EXPANSION BY HEAT.] 



METEOROLOGY. 



1127 



the flame of a spirit-lamp, or a basin of hot water the 

 heated bar will no longer fit into the gauge. In this 

 way the student may demonstrate the fact that each dif- 

 ferent solid possesses its own definite rate of expansion 

 for equal degrees of temperature. 



Investigations of the law regulating the thermal ex- 

 pansion of bodies, under every condition, are attended 

 with extreme difficulty. They have been conducted by 

 Regnault, Rudberg, and others, with great industry and 

 much success ; but, as in most cases where the investiga- 

 tion of natural phenomena through long ranges are con- 

 cerned, the results are merely approximate. To give the 

 reader a general notion of one of these difficulties, let it 

 be assumed that A B C D stand for successive equal in- 

 tervals of thermonietric graduation. Let it be assumed 

 that the rate of expansion of a substance from A to D 

 be known as equal to a quantity expressed by Y. It by 

 no means, however, follows nor do philosophers believe 

 that, because the rate of expansion of the body 

 between A and D is equal to Y, therefore the rate of 

 expansion of the same body between A and B is equal 



Y 



Further consideration of this matter may, however, be 

 omitted in a Treatise on Meteorology. We merely want 

 to be acquainted with approximate results of the law, 

 in order to allow for practical discrepancies between the 

 apparent and the actual indications of the instruments 

 employed in the course of our researches. 



To convey a general notion of this kind of knowledge 

 to the meteorological observer, the student's attention 

 may be directed to the fact, that, supposing a barometer- 

 scale to be made of brass,- and the tube to be filled, as 

 usual, with mercury, then the amount of expansion of 

 mercury by heat, and for which allowance baa to be ' 



made, will be determined by the ratio y , if M stand for 



the co-efficient of expansion of mercury, and B for the 

 co-efficient of expansion of brass. By the term, "co- 

 efficient of expansion," is meant the number indicating 

 the amount of expansion peculiar to any body for given 

 ranges of temperature. 



III. The Volume of all Liquids is Increased by Adilitinn 

 of Heat. Investigations prosecuted for demonstrating 

 this law, are attended with a difficulty which does not 

 apply to the previous case. Liquids require vessels to 

 hold them, and these vessels are themselves amenable to 

 expansion. This difficulty has been very ingeniously 

 avoided by MM. Petit and Dulong, who determined the 

 expansion of liquids by a method founded upon the well- 

 known hydrostatic principle, that the vertical heights of 

 two fluids, communicating by a horizontal tube, are in 

 inverse ratio to their densities. The apparatus shown 

 in Fig. 18 was employed in their experiments. A, B, 

 C, D is a tube bent twice at right angles, and enlarged 



Fig. 18. 



at either extremity ; the two vortical tubes are connected 

 interiorly, by a horizontal tube of exceedingly fine bore. 

 By virtue of the hydrostatic law just mentioned, it 

 follows, that if any liquid of homogeneous density be 

 poured into the vertical leg of one side, it will rise to a 

 corresponding elevation in the vertical leg of the other ; 

 and if the fluid in one vertical leg be now heated, and 

 consequently expanded, its height will be in excess of the 

 columnar height of the other, by a definite quantity. 

 By an eay train of mathematical reasoning, the ex- 



pansiou due to heat can be deduced from a consideration 

 of the different levels and the different temperatures of 

 the two vertical tubes. Our diagram represents each 

 vertical tube surrounded with a cylindrical vessel. These 

 vessels are for the purpose of commanding variations of 

 temperature ; one tube filled with ice, whilst the other 

 is filled with hot water. 



By an experiment of this kind, the co-efficient of 

 thermal expansion of mercury from to 100 of the 

 centigrade scale, is $ ; whence, assuming its rate of 

 expansion equal throughout, the expansion for every 

 centigrade degree will be ys 1 ^, or, for every degree 

 of Fahrenheit, Q^ O ; in decimals = -000101 ; or, ex- 

 pressed in round numbers, one ten-thousandth part of 

 its bulk. 



IV. The, Volume of all Gases is Increased by Addition of 

 Heat. Though the consideration of this law is not re- 

 lated, like the two preceding, to the construction of the 

 barometer, it is intimately connected with the functions 

 of that instrument, more especially as regards its ap- 

 plication to the measuring of elevations ; we shall do 

 well, therefore, to consider it at once. 



It has already been remarked, that the rate of expan- 

 sion of all solid bodies for giving increments of tern 

 perature is various ; and a similar remark applies to 

 liquids. The rate of expansion of gases was first closely 

 investigated by the immortal Dalton, who arrived at the 

 conclusion, that all gases were equally affected by equal 

 increments of heat, expanding to j^jth parts of their 

 volumes at 32 Fah. for each of the 180, between 32" 

 Fah. and 212 Fah. As regards temperature, above 212 

 Fah. and below 32 Fah., it was ima-jfined by Dalton 

 that the same law of expansion held good. Various 

 theoretical reasons exist of a nature to create a doubt as 

 to the large generalisation of Dalton ; and these doubts 

 have been fully substantiated by M. Regnault. He 

 finds that all gases do not dilate to the same extent be- 

 tween equal limits of temperature, neither is the dila- 

 tation of the same gas, between the same limits, inde- 

 jxmdent of its primitive density. Those are interesting 

 facts : they prove that to assume one co-efficient of dila- 

 tation for all gases is obviously incorrect ; nevertheless, 

 his experiments go to prove that such a universal gaseoua 

 co-efficient of dilatation may be adopted for convenience, 

 without appreciable error, within the theoretical limits 

 of ordinary experiment. We must not, however, con- 

 tinue to adopt jjijth ns ollr working gaseous co-efficient 

 of dilatation for every degree of Fah. between 32 and 

 212; nor jj, as subsequently adopted by MM. Petit 

 and Dulong, but jj^. 



THE ATMOSI-HKHE ACTUALLY OR PRACTICALLY CON- 

 SIDERED. We have hitherto regarded the atmosphere 

 as a compound or mixture of nitrogen and oxygen gases 

 only ; but the reader need not be informed that such an 

 atmosphere is altogether theoretical. Besides nitrogen 

 and oxygen gases, there always exists a portion of car- 

 bonic acid, and aqueous vapour, either visible or in- 

 visible. These are invariable components of the atmo- 

 sphere, indispensable to its functions, and adapting ittothe 

 purpose of this world's economy. The atmosphere con- 

 tains also other materials, the resiilts of local operations 

 in nature, no less than the operations of man. As the 

 subject of our present investigations, let us consider 

 the atmosphere as a mixture of the theoretical atmo- 

 sphere, plus aqueous moisture and carbonic acid. 



Limits of the Atmosphere. It follows, from a con- 

 sideration of the laws of elasticity, that the atmosphere 

 must vary in density for every difference of elevation. 

 The atmospheric layer nearest to the earth must be 

 pressed upon by the superincumbent atmosphere above 

 it ; whence the deduction follows, that when we speak 

 of 100 cubic inches, or any definite measure of the at- 

 mosphere, weighing a certain number of grains, certain 

 conditions and limitations are implied. Some of these 

 have reference to the composition of the atmosphere 

 chemically considered ; others have reference to the at- 

 mosphere merely regarded as an elastic medium. To 

 the latter consideration alone the reader's attention will 

 be now directed. 



