heated on one side and cooled on the other side by radiation from two plates whose total difference of temperature is 2,000°.

An interesting feature of Miss Bryant's experiments is that they show that the water surface of the heated plate is several degrees hotter than the water. Whether this is strictly true, or whether the water near the plate is not slightly superheated (see p. 62), has not been proved. It is also evident from the irregularities in these temperature differences, and especially in the tendency for these differences not to increase with increased evaporation, that they are affected by circulation of the water, for it is evident that the greater the evaporation the greater the circulation and the less need for a large difference of temperature. Roughly speaking, these experiments show that with a difference of temperature between plate and water of 1° F., about 2 lbs. of water per hour can be evaporated. If there were water on both sides of the plate, then 2° F. would transmit as much heat as would evaporate 2 lbs. of water, or, roughly, 1° difference would transmit 1,000 heat units per hour.

Kirkaldy's corrugated evaporator tubes are said to transmit about 600 units. G. A. Hagenau's (C. E.,' 1884, vol. lxxvii. p. 311) experiments are very exhaustive, and were undertaken to show the influence of the steam temperature, the water temperature, and the velocity of the cooling water. Unfortunately the results disagree amongst themselves, and it is to be feared that the precautions taken to guard against the presence of air were not sufficient, and possibly the external radiation may have varied. However the general results are, that the units of heat transmitted per square foot per hour per degree of difference of temperature sometimes amount to as much as 600.

Comparing even the lowest of all these values with those for the transmission of heat from metal to air, we find such a very great difference that there should be no hesitation in accepting the conclusion, that water is far more efficient than air in abstracting, and therefore also in imparting, heat.

Of more importance than the theories as to how the heat transmission takes place is the question of how much heat can be transmitted. This very soon resolves itself into the oft-debated subject as to the relative merits of the heating surfaces of the furnaces and of the tubes. Unfortunately few experiments have been carried out, and those few are very incomplete.

De Pambour was the first to raise the question ('Comp. Rend.,' 1840, vol. x. pp. 32, 111, 480), and to make comparisons, but these are valueless.

C. W. Williams (Engineer,' 1858, vol. v. pp. 223, 243, and N.A.,' 1862, vol. iii. pp. 122) made experiments on the heat transmission of tubes.

J. Graham (Manch. L. Ph.,' 1860, vol. xv. p. 8) experimented on the heat transmission of flat surfaces.

M. Geoffroy (Couche,' 1877, vol. iii. p. 28) made experiments on a locomotive boiler whose length was subdivided.

P. Havrez (An. Génie,' 1874, 2nd ser. vol. iii. p. 520) and J. A. Longridge (C. E.,' 1878, vol. lii. p. 101) give analyses of these experiJ. Durston, N. A.,' 1893, vol. xxxiv. p. 130.

ments.

Reference is also repeatedly made to M. Petit's experiments, but

details are wanting. They seem to have consisted of two series: in the one lot coke was burnt, and in the other briquettes; and the draught was in. in the one case and 4 ins. in the other. Compare P. Havrez (see above), p. 550, and Chron. Ind.,' 1873, vol. ii. p. 425. C. W. Williams (Engineer,' 1858, vol. v. p. 206) also mentions experiments on a subdivided boiler carried out by Messrs. Wood and Dewrance, but all details are wanting.

Tube-Heating Surface. Of the above-mentioned experiments those by Mr. Williams are the most complete, as far as he attempted to go; but the conditions are such that the external radiation must have been out of all proportion to the heat received by the solitary internal pipe. Some of the compartments could not even be raised to the boiling point of water. All the other experiments are still more unsatisfactory, as will be found when examining them.

M. Geoffroy's experiments, of which the results are reproduced in D. K. Clark's work (1890), have been analysed by the author, but under great difficulties, for no mention is made of the steam pressure, except that it is high; no statement can be found whether the boilershell plates were lagged; the calorific value of the fuel is not given, nor the temperature or weight of the waste products. A very cursory examination showed that experiments Nos. 5 and 10 differed too much from the others to be relied upon. By trials and corrections of errors it was found that the ratio of products of combustion to fuel burnt must roughly have been as follows:

In these experiments it appears that E, the weight in pounds of water evaporated per square foot of heating surface per hour, can be estimated by the formula

E = ct", or log E = log c + n log t.

Here t is the difference of temperature between the boiler water and the hot gases at any particular point of the tubes, and c and n are constants. The closest agreement with the whole number of experiments is obtained by assuming that the calorific value of the fuel is 123 lbs. of water evaporated under the conditions of the trial, or, say, 151 lbs. from and at 212° F., further that log c= −5·4, c = 250000, and that n = 2. Then

E =

t2 250000

and e, the units of heat transmitted, is found by multiplying E by 1,150, viz.

e=

t2 217

The importance of these experiments is that they show that, as in the case of radiation, the heat transmission is proportional to the square of the difference of temperature.

In order to obtain an idea of the distribution of the evaporation

along the lengths of the tubes, it will be necessary to remember that, while the gases move on, they are being gradually cooled. The amount of cooling, or drop of temperature, depends on E or e, the amount of heat abstracted, and on the velocity with which Q, the weight of air, passes over 1 square foot of tube surface per hour.1 In these experiments

Here At is the drop of temperature of the gas which passes over 1 square foot of heating surface, o is the specific heat of the gas-say, 0.237; so that

Here to is the initial and t the final difference of temperature, and S the heating surface of the tubes in square feet.

The quantity of water evaporated by this heat, which is abstracted from the gases, is EQ. (tot)

o

1150

=

to.Q.237
1150

(1

51.5 Q 515Q+S.to

In M. Geoffroy's experiment No. 1 it has been assumed (see above) that the products of combustion are 27 times as heavy as the coke burnt. Q = 27 × 436 = 11,772 lbs. of waste gas per hour. The heating surface of each compartment of tube surface being 179 square feet, and the theoretical evaporative value of the fuel having been assumed to be 12.3 lbs., the temperature of the flame as it leaves the fuel would be

To this has to be added the initial temperature of the air, and the temperature of the boiler water has to be subtracted, leaving, say, 1,980° F.

A further subtraction has to be made on account of heat lost in the fire box; this, according to the experiment, is 710° F.; so that the initial temperature of the gases which enter the tube plate is to 1,270° F. in excess of the water temperature.

=

The quantity of water evaporated in one, two, three, and four compartments of tube surfaces of the experimental boiler can now be calculated.

The heat transmission also seems to be affected by the velocity of the gases See p. 121.

Here n is the number of compartments, and we have

The evaporations in pounds per hour in each compartment are the differences of these values, viz.

838 lbs., 488 lbs., 312 lbs., 214 lbs. ;

but the experiments show

996 lbs., 430 lbs., 228 lbs., 128 lbs.,

and the differences are:

- 158 + 58

+94 + 76

Priming, which is mentioned, would account for the large experimental readings in the first compartment, while the other differences are accounted for by radiation. The external surface of each cylinder being 31 sq. ft., the mean amount of radiation is equal to 24 lbs. of steam condensed per sq. foot per hour. This is not an excessive amount (see p. 97). The calculations which have been carried out on the other experiments lead to similar results, so that until more accurate experiments are made this formula may at any rate be used for comparisons.

Roughly speaking, one square foot of tube heating surface should transmit about 200 thermal units per hour. Sir John Durston ('N.A.,' 1893, vol. xxxiv. p. 141, and Plate VII.) has measured the temperature of the waste gases in a boiler smoke tube. There were some irregularities near the combustion chamber end, but generally then the temperatures decreased as follows.

Distance from back!
end.
Inch
Temperature of Gas °F.

14 1368

20 32 44 56 68 80 1295 4 1197.8 1105.8 1014·9 925-6 887

In this case, although the readings are not quite regular, the first six give fairly constant differences, which would imply that the transmission of heat is independent of the difference of temperature, instead of being proportional to its square. This result is an unreasonable one, and to settle the point further experiments are needed.

It also shows that the statement, that the value of tube surface for heating purposes is a definite fraction of that of the combustion chamber plating, is quite wrong. It is simply a question of temperature, and if the heat is not taken out of the flame in the fire box, it will be taken out of it by the tube surface. If the gases are hot enough, the tubes may be as effective as the thicker plates, if not more so, as will be seen from the following values calculated from the previous formula (p. 122):

These few figures give an indication of the relative heating value of the last few feet of tube-heating surface as compared with the radiating surface of the shell. If, for instance, the gases on nearing the ends of the tubes have been cooled down to 200° above the water temperature, then every extra square foot of heating surface will only supply lb. of steam per hour, and this small performance may be too dearly paid for, particularly if the boiler is not lagged. It has, in fact, been found that by increasing the length of a marine boiler its efficiency is reduced.

Furnace-Heating Surfaces.-A further very important question is the value of that heating surface which is exposed to the direct action of the flame and to the radiation from the fire.

Geoffroy's experiments would be exceedingly valuable for the purpose of this determination if he had only measured the temperatures, &c. J. A. Longridge (C. E.,' 1878, vol. lii. p. 101) assumes it to be proportional to the difference of temperature, and fixes it at 11 units. per square foot for every degree, which works out to about 22 lbs. of water evaporated per square foot per hour with good fires, but in some of M. Geoffroy's experiments it exceeds 40 lbs.

On the other hand, most text-books adopt Dulong and Petit's views (An. Ch. Ph.,' 1817, vol. vii. pp. 113, 225, 337), that the cold as well as the hot object radiates heat at a rate which is expressed by an exponential function c, where c is a coefficient and t the temperature. The amount of heat absorbed by furnace plates would then be cac, where b and a stand for the respective temperatures of the boiler plate and of the fire. These formulæ are constructed on the basis of experiments in which b ranged from 32° to 140° F., and a from 140° to 500° F., and, as more recent experiments do not confirm these, there is no need to employ a formula which is very complicated in its working. A. E. Kennely (Elect. W.,' 1889, vol. xiv. p. 374) and N. Barbieri (Elect. Z.,' 1891, p. 27) both experimented on this subject by heating wires by means of electricity, and measuring their temperature by means of their elongation. The temperatures do not exceed 350° F. Roberts Austen (M. E.,' 1891, pp. 565, 590, plate 119) gives the photographic record of the cooling of a red-hot steel ingot. The amount of heat lost per hour per square foot of surface amounts to about 50 evaporative units for a difference of 1,500° F., or at the rate of about 03 evaporative unit per degree of difference of temperature. Below 1,000 F. the radiation seems to be reduced to about 015 evaporative unit per degree of difference. These estimates are based on the assumption that the specific heat of iron is the same at both these temperatures, though there is evidently a marked change between the two. No great reliance can, therefore, be placed on these deductions. But that there is also a change in the rate of cooling, depending on the temperature, will be evident by analysing the case