On the Surface-Condensation of Steam

VIII. On the Surface-condensation of Steam. By J. P. Joule, LL.D., F.R.S., President of the Literary and Philosophical Society of Manchester, &c. Received October 10,—Read December 13, 1860. The laws which regulate the transmission of heat through thin plates of metal under various circumstances, although of extensive practical application, and although their elucidation would necessarily involve scientific conclusions of great interest, have hitherto received little of the attention of natural philosophers. Two great divisions of the inquiry are, first, the communication of heat from the products of combustion to a boiler; and second, the application of cold to a vessel employed for the condensation of steam. With a view to supply some information on the latter subject I have, with the assistance of a grant from the Royal Society, undertaken the present research. The adjoining sketch (p. 134) will explain my apparatus. B is a steam-boiler into the side of which a pipe P furnished with a stopcock T is screwed. Jointed to this by a caoutchouc tubulure t is the condensing pipe s, connected at the lower end to a short pipe q, which in turn is connected with the copper receiver R, closed at the bottom by a screw-nut n furnished with a washer of india-rubber. The refrigerating water is transmitted through the channel E D C, consisting of a pipe $1\frac{1}{4}$ inch in diameter, and the concentric space between the steam-condensing pipe and an exterior pipe of larger diameter. The refrigerating water on flowing away is collected in V, the vessel in which it is afterwards weighed. In order to avoid the necessity of applying a large correction to the temperature of this water, it is, when its quantity is not very great, received in the first instance by the small can U, in which a thermometer is plunged. A branch pipe p, screwed into the main pipe, is connected to the barometer tube b in order to measure the degree of vacuum. The pipe P enters the boiler at 8 inches above the surface of the water. Separate experiments showed that no water came up to this height by "priming." On the other hand, the arrangement of the boiler, the flue of which is entirely below the level of the water, prevented the steam being surcharged with heat to any notable extent. By careful experiments I found that a thermometer of which the bulb was held six inches above the water of the boiler, indicated exactly the same temperature whether the boiling was carried on very slowly or very rapidly. But when the bulb was immersed 3 inches below the surface, the temperature with slow boiling was $0^\circ.532$ higher than that of the steam, which difference was further increased to $0^\circ.538$ by rapid boiling. This would lead to the belief that the steam must have been a little overcharged with heat by passing through superheated water; but as there was a trifling cooling effect by the influence of the atmosphere on the pipe P, the steam passing through the stopcock might be safely considered as neither superheated nor mixed with water. MDCCCLXI. Up to the stopcock T the temperature of the pipe may be considered as that of the boiler; beyond it the temperature becomes gradually that of the condenser. A certain, though very small, quantity of heat is thus conducted along the tube from the stopcock T as far as the india-rubber junction t. Any water condensed in P falls back again into the boiler; that between the stopcock and t falls into the receiver; so that the small quantity of conducted heat just mentioned is probably compensated by the trifling cooling effect of the atmosphere between T and the refrigerating water. The short continuation pipe q exposes to the water an effective length of 3 inches, which, on account of the wideness of the channel there, could not generally have had an effect greater than that due to 2 inches in the narrower part. As, however, a length amounting to an inch and a half of the ends of the condensing tube is overlapped by the vulcanized tubing, the entire amount of condensation may, without appreciable error, be laid to the account of the condensing pipe. The receiver R and the pipes C, P, and p are enveloped by a thick coating of cotton-wool and flannel, so as to prevent as far as possible the refrigerating effect of the atmosphere. Great pains were taken to make every part of the apparatus in which the pressure is below that of the atmosphere, perfectly air-tight. It will be seen that the form of the stopcock T effectually prevents any leakage except from the high pressure side into the atmosphere, which is of no consequence. The india-rubber junctions were at first made by simply binding on the ends of the tubes short lengths of vulcanized caoutchouc; but it was soon found that enough air passed to vitiate the experiments, which were consequently rejected. The method afterwards adopted was to smear the ends of the tubes with melted vulcanized caoutchouc before the short india-rubber tubes were bound on. This plan was found to be so efficacious that air appeared to be perfectly excluded, and the vacuum wholly unimpaired, however long an experiment was carried on. The vacuum-gauge glass tube is 0·45 of an inch in internal diameter. It is plunged into a wide dish of mercury, from the surface of which the height of the column is measured. The temperature of the mercury in the gauge was always nearly that of the barometer which registered the atmospheric pressure. During each experiment a small quantity of condensed water settled by degrees on the top of the mercury, the length of which, divided by 13·56, gave the correction to be supplied to the height of the column. It will be observed that the pipe leading to the vacuum-gauge is inserted near the stopcock which admits the steam. It was important to ascertain whether the gauge would stand at the same level if it were connected with other parts of the vacuous space. To determine this, a pipe was attached to the receiver at r, and connected with a gauge placed side by side with the first gauge, and dipping into the same dish of mercury. The gauges were observed during rapid and slow condensation, at different and at varying pressures; but the height of the columns appeared to be in general exactly the same: if any difference could be observed at any time, I would say that the receiver gauge indicated the less perfect vacuum of the two; the difference, however, amounted in no case to more than $\frac{1}{30}$th of an inch. The following is my method of experimenting. The nut \( n \) being unscrewed, the dish of mercury removed from under the gauge-tube, and the water being completely discharged from the tap \( W \), the cock \( T \) is partly opened, and the steam is blown through the steam-pipe \( s \), the gauge \( b \), and the receiver \( R \) until they are completely freed from air. The nut \( n \) is then screwed on, \( W \) closed, and the water let on, the three operations being performed as simultaneously as possible. At the moment when the steam is about to cease issuing from the gauge-pipe, its end is introduced into the dish of mercury. After an interval of time, varying from half a minute to three minutes, the condensation goes on with perfect regularity, and the mercury in the vacuum-gauge remains steady. The temperature of the water flowing away and the gauge are observed every two or three minutes. The experiment is terminated by simultaneously shutting off the steam and the water, and opening the tap \( W \) to let off the water remaining in the pipe. The nut \( n \) is then removed, and a quantity of air having entered the receiver, the condensed water is caught by a small can (held close and containing a thermometer), which overflows into a larger vessel in which the water is immediately afterwards weighed. The values of several small corrections which had to be applied to the observations were obtained from data derived from separate experiments. Of the thermometers employed, one was made by Fastré, in which each division is equal to \( 0^\circ.225 \); the two others were from Kew Observatory, and have for each division the values \( 0^\circ.1 \) and \( 0^\circ.0994 \) respectively. A correction had generally to be applied in consequence of the non-immersion of the stems. The cooling effect of the atmosphere on the receiver \( R \) operates partly to condense steam and partly to cool condensed water. The correction on the former account was found to be equal to the continual product of the time in minutes, the proportion of acting surface, and the difference between the temperatures of the receiver and atmosphere, divided by 77 times the difference between 640 and the temperature of the condensed water: the result had to be subtracted from the weight of condensed water. The correction on the latter account is equal to the continual product of the time, acting surface, and difference of temperature, divided by 77 times the weight of condensed water; it had to be added to the observed temperature of the condensed water. The correction on account of the cooling of the refrigerating water on flowing through \( C \) into the vessel \( U \), was found to be equal to the difference of temperature between the water and the atmosphere, multiplied by \( 0^\circ.51 \), and divided by the quantity of water flowing per hour. This rule applies to the case in which the external pipe \( C \) was 4 feet long and 1 inch in diameter. Corrections in the instances in which other tubes were used were made by calculation without express experiments, inasmuch as they were of very trifling amount. The slight loss of water by evaporation, before and during the process of weighing, was allowed for in the weighing both of the refrigerating and condensed water. The metal of the steam-pipe and receiver is necessarily at \( 100^\circ \) at the commencement of an experiment, and therefore communicates some heat during the first few moments. On the other hand, the small quantity of water drawn off at W at the termination of an experiment is always more or less heated. Corrections on both these accounts were easily applied. I had at first some doubts whether the vacuum would not become gradually impaired by air coming over from the boiler; for it has been frequently asserted that water becomes perfectly free from air only after long-continued boiling. I found, however, that after boiling had taken place for only two or three minutes, the air was entirely expelled, and that even if condensation were afterwards carried on until the receiver was entirely filled with water, no change took place in the height of the gauge. Hence, by blowing off steam for ten minutes at the commencement of a day's experimenting, I effectually secured myself against any risk of the interference of air*. The Table of experiments requires little explanation. It will be seen that column 5 contains some numbers with the negative sign. This might be expected where a small quantity of water was used, on account of its being raised in temperature during its ascent. When the water was intended to go in the same direction as the steam, it was poured in at the upper end of the outer tube, and flowed away at the lower end, the pipe E being removed. Each number in the 14th column is the average of all the observations of the pressure in the condenser after it became constant; and column 17 contains the averages of all the observations of the temperature of the refrigerating water at its overflow made at the moments of gauge-observation. Hence this column contains numbers generally a little different from those of column 7, which, being taken for the purpose of deducing the total heat of steam, are the averages of all the temperature observations of the overflow water in the several experiments. In order to explain the principle on which the 18th column is based, I cannot do better than give textually the extract of a letter I received from Professor Thomson, to whom at the outset I communicated my design, and who, with his usual zeal and kindness, immediately offered me very valuable suggestions. "Steamer Venus, August 10th, 1859. "If the resistance to equalization of temperature between the steam and water depended on conduction through the separating metal alone, the heating effect would take place according to the law you name. The formula would be thus found, \[ w \frac{dv}{dt} = -k \frac{Adx}{a} v, \] where \( w \) is the mass of water passing per unit of time, \( dv \) the augmentation of the * I could not discover any alteration in the composition of the air after it had remained in the boiler some days. There appears to be no truth in the hypothesis which ascribes boiler explosions to the formation of hydrogen. The obvious cause is over-pressure; and it is not wonderful that, when multitudes of boilers are worked at a very considerable proportion of the pressure calculated to burst them when new, accidents occasionally occur. I have repeatedly insisted upon the absolute necessity of periodical testing, and have proposed a method requiring no extra apparatus or expense, which consists simply in lighting a fire under the boiler when completely filled, and so producing the proof pressure by the expansion of water by heat. I try my boiler every six weeks by this process, which appears to answer the end in view in every respect. difference of temperatures inside and outside in a length from $x$ to $x+dx$, $v$ the difference itself at any point $P$, $k$ the conducting power of the metal, $A$ the area of the tube per unit length, $a$ its thickness. By integrating, we find $$\log \frac{V}{v} = \frac{kAx}{aw},$$ where $V$ denotes the difference of temperatures at the entrance end. $A$ will be the area corresponding to a mean diameter calculated by the formula $\frac{2a}{D}$, when the outer diameter $D$, and the inner $D-2a$ differ so much that it will not do to use one or the other indifferently. For all practical purposes, with such tubes as are actually used, it will do to take as the mean diameter the arithmetic mean $D-a$. "The truth, however, is that, except with a very great velocity of the water, there will be a heated film close to the metal much higher in temperature than the average temperature of the water in the same section, and the abstraction of heat will be much slower than according to the preceding formula. It is not improbable, however, that some law of variation will still hold from point to point in the direction of flow; and if so, the same formula would apply, only that for $k$ something much smaller than the true conductivity of the metal must be substituted. Thus, supposing $k$ to be a function of $w$, smaller the smaller is $w$ and increasing to a limit (the true conductivity of the metal), your experiments might give values of $k$ for different rates of the flow of the water by the expression $$k = \frac{aw}{Ax} \log \frac{V}{v}.$$ It would be necessary to ascertain by experiment how nearly the geometrical law of decrease of the difference of temperatures along the tube holds, as there is no sufficient theory for convection to give any decided indication. "As the results would probably depend but little on the thickness and quality of the metal, it would be better perhaps to take $\frac{k}{a}$ as the thing to be determined: calling it $C$, we have $$C = \frac{w}{Ax} \log \frac{V}{v}, \quad \text{or} \quad v = V \varepsilon^{-CA/w}.$$ $\varepsilon$ being the base of the nap. log, $\varepsilon^{-CA/w}$ is the fraction expressing the reduction of the difference per unit of length, and therefore $(1 - \frac{CA}{w})100$ is the percentage of difference lost per unit of length. If this be called $\theta$, we have $$v = V(1 - \theta)^x, \quad \text{or} \quad \log \frac{1}{1-\theta} = \frac{1}{x} \log \frac{V}{v},$$ where log denotes any kind of log. These are, in fact, the compound interest formulæ, and are perhaps the most convenient for numerical reductions." The results of my experiments were quite in conformity with Professor Thomson's view as to the smallness of the resistance to conduction through the thickness of the metal compared with the resistance at the surfaces of the tubes through the closely adhering film of fluid. I therefore sought to discover in each instance the entire conductivity by the formula \[ C = \frac{w}{a} \log \frac{V}{v}, \] where, \( a \) being the area of the tube in square feet, and \( w \) the quantity of refrigerating water transmitted per hour, \( C \) represents the number of units of heat, in lbs. of water raised 1°, which would be conducted through a surface of 1 foot area, the opposite sides of which differ from one another by 1°. The determinations of \( C \) in each instance will be found in column 18. I generally obtained observations of the vacuum-gauge directly after the stoppage of the condensation. The results of these, reduced to the value they would have had at the precise time of the closing of the stopcock, are given in column 15 of the Table. The effect of stopping the condensation was generally a diminution of pressure, which took place rapidly at first, and afterwards slowly and with great regularity. I believe that this diminution of pressure is owing to the water collected in the receiver, which, having fallen somewhat in temperature during an experiment, governs the vacuum as soon as the fresh hot condensed water ceases to be supplied to its surface. In some few instances the mercury in the gauge was observed to fall immediately on the stoppage of the condensation. In these the vacuum appeared to be more perfect while the condensation was being carried on than was due to the temperature of the condensed water. It was long before I was able to form any conjecture as to the cause of this anomalous circumstance. I now think that it might have been occasioned by a stricture in the india-rubber junction which connected the gauge with the steam-tube \( p \). It is not, however, easy to see how this can account for the sudden fall of the gauge at the moment of the stoppage of the condensation. In the Table, I have marked those results which I suspect to have been influenced by a contraction at the junction, by a note of interrogation. I may observe that the india-rubber tubulures were frequently renewed, in order to prevent the chance of a stricture, which, moreover, I always endeavoured to detect at its first approach, by observing whether the mercury descended instantaneously on the admission of the first bubble of air into the receiver when the nut was unscrewed. Great care was always taken to keep the flow of steam and refrigerating water as constant as possible during each experiment. If this had not been done, the temperature of the water collected in the receiver during the former part of an experiment would have influenced to a certain extent the vacuum observed at the latter part. It was easy, by first condensing rapidly, and afterwards slowly by partially closing the steam-cock, to maintain for some time a vacuum much more perfect than that due to the temperature of the water in the receiver. In this case "bumping boiling" took place in the receiver, whilst the pressure gradually decreased to the value due to the new conditions. ### Table I | Description | No. | Duration of experiment, in minutes | Total pressure of steam in the boiler, in inches of mercury | Head of refrigerating water above its overflow, in inches | Mean temperature of refrigerating water | |---------------------------------------------------------------------------|-----|-----------------------------------|-------------------------------------------------------------|----------------------------------------------------------|----------------------------------------| | Copper steam-tube, s, 4 feet long, exterior diameter 75 inch, interior 63 inch, mean area a = 7295 sq. ft. Outer tube C 1-4 inch in diameter. Refrigerating water moving in a direction contrary to that of the steam. In the experiments 10–16 the receiver was in communication with the atmosphere. | 1 | 60 | 48·2 | 0·2 | 5·18 | | | | | | | 20·21 | | | 2 | 60 | 41·88 | 0·1 | 5·18 | | | | | | | 40·38 | | | 3 | 30 | 46·23 | 1·13 | 5·15 | | | | | | | 19·21 | | | 4 | 30 | 48·36 | 1·2 | 4·96 | | | | | | | 17·63 | | | 5 | 45 | 91·47 | 0·47 | 4·78 | | | | | | | 16·13 | | | 6 | 37 | 120·14 | 0·66 | 4·81 | | | | | | | 19·19 | | | 7 | 50 | 114·27 | 0·51 | 4·93 | | | | | | | 15·23 | | | 8 | 60 | 39·29 | 0·47 | 4·67 | | | | | | | 13·62 | | | 9 | 52 | 35·68 | 0·54 | 4·7 | | | | | | | 14·17 | | | 10 | 60 | 51·98 | 0·12 | 4·94 | | | | | | | 11·58 | | | 11 | 30 | 45·22 | 0·12 | 5·17 | | | | | | | 31·6 | | | 12 | 30 | 48·02 | 0·48 | 5·12 | | | | | | | 22·02 | | | 13 | 20 | 50·31 | 0·97 | 5·39 | | | | | | | 22·21 | | | 14 | 30 | 54·4 | 0·1 | 5·37 | | | | | | | 48·35 | | | 15 | 20 | 45·6 | 1·35 | 5·12 | | | | | | | 26·1 | | | 16 | 18½ | 50·9 | 1·04 | 5·37 | | | | | | | 29·62 | | The same copper steam-tube. The outer tube 87 inch in interior diameter. Experiments No. 30, 31, 32, and 33 were made when the steam-tube had been recently cleaned by dilute sulphuric acid. Refrigerating water moving in a direction contrary to that of the steam. | 17 | 60 | 44·91 | 4·37 | 6·57 | | | | | | | 16·5 | | | 18 | 60 | 48·8 | 1·4 | 6·22 | | | | | | | 81·08 | | | 19 | 120 | 47·77 | 0·13 | 6·62 | | | | | | | 50·51 | | | 20 | 120 | 45·27 | 0·6 | 6·86 | | | | | | | 25·61 | | | 21 | 50 | 48·71 | 0·49 | 6·36 | | | | | | | 88·08 | | | 22 | 60 | 48·61 | 1·19 | 6·42 | | | | | | | 52·07 | | | 23 | 44 | 45·25 | 6·45 | 6·24 | | | | | | | 27·32 | | | 24 | 19 | 47·1 | 14·07 | 6·04 | | | | | | | 34·48 | | | 25 | 555 | 40·78 | 0·08 | 6·2 | | | | | | | 16·7 | | | 26 | 26½ | 49·86 | 14·73 | 5·36 | | | | | | | 26·94 | | | 27 | 27 | 46·68 | 21·45 | 5·22 | | | | | | | 22·67 | | | 28 | 20 | 51·5 | 23·29 | 5·22 | | | | | | | 26·75 | | | 29 | 435 | 46·27 | 0·63 | 5·22 | | | | | | | 53·73 | | | 30 | 24 | 53·13 | 12·9 | 8·5 | | | | | | | 32·135 | | | 31 | 18½ | 52·09 | 20·12 | 8·4 | | | | | | | 30·014 | | | 32 | 30 | 52·09 | 14·15 | 8·46 | | | | | | | 13·518 | | | 33 | 30 | 53·81 | 11·48 | 8·44 | | | | | | | 20·66 | | Refrigerating water moving in the same direction as the steam. | 34 | 30 | 48·99 | 48 | 8·655 | | | | | | | 22·55 | | | 35 | 15 | 46·51 | 48 | 8·62 | | | | | | | 22·955 | | | 36 | 12 | 46·51 | 48 | 8·62 | | | | | | | 27·78 | | | 37 | 11½ | 49·07 | 48 | 8·63 | | | | | | | 29·739 | | | 38 | 10 | 48·09 | 48 | 8·64 | | | | | | | 29·817 | | The same copper steam-tube. The outer tube 0·8 inch in internal diameter. Experiments 53–61 inclusive, were made when the steam-tube had been recently cleaned with dilute sulphuric acid. Refrigerating water moving in a direction contrary to that of the steam. | 39 | 60 | 43·81 | 12·8 | 6·73 | | | | | | | 38·69 | | | 40 | 60 | 41·32 | 0·1 | 7·27 | | | | | | | 89·146 | | | 41 | 60 | 42·77 | 37·16 | 7·13 | | | | | | | 22·852 | | | 42 | 57 | 43·05 | 35·61 | 6·87 | | | | | | | 47·62 | | | 43 | 60 | 45·78 | 18·33 | 6·95 | | | | | | | 56·784 | | | 44 | 120 | 44·75 | 0·5 | 6·95 | | | | | | | 54·01 | | | 45 | 60 | 45·33 | 9·92 | 6·61 | | | | | | | 35·29 | | | 46 | 60 | 45·06 | 28·58 | 6·67 | | | | | | | 18·353 | | | 47 | 60 | 47·16 | 210·2 | 6·51 | | | | | | | 14·317 | | | 48 | 23 | 50·72 | 232 | 6·47 | | | | | | | 36·732 | | | 49 | 17 | 48·52 | 206·3 | 6·84 | | | | | | | 45·882 | | | 50 | 15 | 51·97 | 211·7 | 6·82 | | | | | | | 47·496 | | | 51 | 14 | 51·67 | 237·2 | 6·82 | | | | | | | 47·371 | | | 52 | 30 | 53·76 | 293·06 | 6·82 | | | | | | | 24·312 | | | 53 | 60 | 62·4 | 28·74 | 7·09 | | | | | | | 25·343 | | | 54 | 30 | 55·06 | 28·6 | 6·7 | | | | | | | 41·49 | # DR. J. P. JOULE ON THE SURFACE-CONDENSATION OF STEAM. ## TABLE I. | | Weight of refrigerating water, in pounds. | Temperature of the condensed water. | Barometer, minus vacuum-gauge, or pressure in the condenser, in inches of mercury. | |-----|------------------------------------------|------------------------------------|----------------------------------------------------------------------------------| | 8 | | Per hour (w) | Total heat of steam. | | 9 | | Per hour | | | 10 | | In the experiment | | | 11 | | In the experiment | | | 12 | | Per hour | | | 13 | | In the experiment | | | 14 | Pressure in the condenser immediately after the conclusion of the experiment. | Temperature due to the pressure in the condenser per Regnault (T-f). | | 15 | Temperature of the refrigerating water at its exit, by the times the vacuum was observed (f). | | 16 | Conductance of heat, per square foot of the surface of the steam-pipe, or log (e_2 - e_1)/(e_2 - e_1). | Values: - **Weight of refrigerating water, in pounds:** - 97·64 - 98·73 - 99·85 - 99·99 - 99·96 - 99·62 - 99·33 - 99·04 - etc. - **Weight of condensed water, in pounds:** - 2·374 - 2·381 - 2·389 - 2·390 - 2·430 - 2·430 - etc. - **Temperature of the condensed water:** - 65·4·6 - 65·6·2 - 65·7·2 - etc. - **Barometer, minus vacuum-gauge, or pressure in the condenser, in inches of mercury:** - 4·16 - 4·66 - 4·96 - 5·16 - etc. - **Pressure in the condenser immediately after the conclusion of the experiment:** - 1·49 - 1·56 - etc. - **Temperature due to the pressure in the condenser per Regnault (T-f):** - 3·40 - 3·49 - etc. - **Temperature of the refrigerating water at its exit, by the times the vacuum was observed (f):** - 2·074 - 2·493 - etc. - **Conductance of heat, per square foot of the surface of the steam-pipe, or log (e_2 - e_1)/(e_2 - e_1):** - 9·813 - 15·45 - etc. --- **MDCCCLXI.** X ### Table I. (continued). | Description | No. | Duration of experiment, in minutes. | Total pressure of steam in the boiler, in inches of mercury. | Head of refrigerating water above its overflow, in inches. | Mean temperature of refrigerating water. | |------------------------------------------------------------------------------|-----|------------------------------------|-------------------------------------------------------------|-----------------------------------------------------------|------------------------------------------| | | | | | | At its entrance (°). | | | | | | | At its exit. | | Experiments 62, 63, and 64 were made with the steam-tube greasy by rubbing it with oil. | 55 | 30 | 53·47 | 26·66 | 6·88 | | Refrigerating water moving in a direction contrary to that of the steam. | 56 | 15 | 49·16 | 34·66 | 6·88 | | | 57 | 30 | 51·97 | 231·4 | 6·82 | | | 58 | 30 | 57·88 | 211·3 | 6·82 | | | 59 | 20 | 58·82 | 233 | 6·82 | | | 60 | 13½ | 60·36 | 235·9 | 6·82 | | | 61 | 10 | 58·41 | 223·5 | 6·82 | | | 62 | 20 | 50·03 | 211 | 6·075 | | | 63 | 15 | 49·62 | 193·5 | 6·075 | | | 64 | 10 | 47·65 | 216 | 6·075 | | The same tubes. | 65 | 60 | 50·89 | 48 | 6·97 | | The steam-tube fresh cleaned. | 66 | 30 | 51·84 | 48 | 6·97 | | Refrigerating water going in the same direction as the steam. | 67 | 15 | 49·49 | 48 | 6·97 | | Lead steam-tube 4 feet long, exterior diameter 0·77 inch, interior 0·52 inch, mean area a = 0·6503 sq. ft. | 68 | 30 | 43·24 | 1·57 | 9·4 | | The outer tube 0·87 inch internal diameter. | 69 | 30 | 41·73 | 4·96 | 9·14 | | Refrigerating water moving in a direction contrary to that of the steam. | 70 | 20 | 42·18 | 13·35 | 9·14 | | In experiments 81, 82, and 83 the receiver was in communication with the atmosphere. | 71 | 30 | 36·5 | 1·47 | 7·34 | | | 72 | 30 | 37·08 | 13·3 | 7·3 | | | 73 | 20 | 36·7 | 25·4 | 7·3 | | | 74 | 30 | 35·17 | 1·24 | 7·28 | | | 75 | 30 | 38·08 | 26·5 | 7·24 | | | 76 | 30 | 44·12 | 29 | 6·44 | | | 77 | 20 | 42·34 | 30 | 6·26 | | | 78 | 27½ | 38·29 | 7·4 | 6·2 | | | 79 | 30 | 37·1 | 0·63 | 6·22 | | | 80 | 60 | 36·7 | 1·0 | 5·0 | | | 81 | 30 | 35·77 | 13·4 | 5·8 | | | 82 | 30 | 34·8 | 18·7 | 5·32 | | | 83 | 30 | 35·04 | 1·3 | 5·0 | | Iron steam-tube 4 feet long, exterior diameter 0·74 inch, interior diameter 0·602 inch, mean area a = 0·7026 sq. ft. Outer tube 0·87 inch internal diameter. Refrigerating water moving contrary to the direction of the steam. | 84 | 15 | 43·5 | 14·8 | 13·54 | | | 85 | 20 | 45·5 | 11·0 | 13·54 | | Copper steam-tube 4 feet long, area 7225 sq. ft. Outer tube 0·87 inch interior diameter. A taper glass rod was placed in the axis of the steam-tube; its length was 40 inches, diameter at thick end 0·55 inch, at thin end 0·3 inch. | 86 | 15 | 52·71 | 48 | 8·52 | | The tapered glass rod with its thin end uppermost. Refrigerating water moving in the same direction as the steam. | 87 | 15 | 57·39 | 48 | 8·52 | | | 88 | 9½ | 58·91 | 48 | 8·47 | | | 89 | 10 | 56·43 | 48 | 8·42 | | The tapered glass rod with its thin end uppermost. Refrigerating water moving in a direction contrary to that of the steam. | 90 | 20 | 48·6 | 10·8 | 8·08 | | | 91 | 15 | 52·85 | 30·25 | 8·02 | | | 92 | 15 | 52·15 | 27·66 | 8·02 | | | 93 | 10 | 52·61 | 32·5 | 7·92 | | The tapered glass rod with its thick end uppermost. Refrigerating water moving in a direction contrary to that of the steam. | 94 | 15 | 48·25 | 32·0 | 7·67 | | | 95 | 15 | 49·12 | 25·66 | 7·67 | | | 96 | 11 | 48·6 | 25·0 | 7·54 | | Copper steam-tube 4 ft. long, area 7225 sq. ft. A spiral consisting of 30 turns of copper wire 1/36th of an inch diameter was wound round it. Half of the spiral was right-handed, the other half left-handed. Outer tube 1·4 inch diameter. Refrigerating water moving in a direction contrary to that of the steam. | 97 | 30 | 53·86 | 1·5 | 16·875 | | | 98 | 20 | 60·27 | 1·0 | 16·65 | | | 99 | 15 | 58·64 | 3·0 | 16·425 | | Copper steam-tube 4 feet long, area 7225 sq. ft. Outer tube 1·4 inch diameter. Spiral of 45 turns of copper wire 21 inch thick between the tubes. Refrigerating water moving contrary to the direction of the steam. | 100 | 30 | 47·42 | 1·95 | 15·547 | | | 101 | 30 | 51·8 | 2·06 | 15·66 | | | 102 | 20 | 59·45 | 1·43 | 15·547 | | | 103 | 14 | 55·96 | 4·7 | 15·48 | | Weight of refrigerating water, in pounds. | Weight of condensed water, in pounds. | |----------------------------------------|-------------------------------------| | In the experiment. | Per hour (w). | In the experiment. | Per hour. | | Temperature of the condensed water. | Total heat of steam. | Barometer, minus vacuum-gauge, or pressure in the condenser, in inches of mercury. | Pressure in the condenser immediately after the conclusion of the experiment. | Temperature due to the pressure in the condenser (col.14) per Regnault (t2). | Temperature of the refrigerating water at its exit, at the times the vacuum was observed (t1). | Conduction of heat, per square foot of the surface of the steam-pipe, or \( \frac{w}{a} \log \left( \frac{t_2 - t_1}{t_2 - t_1} \right) \). | | 64-603 | 129-21 | 6-598 | 13-195 | 67-608 | 625-86 | 9-108 | 9-11 | 69-83 | 63-53 | 411-66 | 55 | | 44-447 | 177-79 | 6-164 | 24-656 | 89-197 | 646-9 | 24-947 | 21-95 | 95 | 84-51 | 523-85 | 56 | | 252-385 | 504-77 | 2-732 | 5-464 | 17-437 | 619-46 | 0-831 | 0-831 | 23-17 | 13-035 | 334-13 | 57 | | 248-947 | 497-9 | 5-567 | 11-135 | 31-841 | 639-27 | 1-622 | 1-592 | 34-73 | 20-136 | 446-82 | 58 | | 181-822 | 545-47 | 7-623 | 22-87 | 50-362 | 646-56 | 3-975 | 3-57 | 51-88 | 21-233 | 589-21 | 59 | | 132-56 | 589-14 | 9-687 | 43-055 | 81-526 | 647-47 | 19-83 | 14-83 | 88-89 | 47-807 | 564-26 | 60 | | 977-79 | 586-75 | 7-828 | 46-969 | 86-612 | 642-98 | 25-01 | ..... | 95-06 | 50-857 | 561-39 | 61 | | 158-2 | 474-59 | 2-466 | 7-398 | 25-952 | 680-13 | 1-115 | 1-065 | 28-13 | 15-8 | 381-96 | 62 | | 123-29 | 493-16 | 5-948 | 23-793 | 58-839 | 650-11 | 7-288 | 5-09 | 64-78 | 34-16 | 444-27 | 63 | | 90-42 | 542-5 | 7-458 | 44-747 | 87-877 | 636-57 | 27-27 | 19-97 | 97-42 | 50-112 | 494-05 | 64 | | 150-75 | 150-75 | 5-014 | 5-014 | 28-287 | 624-68 | 1-817 | 1-81 | 36-78 | 26-808 | 228-48 | 65 | | 92-44 | 184-88 | 6-524 | 13-047 | 56-1 | 633-66 | 5-448 | 4-848 | 58-44 | 48-162 | 412-24 | 66 | | 53-187 | 212-75 | 6-451 | 25-805 | 85-906 | 616-42 | 22-77 | 19-37 | 92-54 | 71-317 | 410-55 | 67 | | 14-785 | 29-57 | 1-608 | 3-216 | 65-113 | 598-77 | 10-06 | ..... | 72-13 | 67-185 | 115-51 | 68 | | 77-582 | 155-16 | 6-691 | 13-382 | 78-951 | 671-41 | 18-22 | ..... | 86-7 | 60-235 | 256-55 | 69 | | 139-27 | 417-82 | 7-394 | 22-183 | 81-184 | 694-63 | 21-53 | ..... | 91-05 | 42-08 | 330-53 | 70 | | 16-883 | 33-77 | 1-943 | 3-886 | 74-253 | 624-33 | 11-45 | ..... | 9-45 | 75-19 | 71-09 | 145-75 | 71 | | 197-03 | 394-07 | 7-271 | 14-542 | 66-22 | 644-6 | 9-28 | ..... | 9-28 | 70-25 | 287-3 | 72 | | 218-47 | 655-42 | 9-249 | 27-748 | 81-92 | 634-83 | 21-07 | ..... | 17-1 | 90-48 | 30-89 | 336-18 | 73 | | 16-109 | 32-218 | 2-268 | 4-535 | 84-59 | 598-78 | 16-56 | ..... | 14-26 | 84-86 | 79-53 | 138-2 | 74 | | 312-03 | 624-07 | 1-323 | 2-647 | 18-526 | 710-4 | 1-18 | ..... | 29-11 | 9-955 | 127-19 | 75 | | 328-03 | 656-07 | 2-133 | 4-266 | 15-613 | 712-49 | 1-145 | ..... | 1-425 | 28-59 | 10-65 | 212-67 | 76 | | 264-66 | 793-98 | 9-063 | 27-19 | 78-337 | 666-49 | 15-73 | ..... | 82-96 | 26-1 | 365-43 | 77 | | 101-35 | 221-12 | 9-608 | 20-96 | 88-926 | 631-81 | 27-73 | ..... | 18-7 | 97-89 | 57-67 | 280-2 | 78 | | 15-472 | 30-94 | 2-635 | 5-27 | 88-67 | 575-78 | 25-27 | ..... | 18-07 | 95-34 | 89-19 | 127-19 | 79 | | 18-16 | 18-16 | 1-743 | 1-743 | 60-687 | 640-94 | 6-87 | ..... | 63-46 | 60-7 | 85-27 | 80 | | 162-72 | 325-44 | 2-866 | 4-73 | 20-088 | 662-31 | 29-79 | ..... | 99-88 | 15-14 | ..... | 81 | | 237-66 | 475-32 | 2-991 | 5-982 | 18-907 | 659-18 | 29-82 | ..... | 99-9 | 13-46 | ..... | 82 | | 11-472 | 22-944 | 1-642 | 3-284 | 35-552 | 634-12 | 30-02 | ..... | 100-1 | 90-68 | ..... | 83 | | 139 | 556 | 6-608 | 26-432 | 94-07 | 626-47 | 28-52 | 23-02 | 98-66 | 38-85 | 279-24 | 84 | | 152-2 | 456-6 | 7-917 | 23-751 | 89-09 | 641-98 | 29-54 | 22-64 | 99-64 | 42-3 | 264-16 | 85 | | 137-812 | 551-25 | 4-628 | 18-512 | 50-701 | 634-76 | 4-329 | 3-93 | 53-63 | 28-131 | 435-25 | 86 | | 323-68 | 1294-72 | 7-804 | 31-218 | 54-454 | 617-12 | 5-979 | 5-31 | 60-44 | 22-037 | 540-42 | 87 | | 204-25 | 1290 | 9-718 | 61-379 | 88-654 | 629-53 | 26-244 | ..... | 96-37 | 33-955 | 611-33 | 88 | | 222-94 | 1337-64 | 8-023 | 48-136 | 75-579 | 643-42 | 15-601 | 13-1 | 82-75 | 28-441 | 581-02 | 89 | | 195-1 | 585-3 | 4-408 | 13-224 | 30-844 | 631-12 | 4-354 | 3-4 | 53-74 | 21-346 | 278-07 | 90 | | 246-41 | 985-64 | 3-997 | 15-987 | 39-706 | 644-99 | 2-543 | 1-84 | 43-07 | 17-564 | 433-62 | 91 | | 240-97 | 963-88 | 8-176 | 32-706 | 67-187 | 649-06 | 11-122 | 9-39 | 74-49 | 27-434 | 460-81 | 92 | | 205-04 | 1230-24 | 9-166 | 54-993 | 86-363 | 646-65 | 23-188 | 20-19 | 93-03 | 32-607 | 583-32 | 93 | | 251-97 | 1007-88 | 4-682 | 18-726 | 38-804 | 658-63 | 6-201 | 2-15 | 61-23 | 18-828 | 325-87 | 94 | | 216-1 | 864-4 | 1-825 | 7-301 | 23-365 | 671-96 | 2-375 | 0-775 | 41-77 | 12-834 | 196-48 | 95 | | 172-67 | 941-84 | 9-021 | 49-208 | 84-147 | 651-34 | 25-779 | 19-28 | 95-88 | 36-556 | 519-07 | 96 | | 281-89 | 563-78 | 5-905 | 11-81 | 49-357 | 645-62 | 4-041 | ..... | 52-216 | 29-273 | 337-12 | 97 | | 220-546 | 661-64 | 9-103 | 27-31 | 75-963 | 654-81 | 14-45 | ..... | 80-84 | 40-6 | 427-66 | 98 | | 195-827 | 783-31 | 9-503 | 38-01 | 88-09 | 655-18 | 24-49 | ..... | 94-5 | 44-09 | 474-29 | 99 | | 301-116 | 602-232 | 4-377 | 8-754 | 33-382 | 670-11 | 1-545 | ..... | 33-86 | 24-792 | 586-25 | 100 | | 288-678 | 577-356 | 7-891 | 15-783 | 48-75 | 657-31 | 4-222 | ..... | 53-11 | 32-523 | 478-15 | 101 | | 182-162 | 546-486 | 9-125 | 27-375 | 74-834 | 653-01 | 13-65 | ..... | 79-44 | 45-14 | 470-53 | 102 | | 186-022 | 797-24 | 9-692 | 41-537 | 86-059 | 652-0 | 23-214 | ..... | 93-06 | 45-16 | 532-07 | 103 | x 2 ### Table I. (continued). | Description | No. | Duration of experiment, in minutes. | Total pressure of steam in the boiler, in inches of mercury. | Head of refrigerating water above its overflow, in inches. | Mean temperature of refrigerating water. | |------------------------------------------------------------------------------|-----|------------------------------------|-------------------------------------------------------------|----------------------------------------------------------|------------------------------------------| | Copper steam-tube 4 feet long, area '7225 sq. ft. Outer tube 1 inch interior diameter. Between the tubes there was a spiral of 103 convolutions, composed of copper wire '105 inch thick. Refrigerating water moving in a direction contrary to that of the steam. | 104 | 30 | 39-99 | 21-94 | 14-085 | 36-025 | | | 105 | 30 | 42-01 | 24-36 | 14-04 | 61-013 | | | 106 | 20 | 45-15 | 245 | 13-95 | 37-583 | | | 107 | 15 | 42-1 | 270 | 13-59 | 48-768 | | | 108 | 12 | 45-63 | 257 | 13-59 | 51-97 | | | 109 | 50 | 50-35 | 66-9 | 13-567 | 33-782 | | | 110 | 80 | 40-6 | 58 | 13-545 | 46-27 | | Refrigerating water moving in the same direction with the steam. | 111 | 30 | 50-14 | 48 | 12-44 | 23-135 | | | 112 | 30 | 56-3 | 48 | 12-44 | 40-29 | | | 113 | 30 | 57-66 | 48 | 12-6 | 54-32 | | Copper steam-tube 2 feet long. Interior diameter '63 inch, exterior '75 inch, mean area a='3612 sq. ft. Outer tube, interior diameter 1 inch. Between the tubes there was a spiral consisting of 50 convolutions of copper wire '105 inch thick. Refrigerating water moving in the same direction as the steam. | 114 | 30 | 52-48 | 24 | 12-29 | 26-8 | | | 115 | 30 | 45-42 | 24 | 10-935 | 27-46 | | | 116 | 30 | 48-34 | 24 | 11-07 | 23-17 | | | 117 | 30 | 50-9 | 24 | 11-07 | 28-08 | | | 118 | 30 | 44-02 | 24 | 9-88 | 41-1 | | | 119 | 30 | 44-125 | 24 | 10-17 | 45-73 | | | 120 | 30 | 42-61 | 24 | 10-17 | 59-27 | | Refrigerating water moving in a direction contrary to that of the steam. | 121 | 15 | 44-32 | 176 | 8-01 | 12-93 | | | 122 | 14 | 46-15 | 207 | 8-01 | 22-856 | | | 123 | 15 | 37-96 | 193 | 8-01 | 29-825 | | | 124 | 30 | 44-41 | 8-4 | 7-2 | 23-07 | | | 125 | 30 | 43-84 | 4-47 | 7-2 | 48-74 | | | 126 | 30 | 45-22 | 5-8 | 7-72 | 66-31 | | Copper steam-tube 4 feet long. Interior diameter '63 inch, exterior diameter '75 inch, mean area a='7225 sq. ft. Outer tube, interior diameter 1 inch. Between the tubes there was a spiral consisting of 96 convolutions of copper wire '105 inch thick. Refrigerating water moving in a contrary direction to the steam. | 127 | 30 | 42-14 | 274 | 3-64 | 16-48 | | | 128 | 30 | 45-37 | 248 | 3-64 | 29-93 | | | 129 | 20 | 46-37 | 218 | 3-65 | 51-19 | | Refrigerating water moving in the same direction as the steam. | 130 | 30 | 46-38 | 48 | 3-51 | 32-02 | | | 131 | 30 | 52-24 | 48 | 3-51 | 42-02 | | | 132 | 20 | 49-07 | 48 | 3-51 | 71-81 | | Copper steam-tube 6 feet long. Interior diameter '63 inch, exterior diameter '75 inch, mean area a='1-0837 sq. ft. Interior diameter of the outer tube 1 inch. Between the tubes there was a spiral consisting of 143 convolutions of copper wire '105 inch thick. Refrigerating water moving in a direction contrary to that of the steam. | 133 | 30 | 39-2 | 22-1 | 5-53 | 82-25 | | | 134 | 30 | 38-43 | 24 | 5-65 | 57-77 | | | 135 | 30 | 41-06 | 22-6 | 5-76 | 38-22 | | | 136 | 30 | 47-75 | 341 | 4-95 | 29-72 | | | 137 | 30 | 45-43 | 315 | 4-905 | 32-84 | | | 138 | 30 | 51-01 | 279 | 3-87 | 42-52 | | | 139 | 20 | 44-8 | 261 | 3-87 | 67-27 | | | 140 | 15 | 45-6 | 250 | 3-85 | 77-45 | | | 141 | 30 | 42-67 | 301 | 2-65 | 32-07 | | | 142 | 30 | 42-02 | 301 | 2-65 | 32-96 | | | 143 | 30 | 39-34 | 327 | 3-28 | 37-69 | | | 144 | 30 | 41-62 | 337 | 3-28 | 28-22 | | Refrigerating water moving in the same direction as the steam. | 145 | 30 | 43-88 | 72 | 4-3 | 41-8 | | | 146 | 30 | 43-28 | 72 | 4-3 | 50-32 | | | 147 | 30 | 41-11 | 72 | 4-3 | 76-47 | | Iron steam-tube 4 feet long. Exterior diameter '74 inch, interior diameter '602 inch. Interior diameter of the outer tube '87 inch. A spiral consisting of 55 convolutions of copper wire '055 inch thick was placed between the tubes. Refrigerating water moving in a direction opposite to that of the steam. | 148 | 30 | 37-65 | 48 | 4-72 | 31-11 | | | 149 | 30 | 37-84 | 48 | 4-72 | 61-27 | | Refrigerating water moving in the same direction as the steam. | 150 | 30 | 40-33 | 282 | 4-2 | 21-32 | | | 151 | 20 | 40-57 | 265 | 4-2 | 42-7 | | 8. | 9. | 10. | 11. | 12. | 13. | 14. | 15. | 16. | 17. | 18. | 19. | |------|------|------|------|------|------|------|------|------|------|------|------| | Weight of refrigerating water, in pounds. | Weight of condensed water, in pounds. | Temperature of the condensed water. | Total heat of steam. | Barometer minus vacuum gauge, or pressure in the condenser, in inches of mercury. | Pressure in the condenser immediately after the conclusion of the experiment. | Temperature due to the pressure in the condenser (col. 14) per Regnault (t₁). | Temperature of the refrigerating water at its exit, at the times the vacuum was observed (t₂). | Conduction of heat, per square foot of the surface of the steam pipe, or \( \frac{w}{a} \log \left( \frac{t_2 - t_1}{t_2 + t_1} \right) \). | | In the experiment. | Per hour (w). | In the experiment. | Per hour. | | | | | | | No. | | 86-996 | 173-99 | 3-15 | 6-3 | 36-208 | 642-14 | 1-343 | 1-74 | 31°-37° | 36°-441 | …… | 104 | | 98-037 | 196-07 | 7-628 | 15-256 | 60-985 | 664-7 | 6-566 | 6-53 | 62-47 | 60-931 | 935°-8 | 105 | | 208-775 | 626-32 | 7-965 | 23-894 | 43-349 | 657-79 | 2-287 | 3-18 | 41°-06° | 37°-136 | …… | 106 | | 161-15 | 644-6 | 9-617 | 38-47 | 66-068 | 653-06 | 9-715 | 7-14 | 71°-31 | 48°-176 | 815°-87 | 107 | | 132-525 | 662-62 | 8-68 | 43-4 | 73-931 | 657-8 | 13-518 | 11-42 | 79°-2 | 51°-715 | 798°-15 | 108 | | 147-9 | 177-48 | 4-736 | 5-683 | 34-968 | 666-26 | 1-084 | 1-784 | 27°-65° | 36°-113 | …… | 109 | | 145-15 | 108-86 | 7-836 | 5-877 | 41-66 | 647-84 | 2-391 | 3-69 | 41°-9 | 48°-23 | …… | 110 | | 87-375 | 174-75 | 1-648 | 3-296 | 29-64 | 596-68 | 0-798 | 0-898 | 22°-5 | 23°-755 | …… | 111 | | 73-343 | 146-68 | 3-698 | 7-396 | 45-52 | 597-88 | 1-57 | 3-01 | 34°-142 | 41°-13 | …… | 112 | | 98-25 | 196-5 | 7-456 | 14-912 | 59-77 | 609-53 | 4-85 | 6-95 | 56°-0 | 55°-824 | …… | 113 | | 84-44 | 168-88 | 2-108 | 4-216 | 31-9 | 613-1 | 0-92 | …… | 24°-86 | 26°-856 | …… | 114 | | 100-94 | 201-88 | 2-612 | 5-224 | 32-71 | 671-51 | 1-496 | 1-496 | 33°-28 | 27°-2 | …… | 115 | | 100-87 | 201-74 | 1-902 | 3-804 | 29-99 | 671-7 | 1-116 | 1-686 | 28°-14 | 23°-27 | 700°-44 | 116 | | 55-19 | 110-38 | 1-456 | 2-912 | 31-92 | 676-7 | 1-286 | 1-34 | 30°-6 | 27°-87 | 601°-2 | 117 | | 86-82 | 173-64 | 4-413 | 8-836 | 48-46 | 662-67 | 3-44 | 4-34 | 48°-97 | 41°-07 | 768°-58 | 118 | | 109-63 | 219-26 | 6-368 | 12-736 | 58-018 | 670-22 | 5-741 | 6-84 | 59°-56 | 43°-57 | 684°-5 | 119 | | 102-74 | 205-48 | 8-708 | 17-416 | 79-96 | 639-25 | 15-924 | 17-124 | 83°-27 | 59°-39 | 636°-38 | 120 | | 172-9 | 691-6 | 1-105 | 4-42 | 22-21 | 756-76 | 0-67 | 0-9 | 19°-65 | 12°-22 | 859°-4 | 121 | | 199-65 | 855-6 | 4-845 | 20-764 | 54-14 | 661-32 | 4-57 | …… | 54°-75 | 22°-406 | 872°-28 | 122 | | 194-28 | 777-1 | 7-399 | 29-596 | 78-14 | 649-52 | 15-61 | …… | 82°-77 | 29°-553 | 731°-1 | 123 | | 67-9 | 135-8 | 1-732 | 3-464 | 27-87 | 650-02 | 1-126 | 0-946 | 28°-3 | 23°-17 | 531°-59 | 124 | | 58-53 | 117-66 | 4-155 | 8-31 | 60-86 | 646-05 | 5-837 | 5-83 | 59°-92 | 49°-41 | 522°-6 | 125 | | 67-03 | 134-06 | 7-295 | 14-59 | 80-14 | 618-59 | 17-033 | 17-03 | 84°-97 | 66°-56 | 532°-54 | 126 | | 166-59 | 333-18 | 3-454 | 6-908 | 14-03 | 633-32 | 0-682 | 0-682 | 19°-95 | 16°-48 | 713°-7 | 127 | | 173-59 | 347-18 | 7-395 | 14-79 | 28-68 | 645-81 | 1-699 | 1-94 | 35°-56 | 29°-93 | 833°-78 | 128 | | 108-9 | 326-7 | 8-721 | 26-163 | 56-12 | 649-76 | 5-555 | 5-205 | 58°-86 | 51°-19 | 892°-52 | 129 | | 65-44 | 130-88 | 3-141 | 6-282 | 33-32 | 627-3 | 1-722 | 1-722 | 35°-8 | 32°-02 | 388°-56 | 130 | | 68-0 | 136 | 4-433 | 8-866 | 42-27 | 632-99 | 2-717 | 2-717 | 44°-34 | 42°-38 | 571°-56 | 131 | | 47-87 | 143-61 | 5-906 | 17-718 | 74-47 | 628-06 | 12-173 | 11-173 | 76°-65 | 71°-81 | 539°-75 | 132 | | 37-26 | 74-52 | 5-26 | 10-592 | 79-24 | 622-7 | 16-377 | 15-852 | 83°-98 | 82°-25 | 262°-27 | 133 | | 35-14 | 70-28 | 3-099 | 6-198 | 56-4 | 647-72 | 5-159 | …… | 57°-29 | 57°-77 | …… | 134 | | 31-57 | 63-14 | 1-593 | 3-186 | 35-8 | 678-93 | 1-855 | 1-875 | 37°-16 | 38°-22 | …… | 135 | | 133-01 | 266-02 | 5-266 | 10-532 | 23-82 | 649-47 | 1-345 | 1-245 | 31°-4 | 29°-72 | 676°-6 | 136 | | 123-45 | 246-9 | 5-54 | 11-08 | 22-09 | 644-58 | 1-594 | 1-694 | 34°-41 | 32°-8 | 662°-57 | 137 | | 124-64 | 249-28 | 7-894 | 15-788 | 33-17 | 643-42 | 2-634 | 3-034 | 43°-74 | 42°-52 | 802°-02 | 138 | | 76-88 | 230-64 | 8-266 | 24-798 | 64-68 | 654-34 | 8-458 | 8-258 | 68°-13 | 67°-27 | 918°-05 | 139 | | 60-01 | 240-04 | 7-627 | 30-508 | 72-49 | 651-58 | 13-293 | 12-49 | 78°-79 | 77°-45 | 891°-3 | 140 | | 129-2 | 258-4 | 6-149 | 12-298 | 23-58 | 641-74 | 1-468 | 1-48 | 32°-94 | 32°-07 | 846°-46 | 141 | | 125-57 | 251-14 | 6-116 | 12-232 | 28-55 | 650-86 | 1-596 | 1-55 | 34°-44 | 32°-96 | 710°-76 | 142 | | 128-76 | 257-52 | 7-21 | 14-42 | 28-743 | 643-25 | 2-106 | 2-206 | 39°-51 | 37°-69 | 710°-74 | 143 | | 125-82 | 251-64 | 5-018 | 10-036 | 19-973 | 645-31 | 1-2 | 1-2 | 29°-4 | 28°-22 | 719°-16 | 144 | | 65-25 | 130-5 | 4-157 | 8-314 | 40-9 | 629-53 | 2-649 | 2-75 | 43°-86 | 41°-8 | 355°-84 | 145 | | 63-18 | 126-36 | 5-043 | 10-086 | 49-6 | 626-15 | 3-922 | 3-72 | 51°-6 | 50°-32 | 420°-87 | 146 | | 68-87 | 137-74 | 9-133 | 18-266 | 75-17 | 619-37 | 13-11 | 11-11 | 78°-45 | 76°-47 | 460°-48 | 147 | | 59-5 | 119-0 | 2-571 | 5-142 | 32-82 | 643-56 | 1-601 | 1-6 | 34°-49 | 31°-11 | 368°-43 | 148 | | 68-92 | 137-84 | 6-817 | 13-634 | 65-61 | 637-33 | 8-392 | 8-0 | 67°-95 | 61°-27 | 440°-92 | 149 | | 169-64 | 339-28 | 4-857 | 9-714 | 28-05 | 626-0 | 1-412 | 1-41 | 32°-25 | 21°-32 | 455°-08 | 150 | | 116-89 | 349-17 | 7-786 | 23-358 | 62-45 | 637-97 | 7-192 | 6-69 | 64°-48 | 42°-7 | 505°-87 | 151 | On a cursory examination of the Table, it will become evident that the numbers in column 18, representing the conducting power, increase as the space between the tubes, which serves to convey the refrigerating water, is contracted. It will also be noted that an increase of conduction likewise takes place when the quantity of water transmitted between the same tubes is augmented. I will begin by arranging the results so as to show the effect of altering the velocity of the refrigerating water. Series 1.—Copper steam-tube. Water space between tubes 0·325 inch. | No. of experiment | Quantity of refrigerating water | Conductivity | |------------------|--------------------------------|--------------| | 1 | 97·6 | 98·1 | | 2 | 94·7 | 158·4 | | 5 | 591 | 152·2 | | 7 | 594·4 | 139·6 | | 8 | 597 | 149·4 | | 6 | 631·8 | 138·8 | | 9 | 658 | 184·3 | | 3 | 758·9 | 151·6 | | 4 | 798·2 | 172·5 | Series 2.—Copper steam-tube. Water space between tubes 0·06 inch. | No. of experiment | Quantity of refrigerating water | Conductivity | |------------------|--------------------------------|--------------| | 29 | 16·37 | 80·9 | | 25 | 18·07 | 29·26 | | 18 | 20·41 | 89·62 | | 19 | 43·57 | 143·9 | | 20 | 61·16 | 155·9 | | 21 | 99·24 | 152·67 | | 22 | 76·5 | 279·8 | | 17 | 124·5 | 198·5 | | 23 | 189·47 | 193·8 | | | 343·1 | 202·3 | | 26 | 592·3 | 297·4 | | 30 | 606·3 | 332·8 | | 33 | 611·7 | 300·4 | | 24 | 612·8 | 335·6 | | 32 | 689·04 | 334·31 | | 27 | 739·8 | 256·3 | | 28 | 767·2 | 342·5 | | 31 | 797·3 | 353·6 | Series 3.—Copper steam-tube. Water space between tubes 0·025 inch. | No. of experiment | Quantity of refrigerating water | Conductivity | |------------------|---------------------------------|--------------| | 44 | 11·2 | 53·1 | | 40 | 21·4 | 84·5 | | 39 | 57·5 | 255·6 | | 45 | 45·3 | 257·1 | | 46 | 91·2 | 239·1 | | 43 | 99·4 | 289·4 | | 53 | 103·3 | 305·9 | | 54 | 117·4 | 354·7 | | 55 | 129·2 | 411·7 | | 41 | 133·4 | 303·4 | | 42 | 155 | 303·1 | | 56 | 177·8 | 523·8 | | 47 | 455 | 198·5 | | 63 | 493·2 | 444·3 | | 58 | 497·9 | 446·8 | | 57 | 504·8 | 334·1 | | 49 | 511·1 | 491 | | 48 | 523·1 | 473·3 | | 50 | 533·2 | 498·6 | | 59 | 545·5 | 589·2 | | 51 | 572·5 | 512·7 | | 61 | 586·7 | 561·4 | | 60 | 589·1 | 564·3 | | 52 | 622 | 370·5 | Series 4.—Lead steam-tube. Water space between tubes 0·05 inch. | No. of experiment | Quantity of refrigerating water | Conductivity | |------------------|---------------------------------|--------------| | 80 | 18·2 | 85·27 | | 68 | 29·6 | 115·51 | | 79 | 30·9 | 127·2 | | 74 | 32·2 | 138·2 | | 71 | 33·8 | 145·7 | | 69 | 155·2 | 256·5 | | 78 | 221·1 | 280·2 | | 72 | 394·1 | 252·2 | | 70 | 417·8 | 330·5 | | 75 | 624·1 | 127·2 | | 73 | 655·4 | 336·2 | | 76 | 656·1 | 212·7 | | 77 | 794 | 365·4 | We deduce from the averages in Series 1 . . . . . $C \propto w^{\frac{1}{3·26}}$. " 2 . . . . . $C \propto w^{\frac{1}{2·47}}$. " 3 . . . . . $C \propto w^{\frac{1}{3·57}}$. " 4 . . . . . $C \propto w^{\frac{1}{4·14}}$. Suppose we take the average index, then $C \propto w^{3/25}$ will express the influence of the quantity of refrigerating water on the conductivity with sufficient accuracy. But it is evident that this relation can only be relied on between certain limits, indicated pretty plainly by the experiments. The influence of a change in the quantity of refrigerating water is doubtless gradually lessened as the flow is increased, and ultimately at a very high velocity the conductivity must necessarily reach a constant value. To find the influence of the extent of the water space, successively narrowed by diminishing the diameter of the outside tube, we will select those experiments in which the flow of water was nearly the same in quantity. | Width of water space between the tubes. | No. | Quantity of refrigerating water. | Conductivity. | |----------------------------------------|-----|---------------------------------|--------------| | 0·325 inch. | 5 | 591·01 | 152·24 | | | 6 | 631·85 | 184·3 | | | 7 | 594·47 | 149·44 | | | 8 | 597·01 | 138·79 | | | 9 | 657·99 | 151·6 | | 0·06 inch. | 24 | 612·82 | 335·65 | | | 26 | 592·3 | 297·38 | | | 30 | 606·33 | 332·85 | | | 32 | 691·67 | 256·3 | | | 33 | 611·69 | 300·41 | | 0·025 inch. | 48 | 523·12 | 473·3 | | | 49 | 511·08 | 490·99 | | | 50 | 533·23 | 498·64 | | | 51 | 572·52 | 512·66 | | | 52 | 621·95 | 370·49 | | | 57 | 504·77 | 334·13 | | | 59 | 545·47 | 589·21 | | | 60 | 589·14 | 564·26 | | | 61 | 586·75 | 561·39 | Reducing the conductivity in each case to the flow of 618 lbs. of water, by the rule just found, we deduce for the spaces ·325, ·06, and ·025, the conductivities 156, 303·7, and 504·4 respectively. Whence, for the circumstances of the experiments, it follows that $$C \propto S^{1/2185}.$$ The above laws are neither exact, nor universal in their application, but they afford the means of estimating the probable amount of benefit to be anticipated from increasing the rapidity of the refrigerating stream in such tubes as I have employed, which are indeed of the dimensions most likely to be practically adopted. I pass now to the consideration of the effect of cleanliness of surface. In the experiments 62, 63, and 64, the outside of the copper steam-tube was made greasy by rubbing it with oil. In the five immediately preceding these the tube was kept perfectly clean, so that water readily adhered to it. The conductivity with the oiled tube, reduced to 544·8 lbs. of refrigerating water by means of the relation we have deduced, will be 450·6: the closeness of this number to 499·16 shows that the influence of a greasy surface is inconsiderable. The experiments 86 to 96 inclusive, are proper to determine whether any effect can be produced by placing a solid in the axis of the steam-tube. Selecting similar experiments, with the exception that the core was not present, we have The conductivity in the last instance, reduced to 940 lbs. of refrigerating water, will be 367·1, a number which does not differ sufficiently from 439 and 347 to lead us to expect any practical advantage from narrowing the steam space. Let us now inquire into the effect of changing the direction in which the refrigerating water was transmitted. Its usual direction was contrary to that of the steam and condensed water; but by removing the pipe E (see figure) and pouring the water into the upper part of the outer tube C, it could be made to flow in the same direction. The experiments suitable for ascertaining the effect of changing the direction of flow are collected in the following Tables:— MDCCCLXI. Series 1.—Thickness of water space 0·06 inch. | Direction of water | No. | Quantity of refrigerating water | Conductivity | |--------------------|-----|---------------------------------|--------------| | Contrary to the steam. | 24 | 612·82 | 335·65 | | | 27 | 739·8 | 342·5 | | | 28 | 767·16 | 353·6 | | | 30 | 606·33 | 332·85 | | | 31 | 797·34 | 332·89 | | | 32 | 691·69 | 408·89 | | | 33 | 611·69 | 256·3 | | The same as that of the steam. | 34 | 657·25 | 522·1 | | | 35 | 1244 | 466·96 | | | 36 | 1292·2 | 474·32 | | | 37 | 1302·1 | 486·94 | | | 38 | 1296 | 491·56 | Series 2.—Thickness of water space 0·025 inch. | Direction of water | No. | Quantity of refrigerating water | Conductivity | |--------------------|-----|---------------------------------|--------------| | Contrary to the steam. | 41 | 133·45 | 303·45 | | | 42 | 155·04 | 303·08 | | | 53 | 103·32 | 305·89 | | | 54 | 117·42 | 354·74 | | | 55 | 129·21 | 367·11 | | | 56 | 177·79 | 411·66 | | The same as that of the steam. | 65 | 150·75 | 228·48 | | | 66 | 184·88 | 412·24 | | | 67 | 212·75 | 350·42 | Thus with the refrigerating water flowing in a direction opposite to that of the steam, we have the conductivities 332·89 and 367·11; whilst with the water flowing in the same direction as the steam, we have the conductivities (referred to the same quantities of refrigerating water) 417·3 and 320·96. The means for the two directions are 350 and 369·13, whence we may conclude that the conductivity is little influenced by the direction in which the water flows. We will now consider the influence of the kind of metal of which the steam-tubes were made. In the Table will be found results obtained with tubes of copper, iron, and lead. The water spaces around the copper, iron, and lead tubes were respectively .06, .065, and .05 inch wide. By reducing all the mean results to the space .06 and 640.25 lbs. of water by means of the formulae we have already deduced, we obtain for the conducting power with the three tubes the numbers 314.4, 302.2, and 255.1 respectively. Taking into account the thickness of the metal, which was .06 in the copper, .069 in the iron, and .125 in the lead tube, we arrive at the conclusion that the resistance to conduction through the metal itself is so small in comparison with the resistance at the bounding surface of the metal and through the adhering films of water (inside as well as outside of the steam-tube), as to be almost inappreciable. We have seen that the tendency of the water flowing between the tubes is to adhere to their sides, and that a head of water of considerable height is required in order to give the water sufficient velocity to remove the adhering film rapidly. It seemed possible that part of the force due to the head might be employed for the purpose of agitating the water. I have not yet found an opportunity to construct an apparatus for this purpose, but it occurred to me that the same object might be attained by placing a wire bent into the form of a spiral between the tubes. By this means the water would be impelled in a spiral direction, which would contribute largely to the rapid intermixture of the particles of water as they advanced. Accordingly, in experiments 97, 98, and 99, this arrangement was tried for the first time. The spiral (in these three experiments only) was half of it left-handed, and the other half right-handed, so that the rotatory motion produced by the first half was reversed in the second. Although the thickness of the wire which formed the spiral was only one-third of the width of the water space in which it was placed, the effect it produced was marked, as the following results testify:— If we contrast these results with those obtained with the same tubes unfurnished with spirals, we shall find proving that a great increase of conductivity was obtained by the use of the spiral, without entailing the necessity of a much higher head of water. The effect of increasing the velocity of the spirally directed refrigerating water will appear from the following experiments: whence we find $C \propto (W)^{1/4.078}$. By classifying the experiments so as to show the comparative effect of transmitting the refrigerating stream in the same direction with, and opposite to, the steam and condensed water, we obtain the following Table:— | Description | No. | Quantity of refrigerating water | Conductivity | |--------------------------------------------------|-----|---------------------------------|--------------| | Copper steam-tube 2 feet long. | | | | | Water in the same direction with the steam. | 115 | 201·88 | 727·53 | | | 116 | 201·74 | 700·44 | | | 117 | 110·38 | 601·2 | | | 118 | 173·64 | 768·58 | | | 119 | 219·26 | 684·5 | | | 120 | 205·48 | 636·38 | | Copper steam-tube 2 feet long. | | | | | Water moving in the opposite direction to the | 121 | 691·6 | 859·4 | | steam. | 122 | 855·6 | 872·28 | | | 123 | 777·1 | 731·1 | | | 124 | 135·8 | 531·59 | | | 125 | 117·06 | 522·6 | | | 126 | 134·06 | 532·54 | | Copper steam-tube 4 feet long. | | | | | Water in the same direction as the steam. | 130 | 130·88 | 388·56 | | | 131 | 136 | 571·56 | | | 132 | 143·61 | 499·29 | | Copper steam-tube 4 feet long. | | | | | Water in the contrary direction. | 127 | 333·18 | 713·7 | | | 128 | 347·18 | 833·78 | | | 129 | 326·7 | 892·52 | | Copper steam-tube 6 feet long. | | | | | Water in the same direction as the steam. | 145 | 130·5 | 355·84 | | | 146 | 126·36 | 420·87 | | | 147 | 137·74 | 412·4 | | Copper steam-tube 6 feet long. | | | | | Water in the contrary direction. | 136 | 266·02 | 676·6 | | | 137 | 246·9 | 662·57 | | | 138 | 249·28 | 802·02 | | | 139 | 230·64 | 918·05 | | | 140 | 240·04 | 891·3 | | | 141 | 258·4 | 846·46 | | | 142 | 251·14 | 710·76 | | | 143 | 257·52 | 710·74 | | | 144 | 251·64 | 719·16 | | Iron steam-tube 4 feet long. | | | | | Water in the same direction as the steam. | 148 | 119 | 368·43 | | | 149 | 137·84 | 440·92 | | Iron steam-tube 4 feet long. | | | | | Water in the opposite direction. | 150 | 339·28 | 455·08 | | | 151 | 349·17 | 505·87 | The above mean results are collected and averaged as follows: | Direction of stream. | Quantity of water. | Conductivity | |----------------------|--------------------|--------------| | With the steam. | | | | | 185·4 | 686·44 | | | 136·83 | 499·29 | | | 131·53 | 412·4 | | | 128·42 | 500·7 | | Contrary to the steam.| | | | | 451·87 | 674·92 | | | 335·69 | 813·33 | | | 250·17 | 770·85 | | | 344·22 | 684·89 | The conductivities for the different directions of the flow of refrigerating water will therefore be $500 \cdot 7$ and $\left(\frac{145 \cdot 54}{345 \cdot 49}\right)^{\frac{1}{4 \cdot 078}} \times 684 \cdot 89 = 554 \cdot 06$. The difference between the two values is not great. If we average them with the results obtained when the tubes were not furnished with spirals, we shall obtain the following result: | Tubes employed. | Conductivity. Water going in the same direction. | Conductivity. Water going opposite to the steam. | Ratio of conductivities. | |-----------------|--------------------------------------------------|--------------------------------------------------|--------------------------| | Plain | 369 \cdot 13 | 350 | 0 \cdot 9482 | | Furnished with spirals. | 500 \cdot 7 | 554 \cdot 06 | 1 \cdot 1065 | | Mean | ....... | ....... | 1 \cdot 0273 | showing a trifling advantage on the side of the arrangement in which the refrigerating water goes in a contrary direction to the steam and condensed water, which is, however, too small to be attributed to anything beyond experimental errors. The quantity of transmitted water being, *ceteris paribus*, nearly proportional to the square root of the height of the head, it is evident that the limit to the economical increase of the conductivity by diminishing the thickness of the water space, or by increasing the velocity of the stream, is soon attained. Hence, as I have already observed, the importance of any method which promotes the rapid removal of the adhering film of water without necessitating a great initial pressure. I have arranged my results, with reference to the head of water in the following Tables, so as to enable a comparison to be readily made in this respect between the plain tubes and those furnished with spirals. **Table I.—Plain Tubes.** | Description. | No. | Head of water. | Conductivity. | |--------------|-----|----------------|---------------| | Copper steam-tube 4 feet long. Thickness of water space 0 \cdot 325 inch. | 2 | — 0 \cdot 15 | 158 \cdot 46 | | | 1 | 0 \cdot 2 | 98 \cdot 13 | | | 5 | 0 \cdot 47 | 152 \cdot 24 | | | 8 | 0 \cdot 47 | 138 \cdot 79 | | | 7 | 0 \cdot 52 | 0 \cdot 56 | | | 9 | 0 \cdot 54 | 149 \cdot 44 | | | 6 | 0 \cdot 66 | 151 \cdot 6 | | | 3 | 1 \cdot 13 | 184 \cdot 3 | | | 4 | 1 \cdot 2 | 195 \cdot 68 | | | | | 191 \cdot 86 | | Copper steam-tube 4 feet long. Thickness of water space 0 \cdot 06 inch. | 18 | — 1 \cdot 4 | 89 \cdot 62 | | | 21 | 0 \cdot 49 | 279 \cdot 85 | | | 19 | 0 \cdot 13 | 143 \cdot 92 | | | 20 | 0 \cdot 6 | 155 \cdot 91 | | | 22 | 1 \cdot 19 | 176 \cdot 92 | | | 17 | 4 \cdot 37 | 198 \cdot 48 | | | 23 | 6 \cdot 45 | 193 \cdot 77 | | | 90 | 10 \cdot 8 | 202 \cdot 28 | | | 33 | 11 \cdot 48 | 278 \cdot 07 | | | 30 | 12 \cdot 9 | 300 \cdot 41 | | | 24 | 14 \cdot 07 | 332 \cdot 85 | | | 32 | 14 \cdot 15 | 286 \cdot 13 | | | 26 | 14 \cdot 73 | 335 \cdot 65 | | | | | 256 \cdot 3 | | | | | 297 \cdot 38 | ### Table I.—Plain Tubes (continued). | Description | No. | Head of water | Conductivity | |--------------------------------------------------|-----|---------------|--------------| | Copper steam-tube 4 feet long. | | | | | Thickness of water space 0·06 inch. | | | | | | 31 | 20·12 | 408·89 | | | 27 | 21·45 | 342·5 | | | 28 | 23·29 | 353·6 | | | 96 | 25·0 | 519·07 | | | 95 | 25·66 | 26·44 | | | 92 | 27·66 | 196·48 | | | 91 | 30·25 | 402·68 | | | 94 | 32·0 | 460·81 | | | 93 | 32·5 | 433·62 | | | 86 | 48 | 325·87 | | | 87 | 48 | 583·32 | | | 88 | 48 | 435·25 | | | 89 | 48 | 540·42 | | | 34 | 48 | 611·33 | | | 35 | 48 | 581·02 | | | 36 | 48 | 522·1 | | | 37 | 48 | 511·41 | | | 38 | 48 | 466·96 | | | | | 474·32 | | | | | 491·56 | | | | | 479·77 | | Copper steam-tube 4 feet long. | | | | | Thickness of water space 0·025 inch. | | | | | | 40 | -0·1 | 84·55 | | | 44 | 0·5 | 53·1 | | | 45 | 3·11 | 131·58 | | | 39 | 9·92 | 257·1 | | | 43 | 12·8 | 255·6 | | | 55 | 18·33 | 289·44 | | | 54 | 26·66 | 411·66 | | | 46 | 28·6 | 334·74 | | | 53 | 28·58 | 239·09 | | | 56 | 28·74 | 305·89 | | | 42 | 34·66 | 523·85 | | | 41 | 32·95 | 335·07 | | | 65 | 35·61 | 303·08 | | | 66 | 37·16 | 303·43 | | | 67 | 48 | 228·48 | | | 63 | 48 | 412·24 | | | 68 | 48 | 350·42 | | | 69 | 48 | 410·55 | | | 63 | 193·5 | 444·27 | | | 49 | 206·3 | 490·99 | | | 47 | 210·2 | 198·52 | | | 62 | 211 | 381·96 | | | 58 | 208·6 | 422·18 | | | 50 | 211·3 | 446·82 | | | 64 | 211·7 | 498·64 | | | 61 | 216 | 494·05 | | | 57 | 223·5 | 561·39 | | | 48 | 231·4 | 334·13 | | | 59 | 232 | 473·3 | | | 60 | 233 | 589·21 | | | 51 | 235·9 | 486·49 | | | 52 | 237·2 | 564·26 | | | | 292·06 | 512·66 | | | | | 370·49 | ### Table II.—Tubes furnished with Spirals. | Description | No. | Head of water | Conductivity | |--------------------------------------------------|-----|---------------|--------------| | Copper steam-tube 4 feet long. | | | | | Water space 0·325 inch. | 100 | 1·95 | 586·25 | | Spiral of 45 turns of wire 0·21 inch thick. | 101 | 2·06 | 478·15 | | | 102 | 2·43 | 470·53 | | | 103 | 2·53 | 516·75 | | Copper steam-tube 2 feet long. | | | | | Water space 0·125 inch. | 125 | 4·47 | 522·6 | | Spiral of 50 turns of wire 0·105 inch thick. | 126 | 5·8 | 532·54 | | | 124 | 8·4 | 528·91 | | | 115 | 24 | 531·59 | | | 116 | 24 | 727·52 | | | 117 | 24 | 700·44 | | | 118 | 24 | 601·2 | | | 119 | 24 | 686·44 | | | 120 | 24 | 768·58 | | | 121 | 24 | 684·5 | | | 122 | 176 | 636·38 | | | 123 | 193 | 859·4 | | | | | 872·28 | | | | | 820·93 | | | | | 731·1 | | Copper steam-tube 4 feet long. | | | | | Water space 0·125 inch. | 130 | 48 | 388·56 | | Spiral of 96 turns of wire 0·105 inch thick. | 131 | 48 | 571·56 | | | 132 | 48 | 499·96 | | | 129 | 218 | 539·75 | | | 128 | 248 | 892·52 | | | 127 | 274 | 833·78 | | | | | 813·33 | | | | | 713·7 | | Copper steam-tube 6 feet long. | | | | | Water space 0·125 inch. | 133 | 22·1 | 262·27 | | Spiral of 143 turns of wire 0·105 inch thick. | 145 | 72 | 355·84 | | | 146 | 72 | 420·87 | | | 147 | 72 | 412·4 | | | 140 | 250 | 460·48 | | | 139 | 261 | 891·3 | | | 138 | 279 | 918·05 | | | 141 | 301 | 802·02 | | | 142 | 301 | 846·46 | | | 137 | 315 | 710·76 | | | 143 | 327 | 770·85 | | | 144 | 337 | 662·57 | | | 136 | 341 | 710·74 | | | | | 719·16 | | | | | 676·6 | The averaged results of the preceding Tables are collected together as follows: | Description | Head of water | Conductivity | |----------------------|---------------|--------------| | Plain tube ..........| 0·56 | 157·83 | | | 0·69 | 176·92 | | | 3·11 | 155·44 | | Tube with spiral .....| 1·44 | 131·58 | | | 2·53 | 516·75 | | Plain tube ..........| 12·68 | 286·13 | | Tube with spiral .....| 12·44 | 528·91 | | Plain tube ..........| 48 | 511·4 | | | 48 | 350·42 | | | 48 | 686·44 | | Tube with spiral .....| 48 | 499·96 | | | 48 | 532·93 | | Plain tube ..........| 240·7 | 486·49 | | Tube with spiral .....| 246·66 | 820·93 | | | 277·18 | 813·33 | | | 200·88 | 770·85 | The cause of the inferiority of the plain tubes may be attributed in some measure to a want of perfect concentricity and truth in the pipes, resulting in an irregular action of the refrigerating water, the greatest quantity of which would thus be transmitted through the widest part of the water space. In the arrangement with spirals, the width of the water space was too great for any such circumstance to have a sensible influence. I think, however, that the imperfections of the tubes and of their concentricity were not such as to account for the great advantage which appeared to be produced by the spirals in my experiments, and I therefore attribute it to the continuous intermixture of the particles of water favoured by that arrangement. The following is a summary of the principal foregoing results: 1st. The pressure in the vacuous space is sensibly equal in all parts. 2nd. In the arrangement in which the steam is introduced into a tube whilst the refrigerating water is transmitted along a concentric space between the steam-tube and a larger tube in which it is placed, it is a matter of indifference in which direction the water is transmitted. Hence, 3rd. The temperature of the vacuous space is sensibly equal in all parts. 4th. The resistance to conduction is to be attributed almost entirely to the film of water in immediate contact with the outside and inside surfaces of the tube, and is little influenced by the kind of metal of which the tube is composed, or by its thickness in the limits of ordinary tubes, or even by the state of its surface as to greasiness or oxidation. 5th. The narrowing of the steam space by placing a rod in the axis of the steam-tube does not produce any sensible effect. 6th. The conductivity increases as the rapidity of the stream of water is augmented. In the circumstances of my experiments, the conduction was nearly proportional to the cube root of the velocity of the water; but at very low velocities it evidently increases more rapidly than according to this law, whilst at high velocities it increases less and less rapidly as it gradually approaches a limit determined by the resistance of the metal and of the film of water adhering to the inside surface of the tube. 7th. The conductivity increases so slowly in relation to the height of the head of water, that the limit to the economical increase of the latter is soon attained. 8th. By means of a contrivance for the automatical agitation of the particles of the refrigerating stream, such as the spirals I have employed, an improvement in the conductivity for a given head of water takes place. 9th. The total heat of steam above 0° Cent., determined by the average of the 151 experiments, is 644°28 for a pressure of 47·042 inches. The experiments in which air was employed as the refrigerating agent were made in a similar manner to those in which water was used. At high pressures the air was propelled by the condensing pump used by Professor Thomson and myself in our experiments, and at low pressures a large organ-bellows was employed. The temperature of the air at its exit was obtained by placing the thermometer immediately over the concentric space between the tubes, varying its position from time to time so as to obtain an average result for the entire section of the channel. MDCCCLXI. ### Table II.—Atmospheric Air, the refrigerating agent, | Description | No. | Duration of experiment, in minutes. | Total pressure of steam in the boiler, in inches of mercury. | Pressure required to propel the air, in inches of water. | Mean temperature of the refrigerating air. | |------------------------------------------------------------------------------|-----|-----------------------------------|-------------------------------------------------------------|----------------------------------------------------------|--------------------------------------------| | Copper steam-tube 4 feet long. Exterior diameter 0·75 inch, interior 0·63 inch. Outer tube 0·8 inch interior diameter. | 1 | 60 | 73·3 | 231 | At its entrance (t₁). | | | | | | | At its exit (t₂). | | | | | | | | | The same copper steam-tube. Outer tube 0·87 inch interior diameter. | 2 | 60 | 72·16 | 201 | | | | 3 | 60 | 82·1 | 228 | | | The same copper steam-tube. Outer tube 1 inch interior diameter. | 4 | 48 | 62·74 | 31·8 | | | | 5 | 60 | 73·16 | 31·48 | | | The same copper steam-tube. Outer tube interior diameter 1·4 inches. | 6 | 60 | 51·23 | 1·36 | | | | 7 | 60 | 43·58 | 3·5 | | | | 8 | 60 | 41·64 | 3·5 | | | | 9 | 60 | 41·51 | 5·52 | | | | 10 | 60 | 46·53 | 5·52 | | | The same tubes. A spiral of 30 turns of copper wire 1/16th inch thick was wound round the steam-tube. Half of this spiral was right-handed, the other half left-handed. | 11 | 48 | 43·67 | 5·52 | | | | 12 | 60 | 53·16 | 5·52 | | | | 13 | 60 | 48·9 | 5·52 | | | | 14 | 60 | 42·33 | 1·28 | | | | 15 | 60 | 49·05 | 1·3 | | | Copper steam-tube 2 feet long. Exterior diameter 0·75 inch. Outer tube 1·4 inch interior diameter. A spiral of 20 turns of copper wire 0·21 inch thick between the tubes. | 16 | 60 | 43·54 | 1·3 | | | | 17 | 60 | 42·32 | 5·32 | | | Copper steam-tube 1 foot long. Exterior diameter 0·75 inch. Outer tube 1·4 inch interior diameter. A spiral of 10 turns of copper wire 0·21 inch thick between the tubes. | 18 | 60 | 41·76 | 1·44 | | | | 19 | 60 | 46·88 | 3·55 | | | | 20 | 60 | 45·04 | 1·44 | | | | 21 | 60 | 45·06 | 3·55 | | propelled in a direction contrary to that of the Steam. | Quantity of water in pounds, equal in capacity for heat to the refrigerating air. | Weight of condensed water, in pounds. | Temperature of condensed water. | Total heat of steam. | Barometer, minus vacuum-gauge, or pressure in the condenser, in inches of mercury. | Temperature due to the pressure in the condenser per Regnault's tables (t₂). | Conduction of heat per square foot of the surface of the steam-pipe, or \( \frac{w}{a} \log \left( \frac{t_2 - t_1}{t_2 - t_3} \right) \). | |---|---|---|---|---|---|---| | In experiment. | Per hour (w). | In experiment. | Per hour. | | | No. | | 6·614 | 6·614 | 1·09 | 1·09 | 95·29 | 582·48 | 25·88 | 96 | 34·58 | 1 | | 5·622 | 5·622 | 0·754 | 0·754 | 93·55 | 665·15 | 21·19 | 90·63 | 49·08 | 2 | | 6·244 | 6·244 | 0·85 | 0·85 | 71 | 661·39 | 30·5 | 100·56 | 36·75 | 3 | | 5·28 | 6·6 | 0·69 | 0·86 | 71·68 | 595·55 | 22·744 | 92·5 | 18·16 | 4 | | 6·707 | 6·707 | 0·996 | 0·996 | 84·07 | 568·22 | 27·268 | 97·42 | 18·66 | 5 | | 4·562 | 4·562 | 0·661 | 0·661 | 90·31 | 571·35 | 27·26 | 97·41 | 10·36 | 6 | | 8·298 | 8·298 | 0·948 | 0·948 | 90·4 | 653·23 | 27·857 | 98·01 | 16·03 | 7 | | 8·3 | 8·3 | 0·865 | 0·865 | 83·97 | 658·16 | 25·446 | 95·52 | 15·17 | 8 | | 10·157 | 10·157 | 1·129 | 1·129 | 90·55 | 640·23 | 26·328 | 96·45 | 17·94 | 9 | | 10·157 | 10·157 | 1·133 | 1·133 | 92·22 | 643·37 | 26·25 | 96·38 | 18·06 | 10 | | 25·208 | 31·51 | 1·375 | 1·719 | 68·68 | 651·86 | 27·33 | 97·49 | 19·78 | 11 | | 32·085 | 32·085 | 2·076 | 2·076 | 98·43 | 633·8 | 30·01 | 100·08 | 21·19 | 12 | | 32·14 | 32·14 | 2·08 | 2·08 | 97·73 | 634·37 | 30·05 | 100·11 | 21·49 | 13 | | 14·97 | 14·97 | 1·156 | 1·156 | 98·25 | 590·21 | 30·03 | 100·1 | 11·43 | 14 | | 13 | 13 | 1·006 | 1·006 | 97·21 | 600·56 | 30·146 | 100·21 | 10·31 | 15 | | 8·4 | 8·4 | 1·109 | 1·109 | 97·37 | 574·63 | 30·09 | 100·16 | 14·13 | 16 | | 18·5 | 18·5 | 1·92 | 1·92 | 99·39 | 604·48 | 30·366 | 100·42 | 24·29 | 17 | | 4·64 | 4·64 | 0·548 | 0·548 | 102·61 | 610·64 | 30·06 | 100·13 | 13·83 | 18 | | 7·744 | 7·744 | 0·748 | 0·748 | 102·55 | 670·61 | 30·08 | 100·15 | 19·55 | 19 | | 5·578 | 5·578 | 0·506 | 0·506 | 96·86 | 608·81 | 30·04 | 100·11 | 21·14 | 20 | | 9·122 | 9·122 | 0·629 | 0·629 | 99·12 | 657·47 | 30·06 | 100·13 | 27·42 | 21 | On examining the Table of results with air as the refrigerating agent, we may remark,— 1st. That a film of air does not adhere to the surface of the tube so tenaciously as a film of water does. This is evident from a comparison of Nos. 1, 2 and 3, with 4 and 5; from which it appears that for the spaces .025 and .06 inch the pressures able to propel equal quantities of air were as 7·66 to 1, or nearly as the squares of the velocities. When water was employed in the same tubes, these pressures were as 18·8 to 1. 2ndly. That the velocity of the elastic fluid appears to exercise a much more considerable influence on the conductivity than it does in the case of water. 3rdly. That spirals exercise a beneficial influence. This will be noted on comparing Nos. 6 to 15 with Nos. 16 and 17. The very small conductivity when Air is the refrigerating agent will probably prevent its being employed for the condensation of steam, except in very peculiar cases. I must remark, in conclusion, that the above research, however laborious, has left much to be accomplished. One of my chief objects was to obtain figures which might prove useful to practical men, and I have therefore confined myself to such tubes as were most likely to be generally used. In taking up the subject afresh, greater accuracy might be attained by the use of a sheaf of tubes, so as, by condensing a larger quantity of steam, to diminish the amount of temperature corrections. It would also be desirable to employ tubes of great thickness, so as to obtain the conductivity of metals after eliminating the resistance of the fluid film. The effect of irregularities in the water space might also be exactly determined, and the action of arrangements for agitating the refrigerating water more completely discussed than I have been able to do in the present memoir.