‘Resi^t/ances^ rheo^tai;** a>x 40 104 II. 2 19.1 60.2 127.7 147.9 CO C 50 122 II. 6 19.4 60.7 128.1 148.3 0 0 60 140 12.0 19.8 61. 1 128.5 148.6 70 158 12.4 20.2 61.6 129.0 148.9 80 176 12.8 20.8 62.0 129.4 149.2 .0 *-Cj 100 212 13*5 21.4 62.9 130*3 149.8 0 oJ 150 302 15*4 23*4 65.2 132.5 151-3 u 200 392 17.4 25*3 67.4 134*7 152.9 3 The following table* is frequently of greater service than the last. TABLE II. Resistance of Conductors at 20° C. Material K, Temperature Coefficient Authority for Temp. Coef. Silver, Annealed 9-65 .00377 Riviere Copper, Annealed 10.3 .00388 Matthiessen Copper, Hard Drawn 10.5 .00388 i i Aluminum, Annealed 18.73 .00390 Benoit Zinc, Compressed 36.0 .00365 Matthiessen Platinum, Annealed 56.69 .00247 Benoit Iron 63.21 -00453 a Tin 84-57 -00365 Matthiessen German Silver 126.0 .00044 Mascart Lead 126.1 .00387 Matthiessen Platinoid 205.4 .00021 it Manganin A 258.7 negligable Helmholtz Manganese Steel 419.0 .00122 Fleming Mercury 577-6 .00889 Mascart Manganin B 643.6 negligable Helmholtz Bismuth, Pressed 845.2 •00354 Matthiessen Graphite 6734- — .0009 Joubert Arc Light Carbon 37920. — .00052 ( ( Slight discrepancies in the two tables occur because of differences in tests of slightly varying samples. If the resistance is designed to create a definite fall of potential in the circuit, the value of which is E, then the cross section necessary to secure that fall of potential with a given length, L, in feet, carrying the current, i, is, — *A. B. Herrick, Electrical^Engineer Data Sheets, 5711-5. 4 m. Kt X L X i E ( 2 ) The temperature of the resistance conductor when ex- posed to still air may be approximated from the expression T= - (3) 1 X .053 + A X K, where : — T = temperature above the surrounding air in degrees centigrade. P = watts radiated from the surface. A = surface in sq. in. available for radiation. 1 = length of conductor, or coil, in feet. K, = constant which may be taken as .004 for bright metallic surfaces and, depending upon conditions, as high as .012 for rough black surfaces. Where greater facility of calculation than can be secured by the above method is essential, the following modification of a method proposed by Mr. G. Rennerfeltf may be employed. For any form of cross section of conductor used for a resistance we have : — P = m\/x (4) where, — P = the perimeter of the cross section. X = the area “ “ “ m = a constant depending upon the form of cross section. For a square, m = 4 and for a circle m = 2 which ♦ A. E. Kennelly, Heating of Conductors by Electric Currents, Elec- trical World, Vol. 14., p. 336. A. V. Abbott, The Electrical Transmission of Energy, pp. 289-293. C. E. Timmerman, Trans. Am. Inst. Elect. Eng’s., Vol, 10, p. 342. t G. Rennerfelt, ' Formulae for Resistance Coils, Elect. World, Vol. 23, p- 241. 5 is the smallest value possible for m and, for this reason and convenience in manufacture, circular sectioned conductor is always used, except it be for some special reason, such as the frequent necessity of securing a grea*ter proportion of radiating surface to area of cross section, when rectang- ular or corrugated conductor is used. For any form of cross section where m is known we have, — S = py (5) = ymv'x (6) = fi^R (7) where, S = surface of conductor in sq. in. ^y = length of conductor in inches. f = number of sq. in. for each watt radiated. Then, — ym\/x = f FR (8) and from equation (i) we may write, R = (9) where Kj is the specific resistance of the material employed. This may be calculated from the Matthiessen formula for resistance, K, =-K 3 (i +at±bt2) (lo) where t is the temperature in degrees centigrade and Kg is the resistance at zero centigrade. 6 TABLE II. Material K3 a b Copper . .00000066 .0038 .00000126 Aluminum .0000013 .0038 .00000126 Iron .0000040 .0048 .00000126 German Silver .0000090 .00044 .000000152 Combining (8) and (9) we have, — ymy^x = fi^R = fi2y.K, Whence, mx\/x = f i K. mx =v =v m2 (ii) m2 ( 12 ) which give expressions for the area of cross section of conductor. To determine the length of conductor we can place in K V equation (8) x=— which comes from (9) and gives, — R ym ' R fi^R (13) 7 y2 y f2 i4 R3 = K, m2 iRri (14) as the length of conductor in terms of current, radiation, cross section and resistance. In a similar manner, we may express the weight of the conductor as, — W = s.x.y which we get by substituting the values of x and y from equations ( 12 ) and ( 14 ) and where, — W = total weight of conductor in pounds, s =::= weight per cubic inch of material employed. The above forms the basis of the method of calcula- tion, but as the resulting equations would be cumbersome for ordinary use, the following table gives numerical values for most of the terms which may be substituted in the formulae. TABLE III. O fOOO VO cs Om>* O CO O a cu h Ph a tu h VO COVO c^ O VO VO VO M M CO O O O O O O O O O O O O Iw i:^ rh 0\ M i:^ CO c^ O i^^OO ci i:^ G\ !>> VO ^ M 00 M CO O 0\ M M M M o o o o IM CO VO On OvVO On O H CO rj“ O O O O o o o o o o o o NO c^ J>. VO O t-i CO cs M VO O 00 VO Tt- VO !>. C^ M H ON (N 00 M O M H M O O O O VO i:^ J>- On O 00 CO ON Tf O M M O O O O O O O O O O O O Im O CONO CO vooq NO NO VO O 00 VO M VO CO CO O On M !>. H O M M C^ O O O O 03 I.— I a p u P p.’g uc (/} c u o - M M VO vq cq M M H M 00 CO VO M VO CO J>. CM M M, M o o O o q o o o M M H M VO M VO CO CM 00 cq 00 vq M CO CM o NO CO vq vq lO M o o CO On vq q Nq CO CM 1 1 a 1 1 1 1 1 -t-j -t-> o3 6r* m u q M NO . VO • • CM O VO CO M M CM !>. • • M CO H M H O • • NO CO cq M M CM VO • • 00 ^ CM CO M (U u 00 a On VO P CO M cr if) IV O 'O Ij CO 00 u xt" c-i 0 S-l ^ ^ o p i 100 ohms “ with .25 per cent, salt by weight. 7.84 “ “ “ -46 (i (( (( 4-65 “ “ “ .70 ( ( n a 3.12 “ “ “ -93 it n n K) Cj 00 “ “ I. 16 ( ( ( ( ( ( 1.90 “ “ “ 1-39 (( a a 1.48 “ “ “ .174 ‘ ‘ commercial sulphuric acid 4.12 “ “ “ -437 (( (( “ 1.75 “ “ “ .724 ( ( ( ( ( ( “ I.IO “ “ -985 ( ( ( ( ( ( bo Ln The resistances given in the table are for a cubic foot ot solution between plate terminals. Where salt or acid is used in the water, thin plates of carbon are desirable terminals as iron is subject to rapid corrosion. If iron plate terminals are used, sulphate of soda may be employed to reduce the resistance of the water. Tanks for water resistances should be so proportioned as to allow about eight watts radiation per square inch of external surface, though this necessarily depends on conditions of operation. For example, an ordinary barrel having a surface in the neighborhood of 2500 sq. in. is capable of absorbing 20 Kw. from an electric circuit. About one ampere per square inch of surface of electrode exposed toward opposite electrode may be allowed. For resistances of covered wire wound on spools or bobbins a modification of Esson’s expression* may be used to calculate the rise in temperature, ’•'S. P. Thompson, Dynamo-Electric Machinery, Vol. i, p. 374. A. H. and C. E. Timmerman, Trans. Am. Inst. Elect. Eng’s, Vol. 10, p. 336. II K^XP A (i6) where may be given a value from 50 to 120, de- pending upon surrounding conditions. For still air and varnished surfaces, this value may be taken at from 55 to 70, and for coils encased in rough blackened metallic sur- faces, it may be from 80 to 95. A is the entire surface in sq. in. available for radiation. Before the final calculation of resistance and tempera- ture can be made, it is necessary to decide definitely upon the exact method of mounting and arranging the resist- ance material, which cannot always be done before ap- proximate calculations are carried through, but should be done as soon as possible, as the radiation coefficients depend largely upon this decision. In rheostats where it is necessary to subdivide the resist- ance, modern practice indicates the following : — for dynamo field rheostats of all voltages, n == 7 if^Kw -f- 20 (17) for motor starting and speed regulating resistances, — n = 2i^Kw + .5 y/v (18) for theatre dimmers, — (120 volts) n = 20]^Kw (19) where v is the voltage of the circuit and n is the average of several representative manufacturers for the number of subdivisions or steps in the resistance. The number of contacts would then be n + i or n + 2 in case an extra " dead ” contact be used. The least area of surface which should be exposed by each contact to the contact arm may be determined from the following table but, in many cases, there should be 12 provided a greater area than is there indicated in order to present sufficient surface and material for mechanical dur- ability and strength of construction. Phosphor-bronze forms desirable contacts and renewable carbon brushes on the contact arm may be employed to advantage where the conditions of operation are particularly severe. TABLE VII. Kind of contact. Amperes per Sq. In. Copper brush - - 150 to 200 Carbon - - 30 44 50 Copper sliding on copper - - 60 4 4 100 Brass “ brass - 40 4 4 75 Copper ( ( “ phosphor-bronze 50 4 4 80 Copper screwed on copper - 100 4 4 200 4 4 4 4 “ brass - - 60 4 4 100 44 4 4 “ phosphor-bronze 60 44 100 There are various methods of supporting the resistance material in the rheostat which in all commercial types must be 'absolutely fire -proof. A method of support that is common and inexpensive, though not economical of space, is to coil the wire into a helix. Where this method is employed the helices should have a space of not less than d == .oiy/v (20) inches between them where v is the voltage at the termi- nals of the rheostat. The outside diameter of the helices should vary with the size of wire used and may be de- termined approximately from the equation, — 100 where d, is expressed in inches. (21) The helices are usually mounted in a vertical position, so as to avoid sagging in the wire when heated, but the hori- zontal position allows convection currents to act more effectively. When mounted horizontally, the vertical dis- tance between helices should be two to three times that indicated by equation 20. The length of helix may vary with the size of wire, and in accordance with the following expression : — * 1 = ifm^ ‘ (22) where 1 is the length of the helix in inches and m^. seldom exceeds 30,000. The number of turns per inch in length of helix should be such that when stretched in position there is about one thirty-second of an inch space between consecutive turns. The several helices of such a resistance may have each end secured by passing through a porcelain bushing in a metallic end plate, which must be carefully proportioned as the combined tension of many helices is sometimes very great. A uniform pressure must be brought upon the porcelain or a fracture may result in a ground on the rheostat frame. Another convenient method of mounting is to place all the resistance in a continuous helix to which leads may be tapped, and which is wound back and forth over large grooved porcelain insulators strung over iron rods at either end of the rheostat frame, or coiled into a flat spiral with asbestos between consecutive turns. *E. K. Scott. Metallic Resistances, The Electrical Review, Vol 43, p. 71 . H ^ A method that is often used, a especially for rectangular con- structor, consists in winding the resistance upon a frame shaped as indicated in the figure. With this construction and for small wire or flat conductor the distance pieces, a, a', are usually wound with asbestos paper and made of square iron rod of such size that the distance between the surfaces of conductors is from tV to inch. The following equation may be applied for the calcula- tion of the resistance conductor : l,=-^fe+1^2_4l,c+4c2 ^ b (23) s.-b ] ( 24 ) (25) y= S1I3 (26) where, c == distance in inches between centres of con- ductors in adjacent layers (may be taken at l//\ to 2 )• 1^ = length in inches of a side of the inside layer (assumed conveniently). = length in inches of a side of the outside layer. I3 = length of a mean turn in inches. b = number of turns per layer. Sj == total number of turns in frame. 15 Another method of mounting ribbon conductor in a rheostat is to wind it spirally with a narrow strip of asbes- tos so as to cover about one-half its surface and, when so covered, to wind the conductor into a spiral which is placed in a frame of proper shape to receive it. Small wire of high resistance can be wound upon mica cards which are packed in a grooved framework holding the cards a small distance apart, or, after being wound, the cards may be stacked with alternating strips of sheet mica to separate them. A very compact rheostat is constructed by winding the conductor on asbestos tubes about one inch in diameter and a foot long. The tubes are then pressed flat and bent into a V shape about 1.25 inches wide and .25 inch depression. They are stacked with iron radiating plates between and held in suitable frames. There are several special types of resistance that consist of a re- sistance conductor embedded in non-conducting enamel or cement in such a manner as to entirely confine the conductor in its posi- tion, whatever may be its temper- ature, and at the same time afford a large radiating surface. The enamel or cement is usually ap- plied to cast-iron plates which afford mechanical support and, by means of corrugated or ribbed surfaces, the radi- ation of heat is greatly facilitated. The enamels used consist of easily fusible salts, such as the silicates and borates of sodium, potassium and lead to which may be added metallic oxides to impart the desired i6 color. The iron radiating plate having been cleaned with dilute sulphuric acid, a powder or paste, in the case of Paris’s composition composed of 130 parts of broken flint glass, 20.5 parts of carbonate of soda and 12 parts of boracic acid, is spread over it and the whole is exposed in a muffle to the moderate temperature of an enamel furnace. Injurious effects of contraction and expansion of the conductor are avoided by the zigzag form into which it is bent so that there is little danger of cracking the enamel from this cause. The result of this construction is to greatly reduce the necessary length and cross section of resistance conductor, as it is not necessary to consider its mechanical strength because of the supporting enamel, and as high as eight or ten, or, in special cases, where the heat is carried away by running water in contact with the radiating plate, 25 watts can be continuously radiated per square inch of resistance conductor surface.* At the tem- peratures usually employed for this class of resistance, in the neighborhood of 200°C, from 1.5 to 2.5 watts per square inch of outside iron surface can be continuously radiated, while, for short intervals of not more than 15 seconds, from 6 to 10 watts may be allowed per square inch. In designing an enamel rheostat or resistance, the fol- lowing expressions determine close approximations to the working conditions : f 'T' ^3 X Pq “ A„ (27) -r 83 X Pr A, (28) ♦C. E. Carpenter, Trans. Am. Inst. Elect. Eng’s, Vol. 9, p. 502. fW. E. Goldsborough, Notes on Electrical Design. 17 ( 29 ) (30) T„ = T, + 94 X P, X d, i.i8 X Pr X d , ■■ Ac + Aj Aj + A, Po + Pj. is the total amount of energy liberated in the re- sistance conductor in the form of heat, and the relative value of Pq and Pr must be determined from the last two equations. Therefore, if; 83 I 94 X d„ _ J. A„ ^ A„ + A, ( 31 ) ( 32 ) ( 33 ) (34) Where : — Tg = the temperature of the conductor above the air in degrees centigrade. T„ = the temperature above the air of the outside surface of the enamel in degrees centigrade. Tr = the temperature above the air of the outside surface of the cast-iron radiating plate in degrees centi- grade. Ac = the area is sq. in. of the surface of resistance conductor. Ao = the area in sq. in. of the outside, or exposed, surface of the enamel. Ag = the area in sq. in. of the surface of contact between the enamel and the radiating plate. Aj. = the area in sq. in. of the outside, or exposed, surface of iron radiating plate. i8 do = the average distance in inches between the sur- face of the conductor and the outside surface of the enamel. dg = the average distance in inches between the sur- face of the wire and the surface of contact between the radiating plate and the enamel. dr — the average distance in inches between the outer and inner surfaces of the iron radiating plate. Pr == the watts radiated from the outside surface of the radiating plate. Pq = the watts radiated from the outside surface of the enamel. To determine the length and size of circular sectioned resistance conductor to be embedded in the enamel, we have : — ( 35 ) (36) K, where L is the length in feet and is taken at the temper- ature determined by equation (30). In applying the above expressions to the calculation of a resistance, the following method is perhaps as convenient as any. Allow the proper rate of radiation fromthe surface of re- sistance conductor, under the given conditions, which deter- mines A^. when the total energy to be liberated is known, as is usually the case. Allow the proper rate of radiation from outside surfaces, which are usually proportioned so that the iron surface is from two to four times the enamel surface and radiates from 60 to 80 per cent, of the heat, thus determining A,, and A„. and may now be determined and values of d„, d,. and d^ assumed so that T,. by both equations has the same value. Usually A„ is the same as A^, and d^ the 19 same as d^, or two or three times greater, depending on conditions of construction, but always as small as possible on account of the low radiating coefficient of enamel. Dj. maybe from .i to .3 inch, depending on the size of plate. It is sometimes convenient to assume d^ and d^ and solve for dj. in the second equation for T^, (30), or to adjust the values of and as indicated by the structural values necessary for d^, dg and d^, but reasonable temperatures must always be employed ; and the value of T,, must be used in obtaining the resistance of the conductor, which, on ac- count of the high temperatures employed, should have a small temperature coefficient. The five accompanying diagrams illustrate several of the 20 1 pdti ing or speed controlling rheostat without protective devices. The second diagram gives connections where the resistance is automatically inserted under a variety of conditions. A magnet which is in paral- lel with the motor armature holds the contact arm in po- sition against the action of a spring so long as there is any considerable counter electro- motive force at the terminals of the armature. Should the current be removed from the mains ; should the shun, circuit of the motor be broken ; or should the coun- ter E. M. F. of the motor for any reason become low, the spring is permitted to r-AM/WWF \c act and resistance is in- serted independently of what may be the cur- rent in the armature. A similar form of rheo- stat having the release magnet in series with the armature is fre- quently used but does not afford as perfect protection. The third Automatic Motor 21 diagram illustrates a type of rheostat which will protect the motor under any possible conditions. It will open the circuit if there is a lower E. M. F. than allowable; if the current through the motor becomes excessive, if the operator attempts to start the motor too quickly ; or if the current be taken from the mains. The motor cannot have the circuit without resistance in series with the armature. The fourth diagram is of a rheostat frequently used where it is necessary to operate a motor automatically or to control it from a distant point. Closing the switch operates the magnet, by the magnetizing coil, c, thus carrying the contact arm to the position shown as the motor increasesi n speed. A more desirable method is to connect the terminals of c at e, in place of d, as shown, when the magnet will be operated simply by a current proportional to the counter E. M. F, of the armature, which protects the motor under all conditions except overload, and such protection may be otherwise provided for by circuit breaker or fuses. The rate of movement of the contact arm may be controlled by means of a dash pot with valve at r or otherwise. With insufficient current in c, the weight of the magnet plunger immediately raises the contact arm throw- ing in all resistance. Similar results are secured by a device represented in the fifth diagram where an autouatic rheostat is secured by belting a to the motor shaft and connecting the magnet, m, across the armature or line as conditions may re- quire. The contact arm, b, is weighted so as to return to position cutting in all resistance whenever m is not mag- 22 netized. In place of this device, a centrifugal governor attached to the motor shaft is sometimes emplo3'ed for mov- ing the contact arm, and in many cases a small motor on an independent circuit is used for the same purpose. The many applications of electricity to the heating of street railway cars, dwellings, public halls, and to laundry, tinsmith, welding, forging, annealing, metallurgi- cal and other work, make the principles of the subject im- portant to the electrical engineer. The relations of the fundamental quantities involved in this work are expressed by Joule’s law : — E2t H = i 2 Rt = = Eit ( 37 ) R i 2 Rt . 24 E 2 t or =.24i2Rt= =.24 Eit (38) 4.2 R where H is the heat in joules and is the heat in gramme- calories. As t is the time in seconds, the heat per hour in gramme-calories is 864 E2 H2 = 864 i 2 R 864 Ei (39) R which is a more convenient expression for most engineering work, and is applicable to any portion of an electric circuit. The temperature produced by a current in a conductor is .24 Eit T, w s (40) 23 where is the rise in temperature, in degrees centigrade, in t seconds and w and s are the weight in grammes and the specific heat of the conductor. This assumes adiabatic action which is only approximately secured when the time is very short and the conductor is well protected from heat transferance. Where the loss of heat is considerable, as is usually the case, the temperature rises until the rate of heat development equals the rate of heat transference by radia- tion or otherwise, which may be expressed as T, K, Kf t = .24Eit (41) .24 Ei Ti (42) where is the temperature above surroundings when con- stant conditions have been reached, is the heat conduc- tivity of the envelope of the conductor, and is a constant depending upon the dimensions and form of the envelope. This is a more general form of equation (i6) in which, when applied to the case of a bare conductor, should be given the value of the emissivity of the substance of which the conductor is built. Equations (3) and (27) to (30) are special developments for the cases considered. Thermal resistivities — reciprocals of conductivities — for the different substances vary considerably with slight differ- ences in composition but, in the absence of exact determi- nations from samples of the material to be used, and de- termined under the conditions of service, the following table may be depended upon for constants. 24 TABLE VIII. MATERIAL , SPECIFIC THERMAL. » KESISTIVITIBS. CONDUCTIVITIES. Silver, •15 to .20 6.66 to 5.00 Copper, . . . .21 (( •25 4.76 a 4.00 Zinc, .... .80 < ( .85 1-25 ti I. 18 Brass, .80 t ( .85 1-25 ( ( I. 18 Iron, «... 1. 10 i i 1.40 .91 ( i •71 Lead, 1.80 i ( 2.00 •55 i i •50 Ger. Silver, 2.25 t i 2.50 •44 i i .40 Stone, 40 ( ( 70 .025 i i .014 Glass, 90 t ( 120 .oil i ( .0083 Sand, . . . 200 i i 300 LO 0 q i i •0033 Gutta-percha, . 400 i i 600 .0025 i i .0017 Clay, .... 500 ( ( 800 .0020 i i .0013 Air, . . . . 1 100 ( ( 1300 .0009 i i .0008 Fine Asbestos, . 1300 1500 .0008 i i .0007 Sawdust, . . 2000 2500 TO 0 0 0 ( ( .0004 Asbestos Paper, 2000 ( ( 2900 .0005 i i .00035 Wool, . . . 2000 ( ( 3500 .0005 i i .00028 Paper, 2200 ( ( 4000 .00045 4 4 .00025 Vulcanized Rubber, 2400 ( ( 4500 .00042 4 4 .00022 Felt, . . . . 2600 ( ( 5000 .00038 4 4 .00020 Slag Wool, . . 3000 ( t 5000 .00033 4 4 .00020 Loose Wool, 5000 i i 6600 .00020 4 4 .00015 The values appearing in the table are expressed in C. G. S. units, so that the heat transferance, expressed in joules, is readily approximated for most conditions likely to arise. While these values are to be considered as only approxi- mately correct, yet they are in most cases within limits of variation occasioned by differences in commercial appli- 'TV 25 cation. Good thermal conductors seem to conduct better, and good thermal insulators to insulate better with decreas- ing temperatures. Oven. One Compartment. In connection with the above the following abridgement of a table, prepared by H. W. Leonard, is convenient in calculating electric heating problems and designs for heat- ing apparatus. 26 TABLE IX. Unit. Equivalent Value in other Units. 1 K. W. Hour = 3,656,400 tt. lbs. 3,600,000 joules. 3,440 heat units. 366,848 kilogram metres. .229 lbs. coal oxidized with perfect efficiency. 3 lbs. water evaporated at 313 ® F. 32.9 lbs. of water raised from 62° to 212® F. 1 H. P. Hour = 1,980,000 ft. lbs. 3,580 heat units. 373,740 k. g. m. .173 lbs. coal oxidized with perfect efficiency. 3.25 lbs. water evaporated at 213 ® F. 17.2 lbs. water raised from 63® F, to 212® F. 1 K W. = 3,656,400 ft. lbs. per hour. 4,424 ft. lbs. per minute. 73.73 ft. lbs. per second. 3,440 heat units per hour. 573 heat units per minute. 9.55 heat units per second. . 23 g lbs. coal oxidized per hour. 3 lbs. water evaporated per hour at 212® F. 1 H. P. = 2,580 heat units per hour. 43 heat units per minute. .71 heat units per second, .172 lbs. coal oxidized per hour. 2.25 lbs. water evaporated per hour at 312 ® P'. 1 Joule .00000278 K. W. hour. .102 k. g. m. .00094 heat units. •73 lbs. Unit. Equivalent Value in other Units. 1 Ft. Lb. = 1.36 joules. .1383 k. g. m. .000000377 K. W. hours. .000291 heat units. .0000005 H. P. hour. 1 Watt = .00134 H. P. . 3.44 heat units per hour. .73 ft. lbs. per second. .003 lbs. of water evaporated per hour. 44.24 ft. lbs. per minute. 1 Heat Unit = 1,048 Watt seconds. 773 ft. lbs. 352 calories, (g. d.) 108 kilogram metres. .000291 K. W. hour. .000388 H. P. hour. .0000667 lbs. coal oxidized. .00087 lbs. water evaporated at 312 ® F. 1 Lb. Bitu- minous Coal Oxi- dized with perfect ef- ficiency = 15.000 heat units. .98 lbs. Anthracite coal oxi- dized. 3.1 lbs. dry wood oxidized. 15 cu. ft. illuminating gas. 4.37 K. W. hours (theoretical value.) 5.81 H. P. hours (theoretical value.) 11.590.000 ft. lbs. (theoretical value.) 13.1 lbs. of water evaporated at ZI3® F. ILb. Water Evapora- ted 212" F.= .33 K. W. hour. .44 H . P. hour. 1,148 heat units. 124,300 k. g. m. 1,319,000 joules. 887,800 ft. lbs. .076 lbs. of ooal oxidized. 27 The heating of street railway cars, because of the con- venience, saving of space, cleanliness, and ease of control offered by the method, is the most important commercial application of electric heating, though the cost of heat de- livered to the car is frequently greater than if furnished by a small stove. In most instances however, the advantages offered by electric heaters so far over balance any adverse difference in cost that they are almost universally employed on electrically operated lines. The conditions under which cars are to be heated vary with climatic differences and character of line on which they are to be used, so that it is sometimes difficult to make an accurate estimate of the energy required, but there is data available which will enable such estimates to be made in most instances and the following will be found of value : TABLE X.* ^CARS.-^ DOORS. WINDOWS. CU. FT. r-TEMP. FAHR.-x OUTSIDE. INSIDE. WIND. MILES. WATTS. 2 12 850-5 28° 51-59° 25 2295 2 12 850-5 7° 34°-44° ' 28 2325 2 12 808.5 28° 47°-52° 25 2180 2 12 913-5 35° 40°-64'’ 3 2745 4 16 1012. 4 7° 4i°-5o° 28 3038 4 16 1012. 4 28° 48°-6o‘’ 25 3160 McElroy gives .08 B. T. U. per second as the amount of heat necessary for a car under average conditions per de- gree Fahrenheit difference in temperature between inside and outside of car.f The fact that an average person radiates heat at about .053 B. T. U. per second has an im- portant bearing, depending upon the crowding of the cars. * Atlantic Avenue (Boston) Railway Tests, t J. F. McElroy, Electrical World, Vol. 26, p. 374. 28 as 40 to 50 people will supply sufRcient heat for the car, 2.5 B. T. U. per second, under average conditions, though 6 to 10 B. T. U. per second may be necessary in the most severe weather. Iron wire, not only because of its low cost, but also be- cause of its high temperature coefficient, is particularly valuable in the construction of heaters, as its resistance will increase so as to keep the current at a safe value, if for any reason the free radiation of heat be interrupted so that the temperature of the heater rises. It is important to use two or more heaters in a car so that, by a properly arranged switch, they may be placed in series, series-parallel, or in parallel across the line, and thus secure a convenient means of regulating the liberation of heat. Menting Coll The following are some methods of mounting car heat- ers. In one heater the German silver wire, bent in a zig- zag form, is embedded in powdered fire clay between two 29 rough iron castings. In another heater No. 20 B. & S. galvanized iron wire is wound in a spiral groove on cylind- rical porcelain tubes slipped over a ^ inch square iron rod. Many other forms are employed but, in general, they may be said to consist essentially of a galvanized iron, or Ger- man silver, wire coiled or wound so as to present as large Portable Heater. , a radiating surface as possible in air, or, to increase radia- tion and convection, and, at the same time, secure the nec- essary resistance within a small space, the wire is often wound in a helix, which in turn is wound on a porcelain or other non-combustible block, tube, rod or pins. The heater must be thoroughly insulated, absolutely fire proof, and, unless the conductor is embedded in enamel, its temperature must be kept below that at which either oxidization or crys- tallization is liable to occur. While the conversion of electrical energy into heat is perfect, so far as the heater is concerned, and the efficiency of an electric heater regarded in this way is the highest attainable, yet, to secure the best diffusion of heat through a given space, the heater should not be operated at too high a temperature and should be so designed as to permit the free passage of air currents over its surfaces. 30 The cost of operating car or other electric heaters varies with the cost of current supply which, in turn, depends upon the price of coal and local conditions of plant opera- tion, so that from 1.5 to 8 cents per Kw. hour may be ex- pected as the conditions are more or less favorable.* Under usual conditions of power development it may cost from 25 to 50 cents per car day of 20 hours, depending upon the weather and size of the railway system. Knowing local conditions of operation in any instance, the foregoing gives a basis of reasonably exact determination of design and costs. Where alternate currents are employed for electric heat- ing, it is usually advisable to design the heater so that the development of hysteresis and eddy current losses in iron coils facilitates the conversion to heat energy, except where the heater may be used on either a D. C. or an A. C. circuit of any wave form or frequency. For the heating of buildings, welding and miscellaneous electric heating apparatus, the following data is of value in designing this class of appliances and in the estimation of costs of operation. Chas. E. Emerj, Cost of Steam Power. Trans. Am. Inst., Elect. Eng’s. Vol. 10, p. 119. 31 Electric Welding. (Thomson System.) TABLE XL* IRON AND STEEL. BRASS. COPPER. Area in Sq. In. Watts in Prim’y of Welders. Time in Seconds. Area in Sq. In. Watts in Prim’y of Welders. Time in Seconds. Area in Sq. In. Watts in Prim’y of Welders. Time in 1 Seconds.] 0-5 8550 33 •25 7500 17 .125 6000 8 I.O 16700 45 •50 13500 22 .250 14000 II 1-5 23500 55 •75 19000 29 •375 19000 13 2.0 29000 65 1. 00 25000 33 .500 25000 16 2.5 34000 70 1-25 31000 38 .625 31000 18 3-0 39000 78 1.50 36000 42 •750 36500 21 3-5 44000 85 1-75 40000 45 •875 43000 22 4.0 50000 90 2.00 44000 48 1. 000 49000 23 TABLE XII. t WELD. 2 in. Iron Bar > Average of 2 Welds, 5 TIME IN SEC. WATTS. 249 42522 in. R’d. Iron Bar, > Average of 15 Welds, > 57 13204 I in. Bessemer Steel Shaft, } Average of 4 Welds, ] > 61 17680 ^ in. Bessemer Steel Shaft, } Average of 4 Welds, ] ; 45 1 1860 in. Bessemer Steel Shaft, } Average of 4 Welds, ] > 26 6789 * Hermann Lemp, Electric Welding and Metal Working. Engineering Mag., Vol. 7, p. 691. tB. A. Dobson, Electric Welding. Elect. Rer. (London; Vol. 35, p. 133. 32 COOKING. An oven roasting meat takes 2750 watts and 7 to 8 minutes per pound of meat roasted. f Frying pan, 275 watts. Coffee pot, 500 watts. Four quart tea kettle, 700 watts, boils one quart in 10 minutes. One quart chafing dish, 500 watts. Two quart stew pan, 700 watts. A ten course dinner has been prepared for 120 people with 60 Kw. hours electrical energy, which at 8 cents per Kw. hour gives cost per person as 4 cents.* Broiler for two steaks, 15 to 20 minutes, 1200 to 1500 watts. Farina boiler 100 to 450 watts for one quart or 200 to 700 watts for two quarts. Small oven, 2100 cubic inches, 350 to 1500 watts. Hot water urn, five gallons, from 450 to 1750 watts. MISCELLANEOUS. Soldering irons, 200 to 350 watts. Laundry irons, 200 to 400 watts. One gallon glue pot, 250 to 1100 watts. One quart glue pot, 700 watts. One pint glue pot, 500 watts. To keep glue melted, 50 to 100 watts. Curling tongs heater, 50 watts. Sealing wax heater, 50 watts. Troy polishing iron, 330 watts. Nine pound heavy laundry iron, 650 watts. Twelve pound goose, 650 watts. Twenty-five pound goose, 800 watts. Heating pad, 400 to 1100 watts. Solder pot, four pounds, 100 to 200 watts; ten pounds, 200 to 400 watts. One joule per second, or one watt, will raise one cubic foot of air .055° F. per second, or 18 watts will raise one cubic foot of air 1 ° F. per second. t A. V. Abbott, Electrical Trans. ofEnergj’^, p. 298 . * Ifouston and Kennelley, Electric Heating, p. i78.