io6 



NATURE 



{June 6, 1872 



RADIATIOy AT DIFFERENT TEM- 

 PERATURES 



gALFOUR STEWART states in his " Elementary Treatise 

 oa Ileal" that "Newton was the first to enunciate his 

 views on the cooling of bodies. He supposed that a heated 

 body exposed to a certain cooling cause would lose at each in- 

 stant a quantity of heat proportionate to the excess of its tem- 

 perature above that of the surrounding air." In order to prove 

 the fallacy of Newton's supposition, Prof. Stewart presents the 

 following extract from the work of MM. I)ub;ig and Petit : — 



" We see at once from this table," says Prof. Stewart, " that 

 the law of Newton does not hold, for according to it the velo- 

 city of cooling for an excess of 200" should be precisely doub'e 

 of that for anexcessof 100' ; now we find that it is more than three 

 times as much." The author of the Elementary Treatise on Heat 

 thus assumes that the velocity of cooling established by Dulong 

 and Petit represents the radiant energy or quantity of heat trans- 

 mitted by the radiator. Consequently, the amoant of energy 



I0'69 

 at 200' IS assumed to be - ' = 6 '14 tunes greater than at So ; 



while, agreeably to Newton's law, the increase of radiant energy 



should be proportional to the diff jrential temperature, viz , 



240 



o — = 3 times that of the tabulated temperature of So°. Modern 



research having established that radiant heat is energy amenable 

 t"» the laws of dynamics, it may be demonstrated that the devia- 

 tion from the Newtonian doctrine assumed Ijy Dalong and 

 Petit is groundless ; bu', before considering the theory, let us 

 examine the practical result of recent elaborate experiments con- 

 ducted with an apparatus containing the spherical radiator ad- 

 verted to in the preceding article on Solar Te.nperature (vol. v. 

 pp. 505-507). The accompanying illustration (Fig. i) represents 

 a vertical section of the said apparatus, a being a spherical vessel 

 5 inches in diameter, suspended within an exterior cising /', 

 filled with water. A spherical radiator, c, 275 inches in diame- 

 ter, composed of very thin coppe', charged with water and 

 coated with lamp-black, is sustained in the centre of the sphere 

 a by means of tubes applied above and beloA'. The upper 

 tube is large enough to admit the lialb of a thermo- 

 meter, the lower one being only sufficiently large to accom- 

 modate a small axle, to which is attached a paddle-wheel, pro- 

 vided with curved paddles, arranged in such a manner that the 

 bulb of the thermometer may be inserted considerably beyond 

 the centre of the sphere, as shown in the illustration. The ex- 

 ternal casing 1/ is provided with nozzles, g and (/, to which tubes 

 are attached for circulating cold wa'er through the annular space 

 during experiments. The air is exhausted from the spherical 

 enclosure through the tube /■, which passes across the annular 

 space. It will be evident that the centrifugal action of the 

 paddles of the wheel applied within the radiating sphere will 

 produce a continuous current from the centre towards the circum- 

 ference, the lluid successively passing over and coming in contact 

 with the inside of the thin shell, then returning to the centre to 

 be again thrown olT by the centrifugal action. The rotary 

 motion of the water, kept up without intermission round the 

 cylindrical bulb of the thermometer, will evidently render its in- 

 dication prompt and reliable. It is hardly nccess.ary to observe 

 that the rapid presentation of fresh particles of water promoted 

 by the action of the paddles, will effectually prevent the reduc- 

 tion of temperature to proceed fas'er at the circumference than 

 at the centre, the radiation at the surface, in virtue of the con- 

 tinuous interchange of particles, affecting almost simultaneously 

 every molecule within the sphere. Consepiently the total energy 

 of radiation will be rendered available in reducing the tempera- 

 ture of ihe contents of the radiator, while the central thermo- 



meter will indicate at every instant the precise degree of tem- 

 perature of the entire mass.* 



The mode of conducting the experiment will be seen by the 

 fi)llowing statement : — A wooden cistern containing 16 gallons, 

 charged with water and crushed ice, is connected by flexible 

 tuljcs to the nozzles ;,■" and d on opposite sides of the annular 

 space, a pump bring applied between the cistern and the said 

 nozzles, by means of which the cold water is forced through the 

 apparatus and then returned to the cistern. 



In view of the great importance of the question at issue, the 

 investigation has been conducted with the utmost care, four 

 operators having invariably been employed during the experi- 

 ments, the labour being thus divided : 1st operator regulates the 

 temperature of the water in the cistern by continual agitation 

 and supply of crushed ice from time to time ; 2nd operator 

 works the pump at a uniform rate ; 3rd operator turns the 

 paddle-wheel, and reads the thermometer under a magnifying 

 glass, calling time for each degree at the instant when the top of 

 the mercurial column is covered by half the thickness of the line 

 on the scale. Lastly, the 4th operator, provided with a Ca.sella chro- 

 nograph, records the time called. It will be seen presently that, 

 notwithstanding this procedure, there is a slight discrepancy in 

 the ratio of temperature and time, viz., the increment of time 

 for each degree is not regular. Obviously the most practised 

 eye cannot determine exactly at what moment the top of the 

 falling column is half covered by the line on the thermometric 

 scile. Again a perfectly graduated thermometer cannot be ob- 

 tained. Bat the discrepancy referred to in reality only disfigures 

 the record, since the computations are based on iiwan time. Re- 

 ferring to the accompanying table, it will be seen that the rate at 

 which the spherical radiator cools has been recorded separately 

 for each degree of differential temperature from 100" to 10', the 

 enclosure being maintained at a constant temperature of 33'. 

 Regarding the construction of the table, it will suffice to state 

 that the time entered in the fourth column is that shown by the 

 chronograph. It will be evident on reflection that the increment 

 of time for each successive degree of differential temperature 

 expresses very nearly the rate of cooling ; but, the recorded times 

 being irregular, from causes already pointed out, the true incre- 

 ment cannot be determined without ascertaining the mean time 

 recorded by the chronograph. This mean time will be found in 

 the fifth column, the true increment, viz., the number of seconds 

 during which the temperature of the radiator falls ona degree, 

 being entered in the last column. 



Let us now examine the accompanying diagram Fig. 2, in 

 which the ordinates of the curve a b represent the observed time 

 for each degree of differential temperature, while the ordinates 

 of the curve a c represent the corrected time. The diagram 

 having been constructed with the utmost exactness, in accordance 

 with the temperature and time in the table, mere inspection will 

 show that the observed and corrected times have produced curves 

 nearly identical. Agreeably to Newton's law the rate of cooling 

 is proportional to the excess of temperature of a body above that 

 of the surrounding medium. Hence the increment of time for 

 ea;h degree, in other words, the number of seconds occupied in 

 reducMig the temperature of the radiator i^ (inserted in the last 

 column of the table) should hi proportional to the dilferential 

 temperature inserted in the third column. For instance the 

 rate of cooling at a differential temperature of 490" being 39 'So 



seconds for l' 



49 X 39 'So 

 it should be — — 62 'go seconds for an 



eqaal thermometric interval at a differential temperature of 31". 

 Referring to the table, it will be found that the rate thus com- 

 puted agrees exactly with the increment of time inserted in the 

 last column opposite the differential temperature 31'. 



.•\pplying a similar test to the other differential temperatures and 

 rales of cooling contained in the table, the same exact agreement 

 will be found to exist. Consequently, our table and diagram 

 prove that the rate of cooling is proportional to the differential 

 temperature, thus establishing the correctness of the Newtonian 

 Uw. Regarding the discrepancy indicated by the slight irre- 

 gularity of the curve (/,'', the writer attributes the same to the 



'* It misht be supposed that the motion of the water within the radiating 

 sphere, prodaced by the action of the paddle wheel, will occasion .in elev.-i- 

 lion of temperature tending to render the indication of the centr.-il thermo- 

 meter inaccurate. The requisite speed of the wheel being 30 turns per 

 minute, experiments have been made to ascertain if at that rate heat is pro- 

 duced : but no elevation of temperature has been observed. The diameter of 

 the wheel being 2"j7in., the maximum speed of the particles of water pro- 

 duced by the rotation is scarcely 3 'Sins, per second, a velocity too small to 

 generate appreciable heat. 



