"925 



BAROTVIETER. 



BAR01METER. 



926 



appears in some barometers and not in others, and why the same 

 barometer sometimes loses the property, and afterwards recovers it. 

 For a full account of the discovery, and of early hypotheses respecting 

 it, see the first volume of De Luc's 'Recherches sur lea Modifications 

 de 1" Atmosphere.' 



In order to compare two barometers which are in different places, 

 the temperature of the mercury must be attended to ; for, as mercury 

 expands with increase of temperature, a higher column of the fluid will 

 be required to counterpoise a given weight of air. To observe the 

 temperature of the mercury, a thermometer is attached to the best 

 instruments, the bulb of which is in the cistern. All observed heights 

 should be reduced to what they would be at some given temperature, 

 say the freezing point of water. And it must be remembered, that the 

 scale itself on which the heights are measured, expands or contracts 

 with the mercury. If the two expanded or contracted equally, there 

 would be no occasion for any correction ; but if the mercury expand 

 more than the scale, it is the difference of the expansions by which the 

 observed height will be wrong. Mercury expands more than the 

 material of any scale which is ever employed. 



In this country the scale is usually engraved on some mixed metal, 

 and no very satisfactory value of the expansion can be given. It will 

 be sufficiently accurate to suppose the expansion of mercury for every 

 degree of Fahrenheit to be '0001 of its bulk at the freezing point, and 

 to neglect that of the scale altogether, which gives the following 

 rule : 



To reduce an observed altitude to that of mercury at the freezing 

 point, subtract the ten-thousandth part of the observed altitude for 

 every degree by which the mercury is above the freezing point (of 

 water, of course). At a height of 30 inches, and a temperature of 50 

 (Fahr.), this correction would be '054 of an inch. 



The expansion of the barometer-tube itself need not be attended to. 

 The consequence of it is, that more mercury is drawn out of the 

 cistern to form the requisite column ; but the height of the column is 

 unaltered. 



(Remember that the cubical expansion, not the linear, must be used 

 for the mercury in the formula.) 



2. The height observed requires another correction for the capillary 

 repulsion, by which it stands somewhat lower than it otherwise would 

 do. On this subject a paper has recently been read to the Royal Society 

 of London by Mr. Ivory, to which we refer for an accurate and clear 

 account of the effects of capillarity on the barometric column, the effect 

 of which is always to depress the mercury by a certain quantity 

 inversely proportional to the base of the tube. The following table 

 shows very clearly the amount of correction to be added : 



Diameter of Tube. 

 Inch. 

 0-60 

 0-60 

 0-45 

 0-40 

 0-35 

 0-30 

 0-25 

 0-20 

 0-15 

 0-10 



Correction for 

 Unboiled Tubes. 

 Inch. 

 0-004 

 0-007 

 0-010 

 0-014 

 0-020 

 0-028 

 0-040 

 0-060 

 0-088 

 0-142 



Correction for 

 Boiled Tubes. 



Inch. 



0-002 



0-003 



0-005 



0-007 



0-010 



0-014 



0-020 



0-029 



0-044 



0-070 



We must observe, that in the siphon barometer, No. 2, and also in 

 the modification of it proposed by Gay Lussac, No. 14, no correction 

 for capillarity is necessary ; for the depressive force is equal on both 

 sides. In all other barometers the capillary action of the cistern is 

 insensible, owing to the magnitude of its diameter, so that only that of 

 the tube need be attended to. Perhaps the best way of settling the 

 exact amount of capillary depression would be by a very large number 

 of observations upon two good barometers of different-sized tubes 

 standing in the same place. The tube must be very exactly cylin- 

 drical, or the capillary correction will not be the same in all its parts. 



3. The index correction must next be applied. This is the amount 

 of difference between the particular instrument and the readings of 

 the Royal Society's flint-glass barometer, or that of the Kew Obser- 

 vatory, when properly corrected. This correction however is generally 

 attended to chiefly in the case of ships' barometers. 



4. The barometer must hang quite vertically; for any deviation from 

 the vertical converts the instrument, pro tanto, into the diagonal baro- 

 meter, No. 7, and makes the divisions on the scale too small. 



5. The scale is usually divided into tenths of inches, and is also 

 furnished with a vernier, by which the height may be measured within 

 the 200dth of an inch. [VERNIER]. Many observers profess to go 

 nearer ; but, considering the uncertainty (if we speak of thousandths of 

 inches) of the corrections both of temperature, capillarity, of the zero 

 Aroint of the scale, &c., this must be considered as mere play. What- 

 ever reliance may be placed on the mean of a large number of 

 observations, we think we may safely defy any one to show an even 

 chance that a single observation will be free from instrumental errors, 

 even as far ns the 200dth of an inch. 



6. The exact determination of the level of the mercury in the cistern 

 is in many barometers impossible. All the best instruments have 

 uome method of adjustment, either as described in Fortin's barometer, 



No. 15, or by placing a float on the surface of the mercury with a needle 

 rising vertically from it, some point of which needle is adjusted by 

 raising or lowering the bottom of the cistern. 



If a barometer be made, which is not a siphon barometer with 

 uniform tube, No. 2, or with means of adjusting the lower level of the 

 mercury, it should certainly be the simplest form of Torricelli's instru- 

 ment, namely, a perfect cylindrical tube immersed in a perfectly 

 cylindrical cistern. The larger the cistern, the less the error arising 

 from variation of the lower level ; the actual error may easily be cal- 

 culated thus : Let K and k be the areas of the sections of the cistern 

 and tube respectively ; let a be the height of the column of mercury 

 above the zero point at any time when that in the cistern is at the zero 

 point, b the corresponding height at any other time, so that 6 a is the 

 difference in apparent height ; and let c be the depression of the mer- 

 cury in the cistern below the zero point at this latter time ; so that c is 

 the error required to be added to the apparent height to give the 

 true height. Now, by the laws of equilibrium of fluids, we shall 

 easily have, 



k x (6 a) = K x c. 



k 

 .'. c = - (6 - a) 



k / k\ k 



.-. The true height required = 6 + -(6 a) = ill + ^ I a 



An imperfect barometer is one into which some air OT gas has pene- 

 trated, and so caused a depression of the upper surface of the mercviry 

 below ita proper level. When the barometer is to be employed in 

 determining the relative heights of ground, it may not be possible to 

 get this air out of the tube by any means in the power of the observer, 

 and it then becomes necessary to have a formula by which a correction 

 may be applied to the observed height of the mercnry at any station 

 in order to have the height at which the top of the 

 column would stand if the tube were free from air. 



For this purpose, before setting out, the height of 

 the column of mercury in the defective instrument 

 must be compared with the height in one which is 

 perfect, in order to obtain the measure of the elas- 

 ticity of the air which is confined in the upper 

 extremity of the tube. Let A c be the length of the 

 bore of the tube above A, the surface of the mercury 

 in the cistern, A B the height of the column in a 

 barometer free from air, and A B' the observed height 

 in the defective instrument. It being' understood 

 that these heights are read at the same time and 

 place, so that the temperature and density of the 

 air may be the same ; and also that both instruments 

 are provided with adjusting screws,- so that the 

 surfaces of the mercury in the two cisterns may be 

 made to coincide with the zeros of the scales of 

 inches. Then the pressure of the external atmosphere 

 supporting the column A B, and the difference be- 

 tween that pressure and the pressure equivalent to the elasticity of 

 the air in c B' supporting the column A B' ; it follows that the weight of 

 a column of mercury in B B' measures the pressure last mentioned ; let 

 this be represented by ml, in which I is equal to the height B B'. 



Now, on removing the instrument to another, suppose a higher, 

 station, let the observed height of the mercury in the imperfect baro- 

 meter (no more air being supposed to have entered) be A D ; then the 

 air which, before, occupied the space c B', occupies c D, and its elastic 

 force is diminished in the inverse ratio of those spaces or heights 

 therefore, if c B' be represented by a, and c D by b, 



'- 



and the last term expresses the pressure of the confined air on D, the 

 top of the column of mercury. This term added to the weight of the 

 column of mercury A D, which may be represented by mh (h being the 

 observed height A D), will be equal to the weight of the column of 

 mercury at the same time and place in a barometer which is free from 



al 

 air. This last being represented by mh' ; it follows that h 1 = h + -r 



or r- is to be added to the observed height, in order to obtain the cor- 

 rected height of the column of mercury at the station. 



Barometrical Measurement. The use of the barometer for Hypso- 

 metry, or the measurement of heights, depends upon the fact of the 

 diminution of atmospheric pressure as we ascend from the earth's 

 surface. The best form of mountain-barometer is described in the 

 article on ' Barometrical Measurements,' in the ' Encyclopaedia Britan- 

 nica.' The humidity of the air also materially affects its elasticity, so 

 that the hygrometer, as well as the thermometer, should be used in 

 correcting these observations ; besides which, we must take into account 

 the decrease of the earth's attraction at the point. The general method 

 is as follows : Let x and x 1 be the heights in feet of the two stations, 

 and let us suppose the atmosphere to consist of strata of one foot 

 thick, throughout each of which the pressure is the same, but that in 

 passing from one to another of them the pressure diminishes in a 



