed, that a different quarter, may be comparatively dry. It is the mean point of deposition for the globe in general, not equality of temperature alone that we must seek for, is about 6° below the average temperature, -though in applying practically the elements of the problem now this assumption, from the limited nature of the obser- under review, but the quantity of moisture coexisting vations from which it is deduced, cannot be received with it. To-day, the air of Moscow may afford a greater Moscow without caution; and if we adopt in addition another proportion of moisture than the warmer atmosphere of and Ispahypothesis, by supposing the same invariable difference Ispahan, and to-morrow the relation may be entirely han. of temperature to be maintained, throughout all the reversed. Contending winds not only influence the atmospheric strata, we may make an approximation to temperature and pressure of the air, but its humidity the whole quantity of moisture contained in the atmo- also; and the peasant of our own country is familiarized spheric columns, by means of the formula

with their different effects, One breeze may bring to
5 407.4

him gentle and fertilizing showers, and another may

burn up the produce of his farm.

(457.) But we need not go to the atmospheric Different wherein f denotes the elastic force of vapour at a tem. columns of different countries to seek for diversities of quantities perature six degrees below the mean temperature of the moisture, since like anomalies are sometimes to be found of moisture place of observation, and the numerator 407.4 the

in same at in different strata of the same column. Saussure reheight in inches of a column of water equivalent in

mospheric marked that his hygrometer, near the surface of the

column. weight to the mean condition of a corresponding earth, often proved the air to be removed 30 or 40 column of the air, and the numerical value of which degrees from extreme saturation, when the presence of formula, will give the mean height in inches of a column clouds in the upper sky demonstrated the entire humiof water, equal to the whole moisture contained in a dity of that region. That eminent observer often re- Effects of column of the atmosphere, standing on the same base. marked this phenomenon when he ascended a mountain clouds. In this way we may compute, that if the atmospheric whose summit was enveloped in a cloud. On the other Of mists. columns at the Equator were to discharge their whole hand he as frequently observed, that when mists covered

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the humi.

know re

as we

Meteor- the plains, and a bright sun gilded the summits of his perhaps from the mean results lines of equal humi- Meteor. ology. noble mountains, the limit of extreme humidity was to dity.

be found below, and air far removed from saturation (460.) It is a great practical problem therefore now
above. Bands of clouds were sometimes also found to ' opened to the ardent enterprise of Meteorologists, to


respecting swim between masses of air necessarily less humid than discover, if possible—and what will not united labour Actual the clouds themselves, Of the effects of clouds in and Philosophical enterprise effect,—some accurate rela- dity of the example of humidity of

augmenting the humidity of the atmosphere, he has tions respecting the distribution of moisture; to trace atmosphere a cloud.

one conclusive observation. When on the summit of some of the varying conditions of humidity, which, for
Mont Brevan, 1306 toises above the sea, his hygro- ever working in the great aerial volume around, is one
meier, at a moment when the sky was free from clouds, of the main springs of the uncertain motions of the air,
indicated a degree of moisture corresponding to 86'.8; and of those changes of the weather, which are not only
but when the summit of the mountain was soon after so much blended with our personal health and comfort,

enveloped in a cloud, the humidity increased to 949.6. but with all the important processes of agriculture. At What we Elastic (458.) Mr. Daniell has also deduced, both from the present moment we can do little more than say, present force of theory and the actual experiments of Captain Sabine, that of this wide-spreading ocean of vapour, we can vapour that the elasticity of vapour does not diminish in an merely estimate its elastic force and quantity at a given humidity

specting the dues not diminish

uniform manner, according to the decrease of tempera- time, and in a general way trace an analogy between of the atuniformly ture and density of the air, but the dew.point re- the course of its changes, and the progress of the mean mosphere.

mains stationary to a great height, and then suddenly temperature of the year. We know not where to look for Not able ! ascend. falls to a large amount. At Sierra Leone, the dew- the data which will enable us to contrast Philosophically contrast t) point at the level of the sea was found to be 70', and at the humidity of different climates, to measure the influ- humidity

different the same hour upon the summit of the Sugar Loaf ence of mountains and valleys in modifying the condi.

climates. mountain, 2520 feet above, it was found exactly the tions of vapour, the sea which exercises its own peculiar Examples. same. At Jamaica also, by the sea-side, the tempera. laws, and the islands and continents which diversify in

ture of the air was 80°, and the point of deposition 73° ; so great a degree all the phenomena of humidity.
while on the mountains, at an elevation of 4080 feet, (461.) It is a useful problem, unquestionably, to deter- Connectic
they were both 68o.5. At a station not 500 feet higher, mine the mean temperature of a place; but it is a pro- of the bar
by an experiment twice repeated, the point of deposition blem of no less interest to discover its mean humidity. dity of the
was found to be 49°, and the temperature of the air 65°. In Great Britain the winds which transport the vapour


with land Mr. Green the aeronaut also found, when ascending may be divided generally into two classes: the land and sea from Portsea, that at an elevation of 9890 feet, the dew- winds blowing from off the great continent of Europe, winds. point was 64°, the same as at the surface of the earth; and which comprise the North-East, East, and Southbut at 11,060 feet it fell to 32°, making a difference of East ; and the sea winds passing over the waters which thirty-two degrees in a little more than 1100 feet; surround us on every side, the North, North-West, affording a decisive example, as Mr. Daniell observes, West, South-West and South. In the former we might of an immense bed of vapour rising in its circumambient expect to find the course of the mean temperature inedium, unaffected by decrease of density or tempera- exactly followed, because the sources which supply the ture, till checked by its point of precipitation; and also vapour must be comparatively shallow streams and re

of an incumbent bed of not much more than one-third servoirs of water, whose temperature readily adapts Proofs the density, regulated, no doubt, as the last, by its itself to that of the surrounding air; but in the unwhich they owu point of deposition in loftier regions. Such pheno. fathomable depths of the great ocean which affords afford of the mena afford strong experimental evidence of the mecha- humidity to the latter, the peculiar law by which the mechanical mixture of

nical mixture of the aqueous particles in the atmosphere, density of water is governed, must at particular periods vapour with and admit of no explanation by any law analogous to maintain a temperature above that of the declining seaair. that of chemical solution.

son, whilst at others, the increasing heat of the latter Want of (459.) We have before lamented the want of correct must outstrip the progress of the former. practical observations to assist us in our inquiries respecting tem- (462.) Here then is a single problem, the elements observa

perature; and with equal reason may we deplore the ab- of which must vary with every locality. Swisserland, tions.

sence of accurate and extended results to illustrate the surrounded on all sides by mountains, must present
much more varied conditions of humidity. The ther- different phenomena from Great Britain, surrounded on
mometer has existed for a long period in an accurate all sides by the sea. For London, Mr. Danieli has Mr. Da-
form to assist the Philosopher in every inquiry respect- found that the vapour of the land winds declines in force niell's ol
ing heat, but an hygrometer which should disclose the from September to January, when it reaches its mini- serratio
absolute circumstances of atmospheric vapour has been mum, and from that lowest point gradually rises to a of the
but recently known. Mr. Daniell's beautiful instru- maximum in August, thus following the course of the peculiar
ment, and which we shall hereafter describe, enables us mean temperature of the air. In the sea winds, how- winds to
to trace with the greatest exactness all the conditions of ever, the vapour declines from September to November,

humidity; but the limited observations hitherto made when an equality appears nearly to take place in the
with it, afford but little information respecting that ge- humidity of the two winds ; but in December, the vapour
neral distribution of vapour, which we are here de- from the land descends below that of the sea, and the
sirous of tracing. As the observations made by the same difference continues to January. In February the
thermometer have enabled us to trace the numberless former rises two degrees, and the latter remains sta-
aberrations of temperature, and to distribute them in tionary. A difference of four degrees continues through

isothermal lines, so, had this hygrometer existed a cen- March, and which is diminished to three degrees Lines of tury ago and been diligently applied, might we have in April and May. In June they again attain equal hus

traced some of the singular mutations of the great their former equality, because the temperature corremidity.

ocean of vapour which surrounds us, and have deduced sponding to the maximum density, caunot be lowered

N.E. E. S.E.

N. N.W.W. S.W. S.






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Metedre till the whole mass of waters has passed this limit; and By attending to the results of this Table we may first Meteor clogy in the deep seas this must necessarily be a process of observe a constant difference of the temperature of the ology.

some duration. The shallow waters on the contrary, Dew point to prevail from September to December, in
over which the land winds pass, must soon acquire the the two classes of winds; but the Dew point belonging to
temperature of the ambient air, and continue to decline the Northerly winds, having reached that of the freezing
with it in heat. Upon the return of Spring a contrary point in the last-mentioned month, continues nearly
effect takes place. The Ocean must again repass the uniformly to preserve the same temperature, during the
temperature corresponding to the maximum density, succeeding months of January, February, and March,
before the waters can again obtain the higher tempera- while in the Southerly winds, the declension continues
ture of the surrounding air. A necessary consequence through January and February only. In March the
of such an arrangement of things must be, an increase Southerly winds impart an increment of six degrees,
of humidity in December and January, and a rapid dimi- but the increase of the Dew point of the Northerly
nution in the four succeeding months, a phenomenon winds does not take place till April, when the addition
found to agree with actual observation. Such is the it receives, amounts to eight degrees, at which point
contrast exhibited by the prevailing land and sea winds it continues with little variation through the whole
peculiar to London. How very different would be the month of May, the absorption of heat during the pro-
phenomena of the winds peculiar to Moscow !

cess of thawing, preventing that accession of tempera-
The numerical results from which Mr. Daniell has ture which is due to the returning influence of the Sun.
deduced these interesting conclusions are exhibited in As soon as this operation, however, has ceased, the
the following Table.

vapour rapidly regains its former relative degree of

force, imparting considerable increments to both classes Table XCVII.

of winds in June and July, until their maximum conOf the Difference of the Dew Point in the Land and ditions are obtained in August

, and are followed of Sea Winds.

course by a decline of both in September.

(464.) We must now take a hasty glance at the Mean reLand Winds. Sea Winds.

few imperfect results we are able to offer respecting the sults of dise Months.

distribution of aqueous vapour during the successive tribution of September


seasons of the year, still, of necessity, limiting our inquiries aqueous
October ..

vapour in to the locality of London.

successive November 41

: Beginning with January, the time at which the minimum seasons of December


temperature prevails, Mr Daniell found, from a mean of the year for January


three years' observations, and a triple observation each London. February


day, the mean elastic force of the vaporous atmosphere

to be also at its lowest point, and represented by, 0.234


inches of quicksilver, the mean temperature being at the


same time 36°.1. As the mean temperature advances


through the month of February to 38°, the force of


vapour increases feebly to 0.239 inches. With the


month of March, however, the mean temperature is Lesce CH (463.) The peculiar locality of Great Britain may augmented nearly six degrees, the elastic force of the w Polare also be supposed in another way to modify the vapour advancing at the same time to .272 inches. In

the kimidts of

production of vapour, by its having to the North, at April the mean temperature of the air rises to 490.9,
one season of the year, enormous masses of ice, which and the elastic force of vapour to.322 inches. In May,
during their formation evolve caloric, and, in the pro- the atmospheric temperature still ontstrips the advance
cess of liquefaction, occasion its absorption. Dividing of vapour, the former amounting to 54°, and the latter
the winds into two classes, Northerly and Southerly, Mr. to .354 inches, the air having then nearly attained its
Daniell has been enabled to trace their effects on the greatest state of dryness. During the month of June
moisture of the air, as given in the succeeding Table.

the advance of the mean temperature and humidity are

nearly uniform, the former being 58o.7, and the force of TABLE XCVIII.

vapour .410 inches. Through July, the moisture ang

ments with rather greater rapidity than the temperaOf the Effect of the Ice in the North Seas upon the

ture, the elastic force being .468 inches, and the mean
Dew Point.

temperature 61°. In August, these phenomena continue

nearly the same, the force of vapour being .481 inches,

and the mean temperature 61°.6. During September, September


the reduction of temperature is first felt sensibly, its


mean sinking to 57°.8, the vapour at the same time


declining to .432 inches. In October, the mean tem-


perature falls to 48o.9, and the elastic force to .336.


During the dark and dreary month of November, the


atmosphere becomes nearly saturated with moisture,


the mean temperature falling to 42o.9, and the mean


elasticity of vapour to .286 inches. December ex-


hibits nearly the same characteristics, the mean tem-


perature being 390.3, and the elastic force of vapour


.261 inches.


(465.) The preceding abstract forms, as

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N.E.N. N.W.


we have

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to pressure




ature of


ature of


Meteor-' stated, the mean results for the respective months; but tity of vapour existing in the air ; and as through the Meteorology. what, it may be asked, are the aberrations exhibited changes of the year, the mean temperature rises and

ology. during each, by particular winds ? a cause which is for falls, in a general way it is found that the quantity of Aberrations

ever modifying all the phenomena of vapour. The fol- vapour in the air must rise and fall with it. In very from the mean re

lowing maximum and minimum temperatures of the short intervals, it is true that aberrations may present sul Dew point peculiar to each month, have been deduced by themselves apparently in opposition to the Principle Mr. Daniell.

which has been advanced, but on a great scale it may be

clearly and satisfactorily traced. TABLE XCIX.

(469.) It is also worthy of observation, that if the Changes of pressure of the aqueous vapour be separated from that of pressure of the aerial, it will in general be found to exhibit changes

air opposite directly opposed to the latter. This can be best disTemper. Temper

of vapour.
covered in the daily fluctuations of the atmosphere; and,
in the graphical projections which inay be made to illus-

trate the two, it will be found that the undulations of
420.5 S. W. 230.5 E.

the curve representing the pressure of the whole atmo-
February 39.5 S. W. 29.0 N. E. sphere, are directly opposed to those of the vapour, a
March 47.0 S. 31.0 N. E. rise in the line of vapour being generally accompanied
April 49.0 S. E. 40.0 N.

by a fall in the barometric curve, and vice versa.

54.0 S. 40.5 N. E.

62.0 S. 49.5 N. or N. E. (470.) Another method, however, of a very different
July 59.0 S. W. 49.0 N. E. kind has been adopted by some Philosophers to discover
August ... 63.0 s. 53.0 N. E. or N. W. the circumstances of atmospheric humidity. Instead of
September 61.0 S. 45.0 N.

regarding the elastic force of vapour, its density, and the
October .. 53.5 S. 38.5


law of its dilatation, as so many independent elements to November 48.0 S.

35.5 N. W. be found, and by an operation connected with some December. 45.5 S. 27.5


functions of the density and temperature, to discover
thence all the conditions of moisture at any given

time or place, an attempt has been made to connect the Attempts to Monthly (466.) Mr. Daniell has graphically illustrated some indications of an instrument with the tensions of vapour connect the results. of his interesting results. In fig. 4, we have an exam at different temperatures, and thence to deduce all the indications

of an instruple of the monthly progress of the mean tempera- hygrometric conditions of the air. Saussure first endea

ment with ture and mean Dew point. The full line exhibits the voured to establish a relation of this kind, but it is to the quan. progress of the former, and the dotted line that of the the later labours of Gay Lussac that we would now tity of valatter, the degree of dryness belonging to each period especially refer. Of the two methods we certainly pre

in the air. being accurately represented by the interval between the fer the former, but we owe to our readers an explicit Relation of two curves. We may hence perceive how closely the account of the latter. vapour and constituent temperature of the vapour follows the mean (471.) To accomplish this object, the celebrated Che- Gay Lussac perature of temperature of the air, by the general resemblance of mist alluded to procured one of Saussures Hygro- employed

Saussure's the year. the two curves ; and also how clearly they exhibit the meters, as accurately and delicately made as the circum

hygrometer comparative dryness of the Spring and summer months, stances of its construction would permit; and placed it for this purand the dampness of the autumn and winter.

in a receiver containing some water, or a solution of a pose. Diurnal (467.) In fig. 5, which has also been derived from Salt of a known Specific Gravity, and then observed the results.

Mr. Daniell, this general accordance of the mean tem- degree which the instrument marked, under the circum-
perature and of the Dew point is rendered still more stances of saturation in which it was placed. This ex-
evident, by the variations of the daily mean for forty- periment was repeated under the same conditions of
five days in September and October 1819. And to temperature, for different tensions of vapour between
exhibit the analysis of this relation more completely, the limits of perfect dryness and absolute saturation. In Results ob-
fig. 6 is given from the same respectable source, de- this way the results of the next Table were obtained for tained by

him at the duced from observations made four times each day, the temperature of 10° of the Centigrade scale, the ten

temperatogether with the daily maxima and minima. An accu- sions of the liquids employed being expressed in parts of ture of ten rate inspection of this last figure most clearly demon- the tension of pure water, which was represented by centesimal strates that there is but little relation between the maxi 100.

degrees. mum temperature and the elastic force of the vapour, Relation of vapour and

and that the vapour appears to be governed principally minimum by the daily minima, thus practically confirming the tempera principle before advanced on the authority of Dr. Anture. derson.

(468.) That the quantity of vapour existing in the atmosphere near the level of the sea, must follow the course of the mean temperature during the successive seasons of the year, may also be inferred from the consideration, that the existence and quantity of vapour in the air, must be governed entirely by its temperature, and that the rate of evaporation is dependent on the same cause. Hence it follows, that whatever influences the temperature, must at the same time affect the quan

pour found

mutan tem

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Specific Tension of the Gravity at Solution at 100 the Temper. of the Centesimal ature of 10° of Scale, that of the Cen

Water being tesimal represented by Scale.


Degrees of
the Hygro-
meter cor-
to the dif-


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y=1 – (r) +
and which by addition will further give

x + y 1
1000 100.0 100.0

3' =

✓ 2
Muriate of Soda. 1096 90.6 97.7

1163 82.3 92.2 (474.) If we select, by way of application, the third Numerical
1205 75.9 87.4

result given in the Table for the muriate of lime, and example, Muriate of Lime. 1274 66.0 82.0

the density of which is 1397, we shall have according to
1343 50.5


the limitation before assigned to the abscissæ
1397 37.6 61.3

x = 0.376,
Sulphuric Acid. 1493 18.1 33.1 and
1541 12.2 25.3

y = 0.613,
1702 2.4 6.1

and which being substituted in the last equation will
1848 0.0 0,0


0.011 y' :

0.00777818; (472.) The relation of these results may, however, Graphic Lokation be more clearly explained by means of a graphic and this being so minute a quantity, the point in the dibesame illustration. For this purpose their author had re

curve to which it refers, may, without any sensible course to a curve whose coordinates u and y should

error, respectively denote the tensions and hygrometric de. But to avoid any unnecessary error, the origin of

be regarded as the vertex of the hyperbola. grees observed. At the origin of this curve, the values the abscissa x' may be assumed at that point of the axis, of r and y were to be severally zero, because that point where the latter is intersected by y'; and then the value of the hygrometric scale answered to extreme dryness ; of (x) may be found by adding 0.376 to the projection and at the other extremity of the scale, the same coordinates were to be respectively equivalent to 100, of y' on the axis of «, or in other words, to y cos x, or because 100 degrees of the hygrometer corresponded to

0.0054996, and which will hence give complete saturation. Between these limits, the experi

(r) = 0.3814996, misse cor- mental results obtained by Gay Lussac afforded many thus determining completely the relations of the two e regions intermediate points for the curve, and which upon in- systems of coordinates. Hence we shall obtain the two e'lypto- vestigation he found to be a hyperbola, having its con- equations zeic le cavity turned towards the line represented by r, and its

x' = (x -0.3815) ✓ 2 - y', axis inclined in an angle of 45°, forming the diagonal and wypadda,

of a square whose base was the abscissa x= 100, and altitude the ordinate 100 corresponding to x = 0; the

V 2 hyperbola being thus symmetrically disposed with re

When x and y are both given, we can readily obtain the spect to the two sides of the square. This result we may renture to say could have scarcely been anticipated tuted in the former of these last equations, will give the

value of y' as before illustrated; and this being substi-
à priori.
beltica (473.) To investigate these conditions analytically, it value of x';. According to this method the following

Table has been computed.
Best will be necessary to transform the original coordinates
I and y, into others and y', likewise rectangular, but

related to the same axis of the hyperbola, and having
their origin in some assumed point of it. This new
line of abscissæ must thus form an angle of --- 45° Primitive Coordinates,

New Coordinates.
with the former abscissæ; and by naming (x) and (y)
as the primitive coordinates of that line, we shall obtain

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0.000 0.000 +0.167384 -0.707107 and

0.122 0.253 +0.074953 -0.441942 y = (3) + 72 (34–).

0.376 0.613 0.000000 -0.007778 These equations, however, may be simplified, by representing by unity the abscissa x corresponding to the

(475.) These elements are sufficient to determine the Equation of tension 100, and which assumption will enable us to obtain the expression nature of the hyperbola. For since its axis coincides the hyper

bola. with the line on which the abscissæ & are reckoned, its y=1- x; and since the primitive ordinates' (x) and (y) are simi- equation must be necessarily of the form larly related, we shall in like manner obtain

y = a + 2 bx! + cx', (y)=1- (x).

the values of the constant coefficients being determined The general equations above given will thus assume the by the respective values of x' and y' in the Table. Thus forms of

we shall obtain

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y' =*+y - 1


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