LIBRARY 
 
 OF THI: 
 
 UNIVERSITY OF CALIFORNIA. 
 
 Received... -NOV 19-1&9J- , 18 
 A ccessions No. ^5/ J74r^ Shelf No. . 
 
THE 
 
 THEORIES AND PRACTICE 
 
 OF 
 
 CENTRIFUGAL VENTILATING 
 
 i: ;;'':- MACHINES. ,' : V 
 
 BY 
 
 DANIEL MURGUE, 
 
 ENGINEER -TO THE COLLIERY COMPANY OF BESSEQES. 
 
 TRANSLATED, AND SUPPLIED WITH AN INTRODUCTION, 
 BY 
 
 A. L. STEAYENSON, 
 
 LONDON: 
 E. & F. N. SPON, 16, CHARING CROSS. 
 
 NEW YORK : 
 35, MUKEAY STEEET. 
 
 1883. 
 

 
 \ 
 
INTRODUCTION. 
 
 LITTLE if anything was done towards the application of 
 machinery to the purposes of ventilation until very recent 
 years, although, so early as the year 1657, Agricola, in his 
 interesting work " De re Metallica," gives particulars and a 
 drawing of a mechanical ventilator for mines, driven by 
 water-power, and at the Hartz mines, nearly 200 years ago, 
 another, somewhat similar to the Struve, was in operation. 
 
 In the year 1849, Mr. Warrington Smyth referred to this 
 in his evidence before the House of Lords' Committee, and 
 at the same time Mr. Struve said his ventilator at the 
 Eaglesbush Colliery, then the only place where it was yet 
 applied, began its work in February 1849. 
 
 Mr. Brunton also then x explained and gave drawings of his 
 centrifugal ventilator. 
 
 But so late as the year 1852 a Committee of the House of 
 Commons reported : 
 
 " Your Committee are of opinion 
 
 " That any system of ventilation depending on complicate 
 machinery is undesirable, since under any disarrangement or 
 fracture of its parts the ventilation is stopped or becomes 
 inefficient. 
 
 " That the two systems which alone can be considered as 
 rival powers are the furnace and steam jet. 
 
 u Your Committee are unanimously of opinion "that the 
 steam jet is the most powerful and at the same time least 
 expensive method for the ventilation of mines." 
 
 a 2 
 
iv INTRODUCTION. 
 
 In 1861 the centrifugal fan at Elsecar was described to 
 the North of England Institute of Mining Engineers by the 
 late Mr. J. J. Atkinson, and to him must be given the credit 
 of having, in several valuable papers on the subject, first 
 shown clearly the superiority of mechanical ventilators over 
 every other system. 
 
 From that time until now the question as to which fan is 
 the best has been a source of constant contention ; every 
 fresh invention being introduced as at least 10 per cent, 
 better than anything which preceded it. 
 
 Numberless experiments have been made by private 
 individuals and committees to ascertain the truth of these 
 questions. Nearly all the results obtained have varied, and 
 the question to-day still remains unanswered " Which ven- 
 tilator is the best ; and which, taking all circumstances into 
 account, should I, as a mining engineer, adopt ? " 
 
 The cause of this unsolved state of the problem is not far 
 to seek. 
 
 The useful effect of a fan is not the only question involved. 
 We must consider 
 
 1. First cost ; 
 
 2. Durability; 
 
 3. Efficiency. 
 
 The enormous first cost and want of durability of some of our 
 largest ventilators, has overshadowed in a great degree the 
 question of efficiency, especially where, as at many collieries, 
 steam is obtained from the heat of coke-ovens. Some of 
 the results published as to efficiency, are the work of experi- 
 menters quite unused to the rigorous accuracy demanded in 
 scientific research, still it is very important, and to appreciate 
 reliable data, such for instance as the recent report of the 
 North of England Institute, there is wanted a general know- 
 ledge of the laws governing the variation in results under 
 varying conditions of work. To supply this hitherto un- 
 
INTRODUCTION. V 
 
 supplied need of the engineer in England, I have been led 
 to translate and publish the very excellent treatise of M. 
 Murgue. Many attempts have been made to follow these 
 laws of ventilators, but nothing approaching the lucidity of 
 his methods has been attained ; a little attention and study 
 on the part of those who care thoroughly to understand the 
 various questions involved, will give a perfect mastery over 
 them, and then when seeking to know which is the best 
 ventilator, they will at least be able to make the selection 
 with their eyes open. 
 
 The leading ideas given by M. Murgue are 
 
 First, That every mine may be assimilated to an orifice in 
 a thin plate, which he calls its " Equivalent Orifice." 
 
 Second, That a ventilator, even whilst exhausting the air 
 from the mine, forms at the same time an obstacle to the 
 passage of this air, causing a sensible loss of duty, so that 
 the depression produced by the ventilator is always higher 
 than what we observe in the galleries of approach, some part 
 of this depression being employed in overcoming the various 
 resistances in the fan ; this he treats as the " Orifice of 
 Passage" 
 
 Third, The theoretical depression or water gauge, due to 
 the speed of the periphery, is in a perfect fan equal to twice 
 the height of column necessary to generate such velocity in 
 a falling body. 
 
 This meets a difficulty experienced by a writer on the 
 subject,* who says " It is especially worthy of notice that the 
 water gauge indicated at the inlet is greater than the 
 theoretical result," the hitherto recognised theory having 
 
 u 1 
 been , where u = speed in feet per second, and g = 32 2. 
 
 ^9 
 Fourth, That there is an initial depression which each fan 
 
 * See 'Proceedings of Northern Mining Institute,' vol. xiv., p. 80. 
 
vi INTRODUCTION. 
 
 gives when acting on a closed space, and which approaches 
 the theoretical limit in proportion to the perfection of the 
 ventilator. 
 
 Fifth, That this depression gradually varies and lowers 
 according to conditions. 
 
 A little further explanation of these theories seems de- 
 sirable for the benefit of those whose time has been more 
 given to the distribution of air in mines, than to its economic 
 production. 
 
 The equivalent orifice depends upon well known laws of 
 the flow of fluids : 
 
 1st. That the speed of flow is the velocity due to the 
 height of fall or height of column of the flowing air, which 
 is represented by the formula for gravity 
 
 = r V = 
 
 2nd. That the quantity which passes through an orifice in 
 a thin plate is two-thirds or 65 that of the quantity due 
 to the area of the full orifice, and the formula then becomes, 
 for what is known as the " vena contracta," 
 
 Q = 8m a A/h, 
 
 where Q = quantity, m = 65, a = area, and h the height 
 which must be reduced to air column, or as M. Murgue 
 puts it 
 
 reducing this we get 
 
 v 
 
 a (or equivalent orifice) = 
 
INTRODUCTION. 
 
 where 8 = 1000, and 8 = 1*2000, or the relative densities 
 of water and air. Simplifying this for water gauge as 
 usually taken' in inches 
 
 V -70V 
 a = =-, or 
 
 " 
 
 't 
 
 and if we assume these as normal densities we may remove 
 the fraction and obtain 
 
 V 0-0243 V 
 
 a - -- - or 
 
 41-26 Vh Vli 
 
 In this case V = volume in cubic feet per second ; but as we 
 generally speak of cubic feet per minute we may say 
 
 0-403 V 
 
 _ 
 
 taking V = 1000 cubic feet per minute, and h = inches of 
 water gauge. 
 
 The great value of this fiction is that it enables us to grasp 
 at once the conditions under which a fan is working. 
 
 We hear of one machine giving 100,000 cubic feet per 
 minute under a water gauge of 3 inches, and of another 
 where 75,000 cubic feet is got with a water gauge of 4 inches ; 
 but this is not a tangible statement. If, however, we are 
 told that the equivalent orifice of the first mine is equal to 
 22 feet, whilst that of the second is only 14, the difference is 
 clearly demonstrated. 
 
 Then as to the Orifice of Passage, as M. Murgue says, 
 the fan suited to blow a cupola may give a depression as 
 great as the largest Guibal, but it would be useless to 
 ventilate a mine its orifice of passage is insufficient. 
 
 To obtain this in any case we must refer to his theory of 
 initial and effective depressions (p. 4) 
 
 h = H - h M 
 
Vlii INTRODUCTION. 
 
 where h represents the deficiency or difference between the 
 initial and effective water gauge ; and we see a little further 
 
 h a 2 
 
 on that ^ = -T, or as the orifice of passage diminishes 
 h o 
 
 the loss of effective depression increases. 
 
 To calculate the area of this orifice of passage we must 
 refer to its value in the equation 
 
 H - h = h = M V 2 , 
 
 V 2 
 or, Ji = 
 
 That is to say, after finding for any ventilation the value of 
 the initial and effective depression, the loss or useless depres- 
 sion is equal to a function of the volume which depends upon 
 the orifice of passage, and from the above equation 
 
 ~v m 
 
 V 2 
 
 62 2 h 2 g 
 
 reducing of course h to the density of air in feet. We are 
 now enabled to understand what is termed " the characteristic 
 curve of the ventilator." 
 
 In order to compare two machines they are regulated to 
 the same speed of periphery, or their results may be easily 
 reduced to equal speeds since the volume varies as the 
 revolutions and the depressions as the squares of the speeds. 
 
 The mine is altered, to say five different conditions : first 
 by obstructing the passages ; then in the normal state ; and 
 afterwards by opening some of the doors. 
 
 With the equivalent orifices of these five different mines, 
 or conditions of mine, plotted as abscissae, and the volumes as 
 ordinates, we get a curve which shows clearly the effective- 
 ness of each fan, and is called its " characteristic curve" 
 
 We are next shown how the effective depression varies and 
 
INTRODUCTION. ix 
 
 diminishes by a function of the volume depending upon the 
 orifice of passage. 
 
 The experiments upon the four different ventilators tested 
 by the Commission of Gard are tabulated, and from them an 
 equation for each is obtained, giving the initial depression 
 and its coefficient of diminution as the volume increases. 
 Taking, say Nos. 1 and 2 experiments on the Creal fan, with 
 the square of the volume and depression observed, we get 
 
 x -y (89,283) = 1-0598, 
 x - y (195,766) = 1-0183, 
 
 and from these constants are found. 
 
 The average of the various experiments should be taken. 
 
 Little more need be added, but a short reference to the 
 remarks on the effect of the natural ventilation of the mine 
 upon such investigations, given in the report of the Com- 
 mission of Gard, of which M. Murgue was a leading member, 
 will be useful.* 
 
 The effect of natural ventilation is much less than is com- 
 monly supposed, since it is not the yields which are to be 
 added, but the depressions, and the volume to be obtained 
 therefore, is like the hypothenuse of the rectangular triangle, 
 thus say in cubic metres x = \/20 2 4- 5 2 = 20 615, and as 
 all conditions additive or subtractive are covered by the 
 equivalent orifice, it may be entirely neglected. 
 
 If then, as is clearly demonstrated, the covered Guibal with 
 evasee chimney most nearly meets theoretical requirements, 
 how can its acknowledged defects in point of size, structural 
 weakness, and heavy cost, be best met, so as to produce a 
 machine perfect in every respect ? The answer is to be found 
 in a ventilator I have recently designed, and which will be 
 at work at Pagebank Colliery by the time this issues from 
 
 * See ' Bulletin de la Societe de 1'Industrie Minerale,' 1878, p. 495. 
 
 6 
 
X INTRODUCTION. 
 
 the press. It is 20 feet diameter, built with, and from, a 
 central wrought-iron diaphragm, like the Kammel and Schiele 
 fans. It has the vanes in shape according to M. Murgue's 
 demonstrations, made of iron and riveted to the diaphragm 
 with angle irons, the sheet-iron cover, evasee chimney, and 
 sliding shutter of Guibal type, with air admitted on both 
 sides. The fan is driven by ropes, and will run about 110 
 revolutions, and much more if needed. 
 
 A. L. STEAVENSON. 
 
 DURHAM, 3rd February, 1883. 
 
THE 
 
 THEOEIES AND PKACTICE 
 
 OP 
 
 CENTRIFUGAL VENTILATING MACHINES. 
 
 IN publishing towards the end of 1872 the first part of this 
 study, I entertained the hope that I should be able shortly to 
 announce a new theory, firmly based on experience with 
 large ventilating machines by centrifugal force a theory 
 which up to that time appeared to me to be still somewhat 
 cloudy. Seven years have since elapsed, and to-day only am 
 I able to keep the promise I then made. This long interval 
 will surprise few people who know how difficult it is to con- 
 duct experimental researches and make them subservient 
 to the exigencies of active life. It has not been altogether 
 sterile, for beyond the unconscious labour of thought which 
 I have given, by the sole aid of time the matter has become 
 much clearer, and it has been permitted to me to add my 
 study on the works incidental to the Commission on Ventila- 
 tion of the district of Gard the results of which have been 
 published in the later volume of 1878 being myself a 
 member of that Commission, with M. Aguillon, then Govern- 
 ment Engineer for Alais. The theoretical study which I 
 propose to develop here comprehends not only that on 
 ventilators with centrifugal force, but also many machines 
 now almost abandoned which draw in the air by oblique 
 surfaces, such, for example, as the ventilator or screw by 
 
 B 
 
 \ 
 
THE THEORIES AND PRACTICE OF 
 
 M. Motte, and the helix, by M. Pasquet, and that with vanes 
 like a windmill by M. Lesoinne. M. Devillez distinguishes 
 them as ventilators by direct impulsion. But to separate 
 these from the centrifugal machine does not seem to me to 
 be justified, these machines being in fact exactly the same as 
 those with centrifugal force, producing in the atmosphere of 
 the mine a certain depression, which is ruled by the square of 
 the speed. If the seam is thin, the circulation obtained is 
 small ; if it is thick the result is considerable, but the depres- 
 sion remains in every case theoretically the same. It is not, 
 however, the same with the pneumatic machines of Fabry 
 and Lemielle studied in the first part of this work, their 
 mode of action being absolutely the reverse. These machines 
 draw the air from the interior, cutting it off and throwing it 
 out, so to speak, in equal quantities. It is not then the 
 depression which remains constant, but the volume drawn. 
 This difference of action between the two classes of machines 
 presents itself with sufficient clearness. We shall show 
 shortly how to replace the word " volume " by the word 
 " depression," and conversely, so as to pass from the one to 
 the other without any change in the theory. Also, having in 
 my preceding memoirs on pneumatic machines, with the 
 approbation of my friends, used the generic denomination of 
 Yolumogen ventilators, I am now naturally led to call the 
 machines which I discuss to-day Deprimogen ventilators, and 
 I will shortly enumerate their principal characteristics and 
 advantages. First, their mechanism is extremely simple ; all 
 is reduced to the rotative system, turning on two bearings if 
 the axis is horizontal, and on a foot-step and collar if it is 
 vertical. Second, they leave free communication between the 
 interior and the exterior air. Third, they can only give in thin 
 seams a feeble result, but for thick seams otherwise. All their 
 characteristics are in complete opposition to those of the well- 
 known volumogen ventilators. I shall apply at every step 
 
CENTRIFUGAL VENTILATING MACHINES. 3 
 
 in the course of the discussion which I am undertaking the 
 method of the equivalent orifice through a thin plate a 
 method which I have developed in my two previous studies. 
 I shall employ as notations the letter a to designate the 
 equivalent orifice, V will be the volume of air yielded per 
 second, h will express the depression, for convenience of cal- 
 culation, in the column of the fluid in movement, that is to 
 say, in the column of air. I am supposing that air is an 
 incompressible fluid, which is perfectly legitimate under 
 the conditions, and on all occasions I shall simplify as 
 far as possible every remark, knowing well that for a 
 theory to be useful, the supreme quality after exactness 
 is simplicity. 
 
 1. ESTABLISHMENT OF Two GENERAL FORMULA FOR 
 DEPRIMOGEN VENTILATORS. 
 
 Let us consider the deprimogen ventilator placed on a 
 mine and turning at a rigorously uniform speed. Profiting 
 by the fiction of the equivalent orifice, let us replace the 
 mine ventilator by an orifice in a thin plate, which we can 
 reduce or increase at will. If we suppose at first the equi- 
 valent orifice equal to zero, that is to say, that the mine is 
 completely shut off, the ventilator will produce in a confined 
 space adjoining the ouie or inlet a certain depression, which 
 I will call H. If now I open out and increase by degrees 
 the equivalent orifice, what will become of this depression ? 
 Theoretically it should remain invariable, the exhausting 
 power of the vanes acting equally well upon the air whether 
 in motion or in repose. But in effect it will be weakened in 
 proportion as the ventilator is traversed by larger volumes, 
 and finally it will disappear when the equivalent orifice 
 
 B 2 
 
4 THE THEORIES AND PRACTICE OF 
 
 is increased to infinity. If I call this gradual reduction of 
 initial depression h , the effective depression may then be 
 expressed by the equation 
 
 Ji = H - h . (1) 
 
 h may increase from zero to H. 
 
 What are the causes of this fall in depression h ? Evidently 
 the frictions and losses of active force which the air experi- 
 ences in passing through the ventilator frictions and losses 
 which increase in proportion to the volume of air yielded, 
 and absorb an increasing fraction of the initial depression. 
 
 Those who have occupied themselves in studying this 
 theory have generally sought to determine by calculation 
 these frictions and losses of active force, which always leads 
 them to complicated expressions. It has appeared to me 
 much more simple to introduce here the method of the 
 equivalent orifice, which evidently lends itself sufficiently 
 well to represent the difficulty of the passage of the air 
 through a ventilator as well as through a mine. I have 
 already spoken in the second part of this work of this new 
 application of the method, and I call it the orifice of 
 passage. 
 
 FIG. 1. 
 
 
 L | 
 
 4- a/ 
 
 t 
 
 I 
 
 We may, then, replace in imagination the mine and its 
 ventilator by two orifices, a and o, placed one behind the 
 
CENTKIFUGAL VENTILATING MACHINES. 5 
 
 other (Fig. 1), and successively traversed by the current of 
 air ; the first in virtue of the depression h, the second in 
 virtue of the depression h volume, depressions, and 
 orifices being connected by the formula for flow through a 
 thin medium : 
 
 V = 0-65a\/~2~pr (2) 
 
 V = 0-650 ~2~0X (3) 
 
 From these two relations I obtain the interesting proportion 
 
 Ji a 2 
 
 r 1 
 h c? 
 
 If now we substitute for h , in the equation (1)," the value 
 which results from this proportion, it will become 
 
 ,;' l =, H -* 
 
 and, resolving it by the proportion to h, 
 
 Such is the formula for the effective depression h. To obtain 
 that of the effective volume V, it suffices to introduce the 
 preceding value of h in equation (2). 
 It becomes then, all reductions made, 
 
 v , 0-65W2JH (5) 
 
 From this we learn at once to determine the initial depres- 
 sion H as a function of the diameter and of the speed. The 
 equivalent orifice of the mine a is supposed to be known ; that 
 of the passage o depends upon the dimensions and arrange- 
 ments of the ventilator, and we see that it may be determined 
 a priori. The depression and the volume of air yielded are 
 found then to be expressed by our two formulae (4) and (5), 
 
THE THEOKIES AND PRACTICE OF 
 
 with the aid of known quantities, which was the object to 
 be gained. 
 
 This forms but the first part of our theory, and there re- 
 mains for us to see how to determine the initial depression H. 
 This determination will be the object of the next paragraph ; 
 but before undertaking it, I have pleasure in showing the 
 wonderful parallelism which exists between the preceding 
 theory and that which I have proposed in the two former parts 
 of this study for the volumogen ventilator. I have said 
 already that to pass from the one to the other it is sufficient 
 to change the word " volume " to that of " depression," and 
 conversely. This will be clearly seen from the following. 
 
 Volumogen. 
 
 In theory the volumogen 
 ventilator should give a 
 constant volume of air, 
 equal to that which it 
 affords when working freely 
 on the atmosphere. In 
 reality the volume obtained 
 is always less than the 
 theoretic volume, because 
 of the unavoidable play of 
 the joints of the machine, 
 which gives place to a re- 
 entry direct from the exte- 
 rior air. 
 
 If W represents the theo- 
 retical volume, Y the re- 
 entry of air, and V the effec- 
 tive volume, I may write the 
 equation 
 
 V = W- V ; 
 
 a being the equivalent orifice 
 of the mine, we will call o 
 the equivalent of the pas- 
 
 Depr Imogen. 
 
 In theory the deprimogen 
 ventilator should afford 
 a constant depression equal 
 to that which it reaches 
 when acting upon a closed 
 space. In reality the de- 
 pression obtained is always 
 less than this initial depres- 
 sion. A great part of this 
 latter will be found to be 
 absorbed by the frictions and 
 losses of active power in the 
 air traversing the machine. 
 
 If H represents the initial 
 depression, h the part ab- 
 sorbed by the frictions, h the 
 effective depression, I may 
 write the equation 
 h = H - Ji ; 
 
 a being the equivalent orifice 
 of the mine, we will call o 
 the equivalent of the passage, 
 
CENTKIFUGAL VENTILATING MACHINES. 
 
 sage, more or less compli- 
 cated by the re-entry of the 
 air. The depression produced 
 by the ventilator being the 
 same over the two orifices, 
 the corresponding volumes 
 will be evidently in the same 
 proportion as the orifices 
 themselves 
 
 ~V o 
 
 V = ~a 
 
 If, then, I substitute for 
 V in the first equation the 
 value resulting from the 
 preceding proportion, I ob- 
 tain the equation 
 
 V= W - V-; 
 
 a 
 
 which, reduced in the pro- 
 portion to V, will give the 
 first formula required 
 
 vvJL 
 
 If, now, in the value of 
 the given depression by the 
 well-known formula for the 
 flow of air through a thin 
 medium, 
 
 /- Y 
 
 V/i = o^7 
 
 If I replace V by the preced- 
 ing value, I obtain the second 
 formula 
 
 W 
 
 0-65 (a + o) 
 
 more or less complicated, 
 formed in the ventilator it- 
 self. The two orifices a and 
 o being traversed by the 
 same volume of air, we easily 
 perceive that the correspond" 
 ing depressions are in the 
 inverse proportion of their 
 squares 
 
 If, then, I substitute for 
 h in the first equation the 
 value resulting from the pre- 
 ceding proportion, I obtain 
 the equation 
 
 which, reduced in the pro- 
 portion to h, will give the 
 first formula required 
 
 ll -"""- _ 
 
 If, now, in the value of 
 the given volume by the 
 well-known formula for the 
 flow of air through a thin 
 medium, 
 
 V = 0-65a 
 
 If I replace h by the preced- 
 ing value, I obtain the second 
 formula 
 
 V _ ' 65a 
 
 o* 
 
8 THE THEORIES AND PRACTICE OF 
 
 We see the parallelism is perfect, and also that their 
 characteristics are absolutely opposite. Thanks to this re- 
 markable reciprocity, the two theories render each other 
 more clear ; and I may say that more than once the volu- 
 mogen ventilator has assisted me to understand the depri- 
 mogen. In reality, it is not between the volume and the 
 depression that the reciprocity is established, but between 
 the volume and the square root of the depression. But 
 that changes nothing in the curious result which I am 
 about to show. 
 
 Of the two formula which we are about to establish, as 
 well for the volumogen ventilator as for the deprimogen, the 
 most important is evidently that which gives the volume of 
 air yielded per second. This volume is most especially 
 interesting. The curve expressed by this formula, the 
 equivalent orifice being drawn as abscissae and the volume 
 of air as ordinates, characterises most distinctly the venti- 
 lator to which it is applied, and furnishes a very simple 
 and sure means to compare different machines. It is this 
 curve which the Commission of Gard has set itself to deter- 
 mine for the six ventilators submitted to their tests. They 
 have given it the name of the characteristic curve of the 
 ventilators. 
 
 2. DETERMINATION OF THE INITIAL DEPRESSION FOR 
 VENTILATORS WITH CENTRIFUGAL FORCE. 
 
 I preserve the name of Initial Depression for that value of 
 the depression which is shown when the mine is shut off and 
 rests virtually constant when we do away with the friction 
 of the air. We know that in the volumogen ventilator 
 the mechanical combinations which give place to the volume 
 
CENTEIFUGAL VENTILATING MACHINES. 9 
 
 engendered, differ absolutely in one machine from those in 
 another, and require each time, for the determination of the 
 volume, special methods of calculation. It is the same for 
 deprimogen ventilators ; each type of machine produces the 
 depression by particular methods, each requiring their special 
 calculation. But I will not occupy myself here except with 
 the centrifugal ventilator, the most perfect and therefore the 
 most interesting of all. I will study first the uncovered 
 ventilators with centrifugal force, such as were made by the 
 first inventors (Combes, Letoret, Lambert, &c.), to whom the 
 cover appeared, no doubt, the greatest obstacle to the free 
 escape of the air into the atmosphere. This manner of 
 looking at it, very plausible at first sight, is in reality quite 
 erroneous. We know that to M. Guibal belongs the 
 honour of having first shown that the cover is indispensable 
 for making the ventilators develop their full useful effect. 
 To-day almost every ventilator at work on the collieries 
 possesses this ingenious addition. In order to proceed with 
 regularity we must begin with those which have not got them. 
 
 To avoid any difficulty in the establishment of my calcu- 
 lations, I will suppose that the air of the mine before reaching 
 the ouie is expanded in a large chamber where its speed may 
 be considered almost nothing. In reality, this vestibule will 
 be more useless than useful, but for our theory it has the ad- 
 vantage of placing the ventilator between two motionless 
 atmospheres, the air being drawn from one and thrown into 
 the other. The situation is clear, and the analysis equally so. 
 
 I propose, then, in the course of this discussion, to 
 consider only an ideal ventilator, presenting no play, nor 
 shocks, nor losses of quantity of any kind. In practice, of 
 course, it is very far from attaining this ideal, the necessity 
 of a simple construction, so as to work with certainty, obliging 
 us to preserve numerous imperfections in detail ; but to 
 introduce these imperfections in the calculation would be to 
 
10 THE THEORIES AND PRACTICE OF 
 
 expose ourselves to inextricable complications. It is much 
 better to go straight to the theoretical result. 
 
 The ventilator with centrifugal force without cover is re- 
 presented in its essential features by Fig. 2, the vanes as 
 drawn showing the profile somewhat bent and approaching 
 the ouie in a manner to afford the desired inclination, so 
 that the air penetrates without shock between these spaces. 
 
 FIG. 2. 
 
 These vanes are sufficiently numerous to assure the regular 
 drawing of the air from the centre to the periphery without 
 eddies or disturbances. I will call r the radius of the ouie 
 or inlet, E that of the external circumference, CD the angular 
 speed of rotation. The result, co E, expresses the absolute 
 speed of the extremities of the vanes. This speed plays a 
 preponderating role in all this discussion. I will call it the 
 tangential speed, and I will mark it by the letter u. 
 
 The depression produced by such a machine will result 
 from a series of actions, some additive and some subtractive. 
 We may, then, determine them successively and in their 
 order, so as to draw the balance. 
 
 First, the motionless air in the vestibule is brought 
 
CENTRIFUGAL VENTILATING MACHINES. 11 
 
 to the speed V , with which it traverses the ouie and 
 penetrates between the spaces of the wings. There is then 
 to the debit of the depression the height generative of this 
 speed 
 
 Second, the air once drawn between these vanes has a 
 double movement, the movement relative to the dragging 
 after the surface of the vanes, and the movement of drawing 
 produced by the rotation of the machine, but theory 
 requires that the total depression should be the sum of the 
 elementary depressions due to each of these movements. Let 
 us look first at the relative movement. 
 
 The interval between two consecutive vanes forms an 
 evasee canal which the air enters with a certain speed Vi, 
 and leaves with a less speed V 2 . From this slowing action 
 results, according to Bernouilli's theory, a gain of depression 
 expressed by the difference 
 
 YL_YI 
 
 20 20* 
 
 But the speed of entry Vi is the resultant of two redt- 
 angular speeds, the one V following the radius, the other &> r 
 equal and opposite to the tangential speed of the wings. In 
 the ideal ventilator which I have here supposed, the interior 
 surface of the wings is directed exactly in accordance with 
 this result, so that the composition of the speeds is produced 
 without] obstacle, and the air slides without shock on the 
 cutting surface of the vanes ; I may, then, replace in the 
 preceding expressions V x 2 by the sum V 2 -f- &> 2 r 2 , and bring 
 to the gain of the depression the algebraic sum 
 
 20 
 
12 THE THEORIES AND PRACTICE OF 
 
 Third, the movement of drawing in, which is a uniform 
 rotation, creates the centrifugal force, which in its turn pro- 
 duces a gradual increase of pressure from the ou'ie to the 
 exterior circumference. If I isolate in imagination a pris- 
 matic element of the air drawn in, placed at a distance x 
 from the centre and presenting a height d x in the direction 
 of the radius, a base S in the perpendicular direction, and a 
 density 8, the mass in this element will be 
 
 SdxB 
 
 and the centrifugal force developed by the rotation 
 
 Sd'xS , 
 d F = --- o> 2 x. 
 
 The increase of depression per unit of surface from one base 
 to the other of this little prism will be got by dividing the 
 preceding expression by S. We will divide again by 8, to 
 have this pressure expressed as usual in the column of air, 
 and we shall have finally for the differential increase of the 
 pressure due to the centrifugal force 
 
 , 7 
 
 d h = 
 
 And integrating from x = r up to x = E, we shall have for 
 a total difference of pressure from the circumference of the 
 ouie to that at the outside of the vanes 
 
 . 
 
 a value to be carried to the credit of the depression produced 
 by our ventilator. 
 
 Our analysis is now complete, and we may make the 
 
CENTRIFUGAL VENTILATING MACHINES. 13 
 
 addition. Many terms, some positive and some negative, 
 cancel themselves, and there will only remain, when 
 designating by the letter u the tangential speed <oK, the 
 simple expression 
 
 an expression which subsists whatever may be the curve 
 given to the wings and the inclination under which they 
 reach the exterior circumference. 
 
 The ventilator which we are now studying is in reality a 
 very bad machine. Although it responds sufficiently well 
 to the first of the two conditions which every machine must 
 fulfil in which fluids circulate, that is to say it receives the 
 air without shock, it is still far from realising the second, the 
 escape without speed. The air extracted from the interior is 
 thrown into the atmosphere with considerable speed, result- 
 ing from the tangential speed u and the speed relative to 
 the outlet V 2 . 
 
 This important defect has not escaped constructors, who 
 have generally sought to provide a remedy. The first means 
 which they have employed, and which presented itself 
 naturally, consists in giving a large inclination to the wings, 
 so that they arrive in an angle more or less sharp at the 
 periphery. In opposing in this way the relative speed of 
 outlet to the speed at the extremity of the vanes, they hope 
 if not to annul at least to diminish to a great extent the 
 absolute speed of expulsion into the atmosphere, and so to 
 improve the result. This arrangement was adopted by 
 Combes, who carried things to an extreme, making his 
 vane tangential to the exterior circumference, that is to 
 say, at an angle of 0. We reproduce (Fig. 3) the curve 
 of his ventilator, but success has not responded to this 
 theoretical view. To understand the cause it is sufficient 
 
14 THE THEORIES AND PRACTICE OF 
 
 to reduce to its value the depression expressed by the 
 difference 
 
 = - 
 
 20 20* 
 
 This difference constitutes in effect a veritable antithesis. 
 To weaken in a sensible degree the absolute speed of expul- 
 sion by opposing to the tangential speed u the relative 
 
 FIG. 3. 
 
 speed V 2 , we must admit for this last a considerable value 
 
 V 2 
 approaching u, but then the negative term ^- increases, 
 
 *9 
 the depression weakens, and the machine loses its power. 
 
 If to recover it we have recourse to an increase of 
 the speed of rotation, we increase at the same time the 
 passive resistance of the machine and its motor, and that 
 which we gain on one side we lose on the other. 
 
 Such is certainly the principal if not the only cause of 
 results so little satisfactory as those given by the experiments 
 of M. Glepin on the Combes ventilator, the tangential 
 speed being almost three times that which is required under 
 
CENTRIFUGAL VENTILATING MACHINES. 
 
 15 
 
 the same conditions by the Guibal ventilator, and the pro- 
 portion of useful work to the motive power measured by 
 Prony's brake has never exceeded 29 per cent. There exists, 
 happily, a very efficient means for improving the resultant 
 of ventilators it is that connected with the name of 
 M. Guibal. 
 
 The ventilator is inclosed in a cover, more or less eccentric, 
 which does not permit of the exit of the air except by a 
 narrow passage a &, Fig. 4, regulated according to the yield 
 
 FIG. 4. 
 
 of the machine. This passage is continued into the long 
 evasee chimney. The speed of expulsion existing in the 
 orifice a b is extinguished little by little, just as the air 
 rising in the chimney fills larger areas, until it becomes 
 inactive at the moment when it is expelled into the 
 atmosphere. This extinction of speed occasions, as theory 
 requires, a considerable depression, which is added to that 
 produced by the centrifugal force, increasing in a marked 
 manner the power of the machine. 
 
 This effect, so remarkable in the Guibal chimney, has 
 
16 
 
 THE THEORIES AND PRACTICE OF 
 
 surprised many persons not familiar with the theory of the 
 flow of fluids. For those who have any doubt I advise a 
 study of the description of the ajutage of Venturi, given in 
 all treatises on hydraulics. This ajutage presents at first a 
 narrowing, then a space gently expanding, like a Guibal 
 chimney. But this theory requires that in this expanding 
 part there should be an integral restitution of active force 
 developed to recover the obstruction ; consequently the yield 
 of the ajutage is the same as if the narrowing did not exist. 
 
 FIG. 5. 
 
 As in our Fig. 5 above, the yield of A will be the same as 
 that of B. We cannot hope, however, in practice, in the 
 Guibal chimney any more than in the ajutage of Venturi, to 
 see realised a perfect restitution of active force. It is 
 certain, however, that this effect is produced to an important 
 degree, as has been witnessed by numerous observers. 
 
 In place of a single chimney we may imagine a series of 
 small chimneys starting from each point in the circum- 
 ference. This arrangement has been proposed by M. Harze 
 in the Revue TJniverselle of Liege, 1870. The effect may be 
 the same, perhaps better, but I do not believe that the idea 
 has ever been carried out. 
 
 What assistance does the Guibal chimney give to the 
 depression ? The answer is immediately given by the theory 
 
CENTRIFUGAL VENTILATING MACHINES. 17 
 
 of Bernouilli, the application of which presents itself at each 
 step in this study. If in effect V is the speed of the air at 
 the bottom of the chimney and W the speed at the top, this 
 theory will immediately give for the corresponding increase 
 of pressure the difference 
 
 V 2 ^y2 
 
 The speed V is that which the air possesses on leaving 
 the vanes; it is thus the resultant of the tangential 
 speed u and of the speed relative to the outlet V 2 . The 
 parallelogram of these speeds furnishes the known relation 
 between them 
 
 V 2 = w 2 + V 2 2 - 2 u V 2 cos a, 
 
 a being the angle at which the vanes strike the exterior 
 circumference. 
 
 In substituting this value of V 2 in the preceding expression 
 we shall have for this latter 
 
 tt 2 Y 2 2 MV 2 COSq_W 2 
 
 The ventilator alone without envelope or chimney has given 
 already 
 
 Adding together, then, it becomes, all simplifications 
 made, 
 
 " J ~ 
 
 u V 2 cos a W 2 
 
 an expression of the total depression developed by the 
 Guibal ventilator. 
 
 We have now this interesting question, Under what in- 
 clination a should the vanes strike the exterior circumference 
 
18 THE THEORIES AND PRACTICE OF 
 
 for the machine to develop the maximum of depression? 
 The reply is simple. It is that this inclination is 90, in fact 
 this value of a makes the negative term 
 
 u V 2 cos a 
 
 g 
 
 disappear, and there remains only for the theoretical 
 depression 
 
 So the vanes of the Guibal ventilator, and in general every 
 ventilator intended to restore the active force, should strike 
 normally to the exterior circumference. We may besides 
 foresee, without any analysis, from the moment in fact that 
 the speed of expulsion is utilised, that a gratuitous waste of 
 power takes place if the vanes are inclined. 
 
 However, this condition was not apparent at once to the 
 inventor, for his first machines generally had inclined vanes. 
 But it has been realised in machines recently constructed, 
 as we saw in the large ventilator which was shown at the 
 Champ de Mars in the Belgian section. 
 
 I will assume now that throughout the remainder of this 
 study I need not trouble myself further as to the angle a. 
 The line which results for the vanes of the ventilator is given 
 by Fig. 6. The vanes begin at the circumference of the 
 ouie with an inclination to enable them to receive the air 
 without shock. They continue upwards with a gentle curve, 
 and end in a right line following the radius. 
 
 One condition still remains to be fulfilled in order that the 
 ventilator may be, so to say, perfect an ideal of which we 
 have spoken above : it is necessary that the air expelled 
 should escape without speed. From the theoretical point of 
 view in which we place it, the solution is clearly shown. We 
 have only to imagine that the chimney is prolonged with an 
 
CENTKIFUGAL VENTILATING MACHINES. 
 
 19 
 
 increasing capacity to a sufficiently great height, so that the 
 speed of the air at its summit may be considered as nothing. 
 Then W becomes equal to zero, and the total depression de- 
 veloped by the perfect ventilator takes the unquestionably 
 simple form 
 
 which we may translate into ordinary language by saying that 
 the theoretical depression is the double of the height created ~by 
 the tangential speed. 
 
 This value forms the basis of the theory, but I repeat that 
 it only applies to an ideal ventilator. In practice, a thousand 
 
 FIG. 6. 
 
 imperfections of detail will prevent the initial depression 
 attaining such an elevated point. We are obliged to intro- 
 duce a coefficient of reduction, and to write 
 
 '". H-K* : . 
 
 9 
 
 K being a fraction more or less near unity in proportion as 
 the constructor shall have made more or less effort to realise 
 the indications of reasoning and calculation. This fraction 
 
 c 2 
 
20 THE THEORIES AND PRACTICE OF 
 
 K, which expresses the proportion of the initial depression to 
 the theoretical depression, is, properly speaking, the useful 
 effect in depression in the ventilator. I will call it after- 
 wards the manometrical yield, reserving, according to usage, 
 the mechanical yield, or the yield, properly speaking, of the 
 proportion of the work utilised to the work of the motor. 
 Already we have seen that for uncovered ventilators the 
 manometrical yield must be always less than half. In fact, 
 
 u 1 V 2 
 the maximum depression in these machines, ^ -^- is 
 
 u* 9 9 
 
 already less than half of . With the covered ventilators 
 
 9 
 
 the yield largely exceeds this limit, but will remain far 
 short of unity. 
 
 I should observe incidentally that this value of the de- 
 pression fully justified the principle admitted by the Com- 
 mission of Gard, that all the ventilators having the same 
 tangential speed are theoretically equal. 
 
 Having thus determined the value of the initial depression, 
 there remains nothing more for us than to carry forward the 
 two formulae established in the preceding paragraph. We 
 then obtain the two following expressions, which comprehend 
 the whole theory of centrifugal ventilators : 
 
 First, The value of the effective depression 
 
 *\ "*"<? 
 
 Second, Value of volume yielded per second 
 0-65 
 
 The ventilator is defined by its tangential speed and its 
 orifice of passage data which depend only on the constructor ; 
 
CENTRIFUGAL VENTILATING MACHINES. 21 
 
 the mine, by its equivalent orifice ; the other terms being 
 constants. In these two expressions there only enter known 
 quantities, which is the object we pursue. 
 
 We easily see, without it being necessary to insist upon it, 
 that these formulae apply equally well to blowing venti- 
 lators as to drawing ventilators. It is sufficient in such a 
 case to replace the word depression by that of compression. 
 
 If we remember that the tangential speed u is equal to the 
 product co R of the angular speed by the radius, the two 
 preceding formulae immediately show the two well-known 
 laws: First, The volume yielded varies as the speed of 
 rotation. Second, The depression varies as the square of 
 this speed. 
 
 .These two laws have effect according to the radius or 
 diameter of the ventilator, with the condition that the angular 
 speed is invariable. Those which connect the volume and 
 the depression with the equivalent orifice of the mine cannot 
 be easily translated in ordinary language. We may say, no 
 doubt, that the volume increases as the depression lowers 
 when the mine is made larger, but it would be difficult in 
 precise and simple terms to express the law of this variation. 
 I prefer to have recourse to a drawing. 
 
 I place on the line of abscissae the increasing value of the 
 equivalent orifice. This line will represent, if we wish, by 
 the aid of a figure, a long rectangular orifice, closed by a 
 sliding door, which we may draw by degrees. In the ordinates 
 will be given the corresponding values of volume yielded and 
 of the depression. We thus obtain the two curves repro- 
 duced in Fig. 7. 
 
 On the first of these curves we see the depression com- 
 mences, when the mine is closed, with its initial value 
 
 9 
 then, in proportion as the mine is enlarged, the depression 
 
 lowers, and is not destroyed altogether except when the 
 
22 
 
 THE THEORIES AND PRACTICE OF 
 
 orifice of the mine becomes equal to infinity. This is the 
 case of the ventilator acting freely in the atmosphere, when 
 in effect the whole depression is absorbed by the interior 
 frictions of the machine. 
 
 The curve of the volume afforded commences at the same 
 point, for when the mine is shut off the yield is naturally 
 nothing. From that it rises rapidly, then bends little by 
 little, and terminates by a long horizontal branch where the 
 
 FIG. 7. 
 
 asymptote has for its ordinate the volume 0' 65 \/2 K o u. 
 This volume is that which the ventilator affords when the 
 mine is suppressed and the air has free access to the ome ; 
 it depends alone on the orifice of the passage and specifies 
 its influence. 
 
 We observe in this latter curve the characteristic curve of 
 the Commission of Gard. The same graphic method permits 
 us to study the influence of the orifice of passage on the 
 volume and upon the depression, but I think it useless to 
 discuss it. Such is the theory which for many years I have 
 
CENTRIFUGAL VENTILATING MACHINES. 23 
 
 had under consideration. If we recall the numerous essays 
 on like theories which have appeared in scientific publi- 
 cations, we shall find that the authors have been generally 
 induced to follow the phenomena step by step from the 
 moment when the air penetrates the passages of access up 
 to that when it escapes into the atmosphere. Each friction, 
 each bend, each loss of air or of duty gives rise to a new 
 analytical expression, where the succession extends often 
 beyond measure. The last work which has appeared, that of 
 M. Ser, Professor at the Central School, concludes with 
 no less than fifteen distinct relations between twenty-six 
 quantities. 
 
 In that which I propose now, all these innumerable facts 
 of detail or of minute analysis will be found stated in a 
 manner easy to be understood and with perfect clearness ; 
 such as are exterior to the ventilator to be studied, being 
 expressed en Uoc by the " equivalent orifice " of the mine. 
 It is, doubtless, unnecessary to add that this fiction is equally 
 adapted to represent the resistance of furnaces, cupolas, and 
 various other conditions as well as the galleries of mines. As 
 to the resistance and imperfections proper to the ventilator 
 itself, they divide themselves into two groups differing in 
 their nature, each one appearing with pleasing simplicity. 
 First, The frictions and losses of duty, all quantities propor- 
 tional to the square of the yield, are expressed simply by the 
 orifice of passage 0. Second, The imperfections of every 
 kind, independent of the yield, which prevent the initial de- 
 
 u" 2 
 pression reaching the theoretical value are summed up in 
 
 the manometrical result K. These two ideas may be trans- 
 lated in ordinary language in a manner which assists their 
 being studied and easily remembered. We may distinguish, 
 in fact, in every deprimogen ventilator that which I will call 
 the depressing power and the power of yield. 
 
24 THE THEORIES AND PRACTICE OF 
 
 A cupola fan may give considerable depressions or com- 
 pressions, but it is incapable of furnishing a yield sufficient 
 for the ventilation of a mine or a hospital. We say of it 
 that its depressing power is high and its yield power low. 
 On the contrary, the large machine, with curved vanes or 
 with a screw, has the -power to afford enormous yields, but 
 can never produce great depressions ; here the two powers 
 must be inversely qualified. But the yielding power has 
 its expression naturally in the orifice of passage and the 
 power of depressing in the manometric yield. 
 
 3. EXPERIMENTAL VERIFICATION. 
 
 I shall stop a little to consider the first two laws resulting 
 from our formulae, which connect the volume of air and the 
 effective depression with the speed of rotation. No one to- 
 day will dispute that the volume is proportionate to the 
 speed of rotation and the depression to its square. All the 
 published experiments up to this time put these facts clearly ; 
 and for my part I have verified them many times. To leave 
 no doubt in the mind of the reader, I have given, in an 
 additional note (B), a few of the most noteworthy of these 
 experiments. 
 
 The influence of the speed of rotation being thus estab- 
 lished beyond question, I may suppose in the remainder of 
 this work that the ventilators studied turn at an invariable 
 strictly regulated speed whatever may be the resistance. 
 Matters are thus simplified, and it will be under these 
 simplified conditions that I shall pursue the experimental con- 
 sideration of the theory described in the preceding paragraph. 
 
 As I have said at the beginning, the work of the Commis- 
 
CENTRIFUGAL VENTILATING MACHINES. 25 
 
 x 
 
 sion of Gard has furnished ine with numerous and sure data, 
 prepared fortunately for the verification which concerns 
 us. We may recall in a few words the object and result of 
 these experiments. 
 
 Four ventilators with centrifugal force have been studied 
 by the Commission, viz. : 
 
 The ventilator of Lalle, a kind of turbine 12J feet in 
 diameter, without cover, and throwing out the air by its 
 whole circumference ; 
 
 The ventilator of La Sagnette, a small machine of 9 feet 
 in diameter, turning at a high speed, having a cover, but 
 without a chimney ; 
 
 The ventilator of Creal, 19 * 68 feet in diameter, covered, 
 and with rectangular chimney ; 
 
 Lastly, the ventilator of Besseges, 16 '4 feet in diameter, 
 representing the Guibal type, with a cover, movable slide, 
 and expanding chimney, but without the last improvements 
 introduced by the inventor, the straightening of the vanes in 
 the direction of the radius. 
 
 By creating and removing obstacles to the course of the 
 ventilation we make for each machine five imaginary mines, 
 corresponding to five degrees of resistance to the circulation 
 of the air, degrees sufficiently marked to distinguish all the 
 usual values of this resistance from the thinnest seams to 
 the thickest. For each of these we measure the speed of 
 rotation, the depression, and the volume of air yielded, 
 without prejudice to the atmospheric observations such as the 
 pressures and temperatures. By the aid of these data we 
 make a calculation of the equivalent orifice ; then we obtain 
 the volume of air observed at the same speed, for comparison, 
 called the normal speed ; lastly, we carry these results into 
 a drawing, the equivalent orifice being the abscissae, the 
 volume in ordinates, and the five points so obtained enable us 
 to draw the characteristic curve of the machine. 
 
26 THE THEORIES AND PRACTICE OF 
 
 We have now to examine these same results, verifying 
 the two fundamental formulae established above. For 
 instance, for the depression 
 
 Kw 2 
 
 f -+ 
 
 for the volume yielded 
 
 _ 0-65 
 
 At the same time, it is not only by these formulae themselves 
 that I establish the verification. 
 
 It is preferable, in order to simplify the matter, to combine 
 these two formulae in one, by eliminating from them the 
 equivalent orifice a. We obtain thus the equation 
 
 K 
 
 It may be written by replacing the initial depression - 
 
 by H, and the constant factor _ - -- , by M. 
 
 0-65 o 2 2g 
 
 Then 
 
 Ti = H - MV. 
 
 With this new equation I find this double advantage : 
 First, the avoiding of the calculation of the equivalent 
 orifice. Second, the obtaining of a straight line by a drawn 
 curve, V 2 in abscissae and h in ordinates. 
 
 Nothing is more easy than the verification when a series of 
 points form a straight line. We may even say, in a general 
 manner, that there is no method more convenient and more 
 
CENTRIFUGAL VENTILATING MACHINES. 27 
 
 qualified to make us certain that experiments are true than 
 when the equations expressing this law can be shown by a 
 straight line. 
 
 I strongly recommend this formula to the study of 
 engineers desirous of making observations or experiments on 
 their ventilators. It forms the exact counterpart to the well- 
 known formula established by M. Trasenster for the volu- 
 mogen ventilator 
 
 V = W - M VA, * 
 
 from which it differs only in the substitution of h for V, and 
 over which it possesses a great advantage, since it shows 
 directly, without previous transformation, the volumes and 
 depressions given by the experiments, as it remains applic- 
 able whatever may be the intensity of the natural action, 
 which at all times governs the mechanical action of the 
 ventilator. 
 
 This latter point is rather difficult to show clearly, and I 
 fear, in wishing to show too much, that I shall not succeed in 
 making myself sufficiently understood. I am led, then, to say, 
 leaving to the reader to use his own discretion, that the 
 natural effect, whether additive or subtractive, should 
 equalise in fact either a diminution or an increase of the 
 resistance which the air must overcome to traverse the mine, 
 the resistance being expressed by the equivalent orifice of the 
 mine. But the connection between h and V is expressed by 
 each of the two formulae, whatever this orifice may be. 
 
 I should observe that these formulae do not change when 
 the depression is expressed in inches of water, as is usual 
 when making such experiments. The transformation neces- 
 sary in effect is to multiply the constants by the proportion, 
 
 c^ 
 
 itself constant, of the densities of the air and water -^ . These 
 
 * W is the volume per second, and M a constant coefficient. 
 
28 
 
 THE THEORIES AND PRACTICE OF 
 
 preliminaries given, I will at once turn to the experiments 
 of the Commission, and first, to those made on the ventilator 
 of Creal, which verify with perfect exactness the formula we 
 have given. These experiments are summarised in the 
 following table : 
 
 i 
 
 Equiva- 
 lent 
 Orifice. 
 
 Speed 
 of 
 Rotation. 
 
 Volume 
 per 
 Second. 
 
 Square of 
 Volume, 
 
 Observed 
 Depression, 
 
 Calculated 
 Depression. 
 
 Difference. 
 
 1 
 
 sq. ft. 
 6-604 
 
 63-66 
 
 cub. ft. 
 298-82 
 
 89283-39 
 
 in. 
 1-0598 
 
 in. 
 1-0582 
 
 + 0-0016 
 
 2 
 
 9-985 
 
 
 
 442-45 
 
 195766-00 
 
 1-0183 
 
 1-0193 
 
 -o-ooio 
 
 3 
 
 12-199 
 
 
 
 532-16 
 
 283194-46 
 
 0-9866 
 
 0-9873 
 
 -0-0007 
 
 4 
 
 14-846 
 
 H 
 
 635-99 
 
 404483-28 
 
 0-9452 
 
 0-9428 
 
 + 0-0024 
 
 5 
 
 20-922 
 
 J 
 
 839-31 
 
 704441-28 
 
 0-8314 
 
 0-8308 
 
 +0-0006 
 
 But if we draw to a scale the numbers of the fourth column 
 in abscissaB, and those of the fifth in ordinates, the five points 
 so got will show with great perfection that the same drawing 
 of the straight line covers everything. 
 
 We may see besides by the numbers of the seventh column, 
 the difference existing between the points and the absolute 
 straight line. 
 
 FIG. 8. 
 
 O Squares of Volumes. 
 
 The equation for this straight line is 
 
 h = 1-0908 in. - -000000365 V 2 , 
 
 from which I may conclude that this excellent verification 
 of the theory established above for ventilators with centri- 
 fugal force is in every case rigorously the expression of facts. 
 
CENTRIFUGAL VENTILATING MACHINES. 
 
 29 
 
 But we shall presently see that it is prudent to make certain 
 reservations. 
 
 I pass to the ventilator of Lalle, and present in a second 
 table the results given by this machine : 
 
 1 
 
 o 
 
 Equiva- 
 lent 
 Orifice. 
 
 Speed 
 of 
 Rotation. 
 
 Volume 
 per 
 Second. 
 
 Square 
 of Volume, 
 X. 
 
 Observed 
 Depression, 
 Y. 
 
 Calculated 
 Depression. 
 
 Difference. 
 
 1 
 
 2 
 3 
 4 
 5 
 
 sq. ft. 
 4-045 
 8-289 
 11-434 
 12-893 
 14-868 
 
 100-52 
 
 H 
 
 j> 
 
 55 
 
 cub. ft. 
 177-98 
 354-75 
 471-34 
 525-80 
 595-76 
 
 31676-78 
 125847-56 
 222163-19 
 276465-64 
 354929-98 
 
 in. 
 1-0303 
 0-9673 
 8976 
 0-8760 
 0-8543 
 
 in. 
 1-0228 
 0-9677 
 0-9114 
 0-8799 
 0-8342 
 
 in. 
 + 0-0075 
 -0-0004 
 -0-0138 
 -0-0039 
 + 0-0201 
 
 Here the five points do not appear with the same perfec- 
 tion as in that of Creal. Still the average straight line is 
 exhibited with sufficient clearness. We may see by the 
 numbers of the seventh column that the divergence exceeds 
 hardly one-third of a millimetre. I may add that at Lalle 
 the section for measuring is in a very inconvenient situation 
 for observers, which will sufficiently explain the slight irre- 
 gularity in the results. The equation for the average 
 straight line is 
 
 h = 1-0413 in. - -00000058 V 2 . 
 
 Let us go, now, to the Guibal ventilator of Besseges, 
 The experiments made on this machine are collected in 
 the third table : 
 
 I 
 
 Equiva- 
 lent 
 Orifice. 
 
 Speed 
 of 
 Rotation. 
 
 Volume 
 per 
 Second. 
 
 Square 
 of Volume, 
 X. 
 
 Observed 
 Depression, 
 
 Calculated 
 Depression. 
 
 Difference. 
 
 
 sq. ft. 
 
 
 cub. ft. 
 
 
 in. 
 
 in. 
 
 in. 
 
 1 
 
 3-921 
 
 76-39 
 
 187-32 
 
 35088-78 
 
 1 ' 1795 
 
 1-3042 
 
 -0-1247 
 
 9, 
 
 7-455 
 
 
 364-79 
 
 135269-26 
 
 1-2779 
 
 1-2763 
 
 +0-0016 
 
 3 
 
 20-914 
 
 J5 
 
 951-05 
 
 904496-10 
 
 1-0665 
 
 1-0681 
 
 -0-0016 
 
 4 
 
 25-521 
 
 fj 
 
 1114-00 
 
 1240986-00 
 
 0-9827 
 
 0-9764 
 
 + 0-0063 
 
 5 
 
 29-343 
 
 5 
 
 1225-15 
 
 1500992-52 
 
 0-8996 
 
 0-9059 
 
 -0-0063 
 
30 THE THEORIES AND PRACTICE OF 
 
 Here the four latter points range themselves in a straight 
 line, having for their equation 
 
 h = 1-3137 in. - -00000027 V 2 . 
 
 The first point is certainly below this line. The variation 
 is much too great to permit this to be attributed to any error 
 in observation. Some experiments made before on the ven- 
 tilator of Creal having always given me the same irregularity, 
 I am led to assert as a fact that for very thin seams the 
 depression is always below the mark which the results give 
 for larger ones. 
 
 If, putting the thing to an extreme, we shut completely off 
 the gallery yielding the air to the ventilator, instead of the 
 initial depression H, we find only a less value. Thus for the 
 ventilator of Besseges 1 128 in. in place of 1 '313 in. 
 
 To what can we attribute this depression, this shortcoming, 
 if I may say so, of the depression in the case of thin mines ? 
 The causes are numerous. A moment of reflection will 
 enable us to discover them. As soon as we lower the 
 movable shutter to accommodate the orifice of the outlet to 
 the diminished yield, we transform this orifice into a straight 
 rectangle, by which the air escapes in a thin stream. The 
 perimeter friction increases in proportion to the section, 
 and the loss of duty assumes a rapidly increasing 
 importance. 
 
 In the second place, the inclination which the vanes at 
 their commencement present to the air so as to strike it 
 without shock, only applies to a given yield ; with a circula- 
 tion of air greater or less, there naturally follows a shock. 
 In general this inclination is calculated for thick mines, 
 and the useless effect, although unfelt, for average seams, 
 rapidly increases for very thin ones, and helps to reduce 
 the depression. 
 
 At the same time, with thin seams it becomes certainly 
 more difficult to obtain a flow with full mouth in the spaces 
 
CENTKIFUGAL VENTILATING MACHINES. 
 
 31 
 
 of the vanes and in the Guibal chimney a flow indispen- 
 sable to realising the full restitution of the vis viva, in the 
 manner of the ajutage of Venturi. This remark seems 
 to be corroborated by the fact that in the case of thin seams 
 the depression lacks absolute fixity : it is so vacillating that 
 measurements taken at a few minutes' interval give quite 
 different results. 
 
 It follows from the preceding remarks that the straight 
 line required by our theory cannot be followed up rigorously 
 to the original ordinate. It bends when applied to very 
 thin seams of from 4-304 sq. ft. to 5 '38 sq. ft. of equivalent 
 
 FIG. 9. 
 
 Square of 
 
 orifice, as is shown in Fig. 9, the inflection beginning more 
 or less quickly according to the machine. On the other 
 hand, they seem to demand an indefinite continuation in the 
 case of thick seams. 
 
 This experiment on the Besseges ventilator shows it 
 in fact as far as a mine of 29 '33 sq. ft. of equivalent orifice, 
 a value rarely exceeded even in England. Mines having 
 seldom if ever been found with less than 4 '30 sq. ft. of 
 equivalent orifice, we may admit that within the limits met 
 with in practice our theory is justified. 
 
 I have not been able to utilise for the verification I seek 
 the results obtained by the Commission with the ventilator of 
 La Sagnette. This machine has a peculiarity which puts it 
 outside of our theory. I said above that in covered ventilators 
 
32 THE THEORIES AND PRACTICE OF 
 
 the outlet constructed for the expulsion of the air should be 
 regulated to the yield of the machine small with thin seams 
 and larger for thick ones. At Besseges, with the aid of 
 the moving slide, at Creal by taking away or adding deal 
 boards to the cover, the Commission was able on each occa- 
 sion to make this previous adaptation. At La Saguette the 
 disposition of things did not adapt themselves to this : the 
 orifice of outlet remained invariable, and would only suit, 
 therefore, a particular mine. With seams thinner or thicker, 
 and with these latter especially, considerable resistances 
 arise, preventing the depression and yield from attaining the 
 values we have a right to expect. The five points in this 
 latter case did not range in a straight line ; the depression, 
 at first feeble, gradually rose to a maximum for the state of 
 mine for which it was intended. 
 
 We may, then, with the aid of the numerical values 
 which we have found for the constants H and M of our 
 equation, determine the characteristic data of the three ven- 
 tilators studied by us. I wish to speak of their manometrical 
 result and of their orifices of passage. We have in effect the 
 two following equations : 
 
 H = ^, 
 
 0-65 o 2 20 
 
 If, taking the first of these equations, I give successively to 
 
 H the three values obtained above, having taken care to 
 
 ^ 
 
 divide them by the proportion ^ of the densities of air and 
 
 water, the following corresponding values of manometrical 
 result will be obtained : 
 
 For the ventilator of Besseges -691 
 
 Creal -572 
 
 Lalle -542 
 
CENTKIFUOAL VENTILATING MACHINES. 33 
 
 These results fully confirm the theory that the Gruibal 
 ventilator fitted with evasee chimney has the best results. 
 That of Creal comes only second on the list, for its chimney 
 is insufficient ; while the Lalle ventilator, which has neither 
 cover nor chimney, necessarily comes last. 
 
 We may, indeed, be astonished that this last machine 
 reaches even so high a result. We have said above that a 
 ventilator without a cover cannot obtain a result in mano- 
 metrical effect superior to 50 ; but if we refer to the report 
 of the Commission we shall find that this machine turns in 
 a semicircular passage, which must certainly affect the yield 
 in the same manner as a cover. 
 
 I reach, then, the second equation and the data affecting M, 
 
 and as I did to H, so the three values obtained in the course 
 
 a 
 
 of this paragraph must always be divided by -. From the 
 
 o 
 
 three equations which result I deduce for the orifice of 
 passage o the following values : 
 
 For the ventilator of Besseges 43-81 sq. ft. 
 
 Creal 37-87 
 
 Lalle 30-02 
 
 The order of the orifices of passage is the same as that 
 of the depressions, but we must not in consequence draw 
 general deductions, for the theory will not warrant it. We 
 understand in effect that the orifice of passage depends above 
 everything on the construction and on the width which is 
 given to the vanes and to the ouie, and to the section which 
 allows the passage of the air. 
 
 The Guibal of Besseges is 7 56 feet in width and 9 84 feet 
 in the ouie. The ventilator of Creal is a large machine of 
 19*58 feet diameter and 11 '5 feet in the owe, but the width 
 has been reduced to 3 6 feet. As to the ventilator of Lalle, 
 
34 THE THEORIES AND PRACTICE OF 
 
 the ouie is not more than 5 8 feet in diameter and the width 
 from 4 32 feet at the axis to not more than 1 95 foot at the 
 circumference. 
 
 We find frequently in the industrial publications results 
 of experiments made on ventilators with centrifugal force, 
 especially since the impulse given by M. Guibal to machines 
 of this class. The authors of these experiments have rarely 
 taken the trouble to vary the resistance of the mine as 
 was done by the Commission of Gard. In general they 
 have only changed the speed of the ventilator, which, in 
 virtue of the proportional law established, is equivalent to 
 only one experiment. Such work cannot be utilised for the 
 determination of the orifice of passage and manometrical 
 result. I must, however, make an exception in favour of a 
 study of great interest published in the Annales des Mines in 
 1860 by M. Tournaire. I reproduce the results obtained by 
 him, but they only apply to the forge fan; still, it is in- 
 teresting to show them in connection with large machines 
 examined by the Commission. 
 
 The ventilator of M. Tournaire was studied with the 
 greatest care in its smallest details, excepting one point, 
 which as we have seen above is of the highest importance 
 it was not covered ; the air being driven out all round the 
 circumference. It was 2*788 feet in diameter, and turned 
 with a speed of 1500 to 1700 revolutions per minute, which 
 gave a tangential speed of 219 to 250 feet per second. 
 Nevertheless, to render these experiments comparable to 
 those of the Commission, I have reduced them all to the 
 tangential speed of 65 6 feet. This new table is drawn in 
 the same manner as the preceding ones. The equivalent 
 orifice which I show in the first column is nothing but the 
 sum of the surfaces of the open orifices : 
 
CENTRIFUGAL VENTILATING MACHINES. 
 
 35 
 
 1 
 
 Equivalent 
 Orifice. 
 
 Speed 
 of 
 Rotation. 
 
 Volume 
 per 
 Second. 
 
 Square 
 of Volume, 
 X. 
 
 Observed 
 Depression, 
 Y. 
 
 Calculated 
 Depression. 
 
 Difference. 
 
 1 
 
 sq. ft. 
 2540 
 
 449-38 
 
 cub. ft. 
 8-94 
 
 79-92 
 
 in. 
 7551 
 
 in. 
 7645 
 
 in. 
 -'0094 
 
 2 
 
 4230 
 
 
 14-48 
 
 209-67 
 
 7142 
 
 7185 
 
 + 0043 
 
 3 
 
 5069 
 
 
 17-34 
 
 300-68 
 
 6996 
 
 6862 
 
 + 0134 
 
 4 
 
 5435 
 
 
 19-95 
 
 398-00 
 
 6831 
 
 6512 
 
 + 0319 
 
 5 
 
 7610 
 
 
 24-86 
 
 618-22 
 
 7000 
 
 6520 
 
 + 0480 
 
 6 
 
 8450 
 
 
 26-03 
 
 677-56 
 
 5512 
 
 5521 
 
 -0009 
 
 7 
 
 9300 
 
 
 27-97 
 
 782-32 
 
 5134 
 
 5149 
 
 -0015 
 
 8 
 
 1-0462 
 
 
 29-77 
 
 886-25 
 
 4807 
 
 4779 
 
 + 0028 
 
 The first three points and the last three range themselves 
 sufficiently near to a straight line, where the equation is 
 
 h = -793- -000355V 2 . 
 
 The two intermediate points place themselves above very 
 distinctly. 
 
 It is difficult to distinguish the causes which produce this 
 difference, perhaps there exists a special yield for which the 
 ventilator is particularly well proportioned. 
 
 The constants of this straight line permit me to calculate, 
 as for the preceding ventilators, the manometrical yield 
 and the orifice of passage of this new machine. I obtain 
 thus the two following values 
 
 Manometrical yield -403 
 
 Orifice of passage 141 sq. feet. 
 
 As the theory requires, the manometrical yield is inferior 
 to 0*50. The addition of an eccentric envelope, following 
 out M. Guibal's idea, certainly increases in a very great 
 measure the compressing power of this ventilator. As to 
 the orifice of passage, its lessened value is explained quite 
 naturally by the small dimensions of the machine. Beyond 
 the interesting data which I have given, I find no observations 
 relating to the same degree of resistance to the circulation 
 of air, or in other words to the same equivalent orifice. 
 
 D 2 
 
36 THE THEOEIES AND PRACTICE OF 
 
 Data so incomplete do not allow us to arrive at a know- 
 ledge of the orifice of passage or of the manometric yield, 
 but for this latter we are enabled to obtain a value roughly 
 approaching it, and which in default of any other may possess 
 some interest and utility. 
 
 The manometric yield, we have said, is the coefficient of 
 reduction to be applied to the theoretical depression to 
 obtain the initial depression before mentioned. 
 
 If, in default of this latter, we are content with the 
 effective depression observed under ordinary conditions, the 
 result obtained will be very poor, and still more feeble as 
 the seam ventilated is thicker ; but, in general, the difference 
 of this approximate value will not be so considerable but that 
 it may aid us in forming an opinion as to the exact value. 
 
 Let us take, for example, the three ventilators of Besseges, 
 Creal, and Lalle, studied by the Commission of Gard. 
 
 The exact manometrical yields of these machines are 
 respectively 
 
 0-691 .. 0-572 .. 0-542. 
 
 If, instead of calculating the manometrical results with the 
 aid of the initial depression, we use the effective depressions 
 observed on the three mines of Besseges, Creal, and Lalle, we 
 shall obtain " approximate results " 
 
 0-569 .. 0-524 .. 0-468. 
 
 Without doubt the differences are very great, especially for 
 the mine of Besseges, which is very thick ; but the order of 
 these values approaches what is their true value, and, in 
 default of more precise indications, they may suffice to 
 compare different types of ventilators. It is with this idea 
 that I have drawn up the table which follows. I have in- 
 troduced all the ventilators, to the number of sixty, of which 
 I have been able to procure any information. The approxi- 
 mate result which is shown in the last column, is calculated, 
 as we have seen above, by comparing the observed depression 
 
CENTRIFUGAL VENTILATING MACHINES. 37 
 
 with the theoretical expression where the expression is in 
 water column W 2 g 
 
 7 *.' 
 
 The error diminishes with thin seams, and increases with 
 thick ones. I have taken into account the manometrical 
 result as an important base for the examination of the 
 equivalent orifice of the mine ventilated. 
 
 The ventilators are given in the order of their perfec- 
 tion. First, the primitive machines without a cover ; second, 
 those simply covered without chimneys ; third, the machines 
 covered, but with a chimney to a constant section ; and lastly, 
 the Guibal, with a slide and cover and the evasee chimney. In 
 each category the order followed is that of increasing diameters. 
 
 Published experiments are rarely accompanied by atmo- 
 spheric observations which permit a calculation to be made 
 of the density of the air. I have allowed in each case for 
 this density the average of 1-200 to 1000 for that of water. 
 With these conditions the formulae which enable me to 
 establish the numerical value of this table take the follow- 
 ing simple form for the equivalent orifice 
 
 0-2V 
 
 a = , 
 
 Jh 
 
 V being the volume given per second, and h the depression 
 observed in inches of water. 
 
 Second, for the theoretical depression 
 
 N 2 D 8 _ 
 
 ~ 800947' 
 
 N being the number of revolutions per minute, and D the 
 diameter of the machine in feet. 
 
 Third, and consequently, for the manometrical yield 
 _ 800947 h 
 
 N 2 D 2 
 
 Sometimes the observation of the yield has been defective, 
 and then the equivalent orifice could not be determined. 
 
38 
 
 THE THEOKIES AND PRACTICE OF 
 
 TABLE 
 
 FAN 
 
 
 
 
 " 1 
 
 )imensions. 
 
 
 
 No, 
 
 Date. 
 
 Mine. 
 
 Exterior 
 )iameter. 
 
 Diameter 
 of Oufe. 
 
 Width. 
 
 
 
 
 
 ft. 
 
 ft. 
 
 ft. 
 
 
 1 
 
 2 
 
 June 25, 1842 
 Mar. 28, 1844 
 
 Shaft No. 5 of Grand Hornu . . 
 Ditto 
 
 5-57 
 5-57 
 
 4-46 
 4-46 
 
 1-11 
 I'll 
 
 
 3 
 
 May 24,1844 
 
 Pit No. 2 at Sauwartan 
 
 6-56 
 
 5-21 
 
 1-31 
 
 
 4 
 
 Apr. 23, 1847 
 
 At Pit St. Caroline of the Colliery of 
 St. Victor Frameries. 
 
 6-26 
 
 
 
 
 
 5 
 6 
 
 June 28, 1849 
 June 1, 1843 
 
 Shaft No. 1 at Escouffiaux Colliery . . 
 Pit No. 3 at Marcinelles 
 
 5-57 
 6-62 
 
 3-28 
 2-06 
 
 3-93 
 1-96 
 
 
 7 
 8 
 
 Oct. 4, 1842 
 Oct. 1, 1849 
 
 Pit No. 3 of Agrappe and Grisceil, at 
 Frameries. 
 Bayemont Colliery 
 
 8-29 
 8-52 
 
 4-26 
 4-48 
 
 3-21 
 3-77 
 
 
 9 
 10 
 
 June 20, 1849 
 Jan. 7, 1848 
 
 Shaft No. 3, Grand Trait, of Agrappe 
 and Grisceil, at Frameries. 
 Shaft called No. 12 at Agrappe, Noir- 
 chain Colliery. 
 
 9-05 
 9-05 
 
 4-92 
 4-92 
 
 4-92 
 4-92 
 
 
 11 
 
 Nov. 28, 1848 
 
 
 
 Large Seam of the Epinois Wood and 
 Elouges Colliery. 
 
 9-18 
 
 4-59 
 
 3-93 
 
 
 12 
 13 
 14 
 
 Oct., 1847 
 Nov., 1847 
 July 30, 1863 
 
 Shaft No. 5 (St. Barbe) at Escouffiaux 
 Colliery. 
 Shaft No. 7 (St. Antoine) at Es- 
 couffiaux Colliery. 
 Great Seam of the Epinois Wood at 
 Elouges. 
 
 9-38 
 9-38 
 9-84 
 
 4-59 
 4-59 
 
 3-93 
 3-93 
 4-10 
 
 
 15 
 
 Nov. 20, 1842 
 
 Shaft No. 1 at Grand Picquery Col- 
 liery, Frameries. 
 
 10-00 
 
 4-78 
 
 3-24 
 
 
 16 
 17 
 
 18 
 
 Nov. 25, 1842 
 Apr. 30, 1865 
 
 Pit Ste. Caroline of St. Victor Colliery, 
 Frameries. 
 Crachet and Picquery Pits, Shaft St. 
 Placide. 
 Shaft No. 12 at Marcinelles Colliery . . 
 
 10-29 
 22-96 
 21-32 
 
 5-24 
 9-84 
 7-38 
 
 3-11 
 5-57 
 4-59 
 
 
 19 
 
 
 Ormont Colliery at Chatelet 
 
 26-24 
 
 
 
 4-59 
 
 
CENTRIFUGAL VENTILATING MACHINES. 
 
 39 
 
 No. I. 
 
 UNCOVEKED. 
 
 
 Publications. 
 
 Authors. 
 
 Equivalent I 
 Orifice. 
 
 i& 
 
 rill 
 
 Remarks. 
 
 
 
 
 sq.ft. 
 
 
 
 
 Memoir on Apparatus 
 
 G. Glepin 
 
 1-88 
 
 132 
 
 Type, Combes ; vertical dia- 
 
 
 applied to Ventila- 
 ting Mines, p. 58. 
 
 
 
 
 meter, 1 ouie, 3 vanes. 
 
 
 Ditto, p. 58 
 
 Ditto 
 
 3-56 
 
 090 
 
 Ditto. The mine being in- 
 
 
 
 
 
 
 creased the yield is diminished. 
 
 
 And also the manner 
 
 Ditto 
 
 2-94 
 
 173 
 
 .. 
 
 
 of working at Combes, 
 
 
 
 
 
 
 Vol. II.. p. 491. 
 
 
 
 
 
 
 Ditto, p. 63, & Combes, 
 
 A. Cabany 
 
 5-54 
 
 400 
 
 Ditto; horizontal axis, 2 
 
 
 p. 499. Notes by M. 
 
 
 
 
 ouies, 2 vanes. Type, Leto- 
 
 
 Cabany. 
 
 
 
 
 ret ; a well-constructed fan, 
 
 
 
 
 
 
 but rather small. 
 
 
 Ditto 
 
 Ditto 
 
 4-22 
 
 476 
 
 Ditto. 
 
 
 Memoir on Apparatus 
 
 G. Glepin 
 
 3-70 
 
 121 
 
 Ditto, 2 ouies, 8 vanes, in sheet 
 
 
 applied to the Venti- 
 
 
 
 
 iron, slightly curved. 
 
 
 lation of Mines. 
 
 
 
 
 
 
 Ditto, p. 49.. .. .. 
 
 Ditto 
 
 3-65 
 
 438 
 
 Ditto ; vanes inclined at 110 
 
 
 
 
 
 
 to the radius, 2 ouies. 
 
 
 Annals of Public Works 
 
 Jochams 
 
 2-91 
 
 323 
 
 Ditto ; 4 vanes at an angle of 
 
 
 in Belgium, Vol. XL, 
 
 
 
 
 130 to 150. 
 
 
 p.l. 
 Notes by M. Cabany . . 
 
 A. Cabany 
 
 8-01 
 
 393 
 
 Ditto. Very strong inclination 
 
 
 
 
 
 
 of vanes. 
 
 
 Ditto 
 
 Ditto 
 
 9-82 
 
 303 
 
 Ditto. Average of 11 experi- 
 
 
 
 
 
 
 ments made with assistance 
 
 
 
 
 
 
 of MM. Toilliez, Albert, 
 
 
 
 
 
 
 Harnel, and Toilliez, J. 
 
 
 Annals of Public Works 
 
 Jochams 
 
 4-11 
 
 285 
 
 Ditto. 
 
 
 in Belgium, Vol. XL, 
 
 
 
 
 
 
 p. 1. 
 
 Notes by M. Cabany . . 
 
 A. Cabany 
 
 4-13 
 
 474 
 
 Ditto. 
 
 
 Ditto 
 
 Ditto 
 
 4-40 
 
 377 
 
 Ditto. Vanes at 110. 
 
 
 Annals of P ublic Works 
 
 Hamal and 
 
 51-43 
 
 368 
 
 Ditto. 
 
 
 in Belgium, Vol. 
 
 Schorn. 
 
 
 
 
 
 XXIL, p. 5. 
 
 
 
 
 
 
 Memoir on Apparatus 
 
 G. Glepin 
 
 2-926 
 
 163 
 
 Ditto. Vanes curved, follow- 
 
 
 applied to the Venti- 
 
 
 
 
 ing a surface inclined to the 
 
 
 lation of Mines, p. 50. 
 
 
 
 
 radius of 137 to 153. 
 
 
 Ditto, p. 46 
 
 Ditto 
 
 3-109 
 
 354 
 
 Ditto. Vanes inclining to 135. 
 
 
 
 
 
 
 Five experiments. 
 
 
 Ventilation of Mines, 
 
 Gille and Fra- 
 
 8-661 
 
 496 
 
 Type, Guibal, before covering. 
 
 
 by M. Devillez, p. 227. 
 
 neau. 
 
 
 
 
 
 Supplement to Account 
 
 
 7-661 
 
 439 
 
 Type, Lambert ; 6 radial vanes. 
 
 
 of Working, by Pon- 
 
 
 
 
 Of two experiments I have 
 
 
 son, Vol. L, p. 395. 
 
 
 
 
 chosen the most favourable to 
 
 
 
 
 
 
 the machine. 
 
 
 Ventilation of Mines, 
 
 Devillez, Le- 
 
 8-199 
 
 455 
 
 Ditto ; 8 radial vanes. 
 
 
 by M. Devillez, p. 181. 
 
 toret, Delhaise 
 
 
 
 
 
 
 and Gilbert. 
 
 
 
40 
 
 THE THEORIES AND PRACTICE OF 
 
 TABLE No. I. (continued). COVERED 
 
 
 
 
 
 Dimensions 
 
 
 
 No. 
 
 Date. 
 
 Mine. 
 
 Exterior 
 Diameter. 
 
 Diameter 
 of Oule. 
 
 Width. 
 
 
 
 
 
 ft. 
 
 ft. 
 
 ft. 
 
 
 20 
 
 Nov. 5, 1876 
 
 Grand Combe Mines, La Sagnette Fan 
 
 9-18 
 
 4-39 
 
 3-93 
 
 
 21 
 
 99 
 
 Aug. 10, 1859 
 Fi-ftTtj Aiig to 
 
 Grisoeil Colliery, No. 10 
 Ditto 
 
 13-12 
 13-12 
 
 5-24 
 5-24 
 
 5-01 
 5-01 
 
 
 
 Oct., 1859. 
 
 
 
 
 
 
 23 
 
 July 25, 1861 
 
 Escouffiaux Colliery 
 
 13-12 
 
 
 
 
 
 
 24 
 25 
 
 June 23, 1861 
 May 28, 1865 
 
 Basse Sambre Colliery 
 Crachet and Picquery Collieries, Shaft 
 St. Placide. 
 
 13-12 
 22-96 
 
 9*84 
 
 5-57 
 
 
 26 
 
 27 
 
 28 
 
 Feb. 19, 1859 
 
 Mar. 22, 1859 
 Jan. 7,1865 
 
 COVEI 
 
 Jean Bart, Cie. d'Anzin 
 Ditto 
 
 IED FAN 
 11-80 
 
 11-80 
 13-12 
 
 9 WITH C 
 
 5-24 
 
 5-24 
 6-56 
 
 HIMNEY 
 
 4-92 
 
 4-92 
 4-92 
 
 Stiring Mines, Pit St. Joseph .. .. 
 
 29 
 
 
 
 Grand Buisson Colliery, Shaft No. 3 
 
 22-96 
 
 9-84 
 
 5-57 
 
 30 
 
 
 
 Society of Hornu Wasmes 
 
 29-52 
 
 9-84 
 
 3-28 
 
 31 
 
 
 COVERED "\ 
 Sainte Hortense at Paturages 
 
 ^ENTlLAl 
 
 13-12 
 
 rORS, WIT! 
 
 6-56 
 
 [ SLIDE 
 4-92 
 
 32 
 
 June 25, 1862 
 
 Verger, Cie. d'Anzin 
 
 16-40 
 
 8-200 
 
 6-56 
 
 33 
 
 Aug. 11, 1861 
 
 Grosse Fosse, Cie. d'Anzin 
 
 16-40 
 
 8-200 
 
 6-56 
 
 34 
 
 
 
 Montceau- Fontaine, Charleroi .. 
 
 19-68 
 
 
 
 
 
CENTRIFUGAL VENTILATING MACHINES. 
 
 41 
 
 FANS WITHOUT CHIMNEY. 
 
 
 Publications. 
 
 Authors. 
 
 Equivalent 
 Orifice. 
 
 Approxi- 
 mate Ma- 
 nometrical 
 Result. 
 
 Remarks. 
 
 
 
 
 sq . ft. 
 
 
 
 
 Minutes of the Mineral 
 
 Ventilation 
 
 7-132 
 
 638 
 
 This quantity follows from the 
 
 
 Society, Vol. XII., 
 
 Commission 
 
 
 
 second experiment of the 
 
 
 p. 533. 
 
 of Gard. 
 
 
 
 Commission. The other four 
 
 
 
 
 
 
 gave a less quantity. 
 
 
 Annals of Public Works 
 
 Hamal and 
 
 12-95 
 
 429 
 
 The nine experiments show an 
 
 
 in Belgium, Vol. 
 
 Gille. 
 
 
 
 action sufficient to destroy the 
 
 
 XXII., p. 5. 
 
 
 
 
 regularity of the results. 
 
 
 Supplement to Account 
 
 Ditto 
 
 13-17 
 
 505 
 
 Concerns, no doubt, the same 
 
 
 of Working, by Pon- 
 
 
 
 
 fan as above. Experiments 
 
 
 son, Vol. I., p. 384. 
 
 
 
 
 do not agree. 
 
 
 Ditto 
 
 Gille 
 
 
 
 682 
 
 E xperiments agree but slightly. 
 The quantity not having been 
 
 
 
 
 
 
 measured the equivalent ori- 
 
 
 
 
 
 
 fice remains unknown. 
 
 
 Ditto 
 
 Masy 
 
 . , 
 
 613 
 
 Same observations as above. 
 
 
 Ventilation of Mines, 
 
 Gille and 
 
 9-50 
 
 491 
 
 Same fan as at No. 17. The 
 
 
 by M. Devillez. 
 
 Franeau 
 
 
 
 covering has been put on but 
 
 
 
 
 
 
 not the slide or the chimney. 
 
 OF CONSTANT SECTION. 
 Notes by M.Cabany.. 
 
 Ditto 
 
 Minutes of the Mineral 
 Society ,Vol.X., p. 437. 
 
 Ventilation of Mines, 
 by M. Devillez, p. 236. 
 
 Ditto, p. 253 .. .. 
 
 Ventilation, by Devil- 
 lez, p. 221. 
 
 Manuscript Notes, M. 
 Cabany. 
 
 Ditto 
 
 Supplement to Treatise 
 on Working by Ponson. 
 
 A. Cabany 
 
 12-00 
 
 583 
 
 First Guibal type, with the 
 
 
 
 
 slide in a groove. The chim- 
 
 
 
 
 ney square from 4-92 feet. 
 
 
 
 
 Average of two experiments 
 
 
 
 
 most favourable to the 
 
 
 
 
 machine. 
 
 Ditto 
 
 17-49 
 
 352 
 
 Ditto. The mine being very 
 
 
 
 
 thick explains the diminution 
 
 
 
 
 of result. 
 
 Laigneaux and 
 
 10-01 
 
 284 
 
 Ditto. The chimney square 
 
 Distinghin. 
 
 
 
 from 4-37 feet. We do not 
 
 
 
 
 see the cause of so poor a 
 
 
 
 
 result. 
 
 .. 
 
 43-36 
 
 626 
 
 Ditto. The chimney has not 
 
 
 
 
 yet its evasee slope in the 
 
 
 
 
 interior. 
 
 
 
 
 
 609 
 
 Special type. The chimney 
 has from top to bottom a 
 
 
 
 
 uniform section of 6-56 feet 
 
 
 
 
 by 5-9 feet. 
 
 ;GUIBAL TYPE). 
 
 
 
 
 
 570 
 
 Yield not given. Equivalent 
 orifice unknown. 
 
 Atkinson, 
 Dickenson,and 
 
 8-57 
 
 651 
 
 Experiments agree, and are 
 good. 
 
 Greenwell. 
 
 
 
 
 A. Cabany 
 
 17-56 
 
 633 
 
 Eesult high, regarding thick- 
 
 
 
 
 ness of seam. 
 
 * * 
 
 6-56 
 
 595 
 
 
42 
 
 THE THEORIES AND PRACTICE OF 
 
 TABLE No. I. COVERED VENTILATOES, WITH SLIDE 
 
 
 
 
 ] 
 
 Dimensions. 
 
 
 No. 
 
 Date. 
 
 Mine. 
 
 Exterior 
 )iameter. 
 
 Diameter 
 of Oule. 
 
 Width. 
 
 35 
 
 Apr. 22, 1866 
 
 
 ft. 
 19 '68 
 
 ft. 
 9 '84 
 
 ft. 
 
 36 
 37 
 
 July 31, 1865 
 Mar 25 1866 
 
 Crachet and Picquery 
 Ditto 
 
 22-96 
 22 '96 
 
 9-84 
 9-84 
 
 5-57 
 5-57 
 
 38 
 
 
 S tiring . . 
 
 22 '96 
 
 9*84 
 
 5*74 
 
 39 
 
 
 
 22-96 
 
 9-84 
 
 5-57 
 
 40 
 
 .. 
 
 Grand Buisson 
 
 22-96 
 
 9-84 
 
 5-57 
 
 41 
 
 Sep. 11, 1870 
 
 Grand Mambourg 
 
 22-96 
 
 9-84 
 
 8-20 
 
 42 
 
 AO 
 
 1866 
 1865 
 
 Nceux (Pas de Calais) 
 Els wick 
 
 22-96 
 22'96 
 
 9-84 
 9 -84 
 
 5-57 
 fi-23 
 
 44 
 
 45 
 46 
 
 July 24, 1869 
 Feb. 14, 1869 
 
 Von der Heydt. Herne-Bochum, West- 
 phalia. 
 Rhein-Elbe, Westphalia 
 Montceau-Fontaine 
 
 29-52 
 
 29-52 
 29-52 
 
 
 9-84 
 9-84 
 
 47 
 
 -.. 
 
 United Collieries at Charleroi 
 
 29-52 
 
 9-84 
 
 5-57 
 
 48 
 49 
 
 Oct. 24, 1869 
 
 Colliery of Grand Mambourg at Mon- 
 tigny-sur-Sambre. 
 Colliery of Rieu t)u Cceur 
 
 29-52 
 29-52 
 
 13-12 
 9-84 
 
 6-56 
 6-56 
 
 50 
 51 
 52 
 
 May 17, 1869 
 June 21, 1869 
 1865 
 
 Colliery of La Louviere 
 Colliery of Grand Buisson 
 Pelton Colliery, Durham 
 
 29-52 
 29-52 
 29-52 
 
 9-84 
 9-84 
 13-12 
 
 6-56 
 6-56 
 9-84 
 
 53 
 
 Apr. 20, 1867 
 
 Middle Duffryn Colliery, S. Wales . . 
 
 29-52 
 
 .. 
 
 9-84 
 
 54 
 
 Mar. 2, 1868 
 
 Gethin Colliery, S. Wales 
 
 29-52 
 
 
 
 9-84 
 
 55 
 
 
 Colliery Lwynpia, S. Wales 
 
 29-52 
 
 .. 
 
 9-84 
 
 56 
 57 
 
 
 
 Ebbw Vale, S. Wales .. 
 Colliery of Trieu-Kaisin 
 
 39-36 
 39-36 
 
 9-' 84 
 
 11-8 
 9-84 
 
 58 
 
 Mar. 25, 1877 
 
 Colliery of Crachet and Picquery 
 
 39-36 
 
 13-12 
 
 8-2 
 
CENTKIFUGAL VENTILATING MACHINES. 
 
 43 
 
 AND EVASEE CHIMNEY (GuiBAL TYPE). continued. 
 
 Publications. 
 
 Authors. 
 
 Equivalent 
 Orifice. 
 
 Approxi- 
 mate Ma- 
 nometrical 
 Result. 
 
 Remarks. 
 
 
 
 sq. ft. 
 
 
 
 Ventilation, by Devil- 
 
 Stoesser and 
 
 10-16 
 
 642 
 
 
 lez, p. 239. 
 
 others. 
 
 
 
 
 Ditto, p. 229 . . 
 
 Gille and 
 
 8-98 
 
 654 
 
 Same as Nos. 17 and 23. 
 
 
 Franeau. 
 
 
 
 Machine complete. 
 
 Ditto, p. 240 .. .. 
 
 Stoesser and 
 
 6-80 
 
 728 
 
 No doubt the same machine. 
 
 
 others. 
 
 
 
 The increase in yield may be 
 
 
 
 
 
 attributed to less equivalent 
 
 
 
 
 
 orifice. 
 
 Ditto, p. 221 .. .. 
 
 
 . , 
 
 598 
 
 Particulars are incomplete. 
 
 Ditto, p. 221 .. .. 
 
 .. 
 
 .. 
 
 579 
 
 Ditto. 
 
 Ditto, p. 236 . . 
 
 
 4-33 
 
 711 
 
 Same as No. 29. Interior circu- 
 
 
 
 
 
 lar casing in chimney complete. 
 
 Ditto, p, 237 .. .. 
 
 De Poitier, 
 
 11-14 
 
 628 
 
 The great width of this machine 
 
 
 Havrez and 
 
 
 
 has no effect on result. 
 
 
 Halley. 
 
 
 
 
 Unknown 
 
 C. Brice 
 
 9-12 
 
 633 
 
 Communicated by M. Brice. 
 
 North of England 
 
 W. Cochrane 
 
 20-15 
 
 590 
 
 Ditto. 
 
 Inst., Vol. XIV. 
 
 
 
 
 
 Annales des Mines, 
 
 Extracted by 
 
 14-72 
 
 684 
 
 Ditto. 
 
 1873, p. 297. 
 
 M. Voisin. 
 
 
 
 
 Ditto 
 
 Ditto 
 
 15-83 
 
 673 
 
 Ditto. 
 
 Supplement to Treatise 
 by Ponson, Vol. I., 
 
 Atkinson and 
 Dickenson. 
 
 13-78 
 
 751 
 
 Volume of air in these experi- 
 ments is very irregular. 
 
 p. 374. 
 
 Ventilation of Mines, 
 
 
 
 583 
 
 The details are very incom- 
 
 byM. Devillez,p.221. 
 
 
 
 
 plete. 
 
 Ditto, p. 21 
 
 
 
 
 
 545 
 
 Ditto. 
 
 Ditto 
 
 Brunier 
 
 11-41 
 
 665 
 
 The two first experiments 
 
 Ditto, p. 237 .. .. 
 
 Eoger 
 
 8'38 
 
 675 
 
 differ ; the seven others agree. 
 Ditto. 
 
 Ditto, p. 238 .. .. 
 
 <t 
 
 25-24 
 
 680 
 
 Ditto. 
 
 Proceedings of S. "Wales 
 Institute, by "W. Arm- 
 
 
 
 21-19 
 
 709 
 
 The three first experiments 
 only ; the others do not agree. 
 
 strong. 
 Ditto, Vol. V., p. 257.. 
 
 G. Wilkinson 
 
 21-83 
 
 307 
 
 We do not see what causes the 
 
 
 
 
 
 bad result. 
 
 Ditto, Vol. VI., p. 67 
 
 M. Bates 
 
 31-52 
 
 661 
 
 It is remarkable that for such 
 
 
 
 
 
 
 a thick seam the result is so 
 
 
 
 
 
 good. 
 
 Annales des Mines (7th 
 
 Leon Lecornu 
 
 24-74 
 
 696 
 
 Details insufficient. 
 
 Series), Vol. XIV. 
 
 
 
 
 
 Ditto 
 
 Ditto 
 
 17-54 
 
 627 
 
 Ditto. 
 
 Ventilation of Mines, 
 
 
 . . 
 
 700 
 
 Ditto. 
 
 by M. Devillez. 
 
 
 
 
 
 Revue Universelle of 
 
 Hubert 
 
 13-78 
 
 668 
 
 The vanes are directly as the 
 
 Mines (2nd Series), 
 
 
 
 
 radius. 
 
 Vol. II., p. 59. 
 
 
 
 
 
44 THE THEORIES AND PRACTICE OF 
 
 From this table result some interesting indications, all 
 conforming to the theoretical views expressed above. For 
 ventilators without cover we find at the bottom of the scale 
 the machines of Combes, of which the manometrical result 
 never exceeds '132. With the arrangement of Letoret 
 the result is better. It gradually improves as the dimen- 
 sions of the ventilators are increased, but without exceeding, 
 as theory would require, the maximum of '500, even for 
 the Lambert ventilator, in which the arrangements are 
 more intelligent, and mark a distinct progress over those of 
 M. Letoret. 
 
 With the covered ventilators without chimneys, there 
 appear to be some results better than 600, which proves 
 that already in the cover a restitution of vis viva has com- 
 menced. However, the experiments made by Messrs. Gille 
 and Franeau on the ventilator of Crachet (Nos. 17 and 25 in 
 the table), before and after putting on the cover, have shown 
 in both cases the same result '496 and '491. There ought, 
 however, to have been a difference, and I cannot understand 
 this anomaly. 
 
 The examples of covered ventilators with a chimney of 
 constant area are not numerous. I have arranged them 
 with Guibal ventilators of the primitive type, those where 
 the movable slide is formed by a door turning on a hinge. 
 
 An apparatus of this kind fixed on the pits of St. Joseph 
 at the mines of Stiring, has only given a very feeble result, 
 284. The cause of this inferiority is not very clear. The 
 second experiment on the pit of Jean Bart gives also a 
 poor result, but here there is a reason, viz. the great thickness 
 of the mine ; the other results are much better and give an 
 average superior to * 600. Is it to the square chimney that 
 this result is to be attributed, or is it due only to the cover ? 
 It is difficult to point out the exact share of these two 
 influences. 
 
CENTRIFUGAL VENTILATING MACHINES. 45 
 
 The long series of Guibal ventilators with the evasee 
 chimney permit us to be more decided. If we strike out the 
 Duffryn ventilator at Aberdare (No. 53), for the very small 
 results from which I can give no reason, we meet with nothing 
 but high results, often exceeding -700, and giving an average 
 of *650. The influence of the evasee chimney is thus 
 manifest. There remain also the comparative experiments 
 made by Messrs. Gille and Franeau on the ventilator of 
 Crachet and Picquery. Before the erection of the chimney 
 the result observed was only *491, and after "654 (Nos. 25 
 and 36 in the table). An experiment still more significant 
 is that which is given without the name of the author by 
 M. Devillez, at page 236 of his treatise on ventilation. 
 Whilst the chimney had an equal section throughout its 
 whole height the result was 626, but after the fixing of the 
 interior casing it increased to '711 (see Nos. 29 and 40 in 
 the table). 
 
 The approximate manometrical result does not seem to 
 increase in any sensible manner with the dimensions of the 
 ventilator. Perhaps, however, it is to this cause that we must 
 attribute the good results presented by the ventilators of 
 Pelton, Gethin, and Lwynpia, notwithstanding the very great 
 thickness of the seams which they ventilate (52, 54, and 55). 
 These machines are not less than 29*52 feet in diameter, 
 and 9 * 84 feet in width. 
 
 The new ventilator of Crachet, however, of 40*56 feet 
 diameter, and with vanes in the direction of the radius as 
 theory requires, which has been the subject of a recent memoir 
 by M. Laguesse, gives only 668. This result is good, no 
 doubt, but it might have been better had not the object of 
 the constructor been less to improve the manometrical result 
 than to obtain with a moderate speed of the engine a great 
 tangential speed. This latter speed is, in effect, the essential 
 basis of the power of ventilators for creating depression. 
 
46 THE THEORIES AND PRACTICE OF 
 
 If we accept as characteristic of our four categories of 
 ventilators the average of the results obtained as they figure 
 in our table, we obtain the interesting series following : 
 
 For ventilators without cover 327 
 
 Covered, without chimney *560 
 
 Covered, with a rectangular chimney .. '606 
 
 Covered, with evasee Guibal chimney .. '650 
 
 This series dispenses with all comment. It is, however, 
 right to remark that the precision of these averages is 
 somewhat illusory, and they form only a rough indication. 
 It follows from these figures that by the dimensions and 
 arrangements actually adopted for ventilators with centri- 
 fugal force, we have obtained almost double the power 
 of depression of the old ventilators of Letoret, but it is 
 necessary to avoid thinking that for the mine-worker the 
 gain is really very considerable. In effect, that which 
 concerns the mine-worker is not so much the depression 
 itself, but rather the circulation of air which it induces 
 in the workings. If we increase the depression the result 
 is only in the proportion of the square root of this 
 increase, so that when we have doubled the manometrical 
 result of a ventilator we have only been able to increase in 
 the proportion of 1 to the square root of 2, or about as 5 is 
 to 7, the volume of air passing through the works. 
 
 This same observation may assist us in judging of the im- 
 provements still possible to be adopted for ventilators. The 
 approximate manometrical results in our table permit us 
 to estimate at *750 the actual manometrical yield of a 
 well-made Guibal machine. 
 
CENTRIFUGAL VENTILATING MACHINES. 47 
 
 4. DETERMINATION OF THE INITIAL DEPRESSION FOR 
 VENTILATORS WORKING WITH DIRECT IMPULSION. 
 
 I define thus, following the example of M. Devillez, the 
 ventilators which act by oblique stroke on the air which 
 they displace. 
 
 Although these machines are falling into disuse, it is 
 better that the reader should know them. Works on 
 mining never fail to devote a few lines to the subject. 
 The three typical machines are First, the screw of Motte, 
 with single or double spiral turning in a cylindrical 
 tube, like the Archimedean screw ; Second, the ventilator 
 with the helix, by M. Pasquet an annular crown fitted 
 with helicoidal partitions, cutting the air with a rapid rota- 
 tion ; Third, the ventilator, with vanes like a windmill, of 
 M. Lesoinne, in which the preceding partitions are replaced 
 by numerous little vanes. 
 
 To these three I should add the Davaine ventilator at 
 the mines of Bully-Grenay, formed of four helicoidal vanes 
 fixed on a thick spindle or newel. This machine has been 
 the object of a notice by M. Sens, in the 'Annals of Mines ' 
 for 1860. 
 
 The whole of these machines are based upon the same 
 principle and differ only in their details. 
 
 Fixed in general on thin mines, this being the condition of 
 most Belgian mines, these ventilators have small power of 
 depression, and have always given an insufficient quantity 
 of air, so that they have been readily abandoned. It is 
 certainly possible, however, in following step by step the 
 indications of a theory, to improve in a great measure the 
 manornetrical results, and even to obtain certain advantages 
 inherent to this kind of machine, and it may be the last word 
 
48 THE THEORIES AND PRACTICE OP 
 
 has not been spoken on this subject. I will consider them 
 presently. 
 
 I need not repeat the general conclusions established above. 
 The theory developed in the first paragraph applies, as I 
 have taken care to show, to all deprimogen ventilators with- 
 out exception. The notion of the initial depression, and of 
 orifice of passage, has not been less evident for ventilators by 
 direct impulsion than for those with centrifugal force. It 
 remains for us now to determine a new analytical value for 
 the initial depression. 
 
 I will take as a type of machine, the ventilator with the 
 vanes of the windmill, since it will present itself to us readily. 
 I will adopt for it, as for the ventilator with centrifugal force, 
 the hypothesis of a perfect ventilator. 
 
 FIG. 10. 
 
 Fig. 10 is a section of the vanes made at a distance se 
 from the axis, consequently following a cylindrical surface 
 of radius #. According to the inventor, the wings should be 
 flat and act by an oblique stroke on the air drawn in. But 
 such a machine can never have any claim to be considered 
 a perfect ventilator. It receives the air with a shock, and 
 allows it to escape with a considerable whirling speed. 
 
 We may remedy the first defect at once by twisting the 
 vanes towards their lower attachment in such a- manner as to 
 make them cut the air, following the resultant of the 
 ascending speed of the air drawn in and of the speed of 
 rotation of the machine at the point in question. It is 
 exactly what we have done for the ventilators with centri- 
 fugal force. As to the second defect it leads by assimi- 
 lation to an artifice of the same nature as a Guibal 
 
CENTRIFUGAL VENTILATING MACHINES. 
 
 49 
 
 chimney. We may reduce the whirling speed of the air 
 thrown out by receiving it in evasee passages, where its 
 speed may be slowly extinguished and its vis viva restored. 
 We should then obtain the following arrangement. The 
 movable wheel of the Lesoinne machine would be surmounted 
 by a second fixed wheel with the vanes inclined in the con- 
 trary way to those in front of them, and forming between 
 them passages of the requisite conformation. Their lower edge 
 would be in the direction following the absolute speed of the 
 air projected by the moving wheel, and their upper edge 
 
 FIG. 11. 
 
 McrvaJble 
 wheel 
 
 would follow in the plane of the axis. This is similar to the 
 arrangement indicated long since by M. Harze in the memoir 
 of which we have spoken above. 
 
 With the machine so completed we have now to determine 
 the depression which it is capable of producing ; like centri- 
 fugal ventilators this depression results from a series of 
 actions, some additive others subtractive, which we must 
 successively pass in review. 
 
 First, The motionless air in the chamber which is in front 
 of the ventilator, is carried with the speed Y to the inferior 
 part of the vanes. We must then at once place to the debit 
 of the depression the generative height of this speed. 
 
 Let it be, 
 
 --^ (1) 
 
50 THE THEORIES AND PRACTICE OF 
 
 Second, Once drawn within the vanes, the air passes 
 through their spaces with a gradually decreasing speed, in 
 consequence of the passages opening out in approaching 
 the upper level. If 'V l is this speed at the entry and V 2 that 
 at the outlet the gain of pressure in this passage will be 
 given, as has already been said, by the theory of Bernouilli 
 
 __ 
 
 20" 
 
 The relative speed of entry Vi being the resultant of the 
 initial speed Y , and of the speed of the drawing in of the 
 vanes &> x, its square Vj 2 may be replaced by the sum 
 
 I may, then, bring to the credit of the depression the 
 algebraic sum 
 
 Third, The air reaching the upper level of the moving 
 wheel is thrown out with the speed V 3 , which is the resultant 
 of the relative speed of outlet V 2 and of the speed of 
 drawing in &> x. 
 
 The parallelogram of these speeds gives for V 3 the known 
 expression, 
 
 Y 8 2 = y 2 2 _|_ W 2 38 _ 2 V 2 CO X COS a, 
 
 a being the angle which the vane makes with the upper 
 level. 
 
 Animated by this speed V 3 the air enters the diffuser ; 
 like the Guibal chimney the evasee passages of the diffuser 
 gradually extinguish this speed, and if W represents the 
 value which it possesses at the outlet, the restitution 
 
CENTRIFUGAL VENTILATING MACHINES. 51 
 
 of pressure will be always, according to the theory of 
 Bernoulli!, 
 
 .Replacing V 3 according to its value as a function of its 
 component parts, I have to carry to the effective side of the 
 depression, the sum, 
 
 Vg 2 o)V 2Y 2 o>acosa W* 
 
 h 2^ + ^' -27 
 
 Here the centrifugal force, acting perpendicularly to the 
 trajectory of thin streams of air, cannot produce any increase 
 in the depression. There remains then only to make the 
 addition of the values (1), (2), (3) which gives, when all 
 reductions are made, 
 
 o>V 2 V 2 <o x cos a W 2 
 H = ------ _ , 
 
 9 9 %g 
 
 an expression of the depression sought. 
 
 I have supposed up to this time that the movable vanes 
 have on the upper surface an inclination a. The preceding 
 expression shows clearly that this angle should be 90, that 
 is to say, that these vanes should be in the plane of the axis. 
 It follows that the middle term disappears, and the theore- 
 tical depression takes the simple form, 
 
 _ <o 2 oj 2 W 2 
 
 "i*' 
 
 If, now, we suppose the passages of the diffuser to be so 
 prolonged in height and width that the final speed of 
 expulsion W may be considered as nothing, there remains 
 as the value of the depression developed by the perfect 
 ventilator 
 
 E 2 
 
52 THE THEOKIES AND PRACTICE OF 
 
 Unfortunately this value only applies to the films of air 
 placed at a distance x from the axis, and here appears the 
 great defect of this class of ventilator. Whilst for the 
 great value of %, that is to say for the region near the 
 exterior circumference, the depressional action is very strong, 
 it remains small over the lesser values of x, that is to say 
 over the whole central part of the machine. The inevitable 
 consequence of this inequality of action is that the expul- 
 sion of the air remains localised on the borders of the wheel, 
 whilst towards the middle is produced a large re-entry of 
 exterior air. In order to avoid this constructors have fitted 
 to the central part of their machines circular diaphragms, 
 gradually reducing the working part of the wheel to a 
 narrow crown. It is thus with the Motte screw of the pits 
 Montceau-Fontaine, where the exterior diameter was 7*41 
 feet. A diaphragm of 5 '57 feet in diameter has been 
 introduced, leaving an annular passage of only 11 inches in 
 width. Under these new conditions a depression appli- 
 cable to the ventilator by direct impulsion will be an inter- 
 mediate, an average between that corresponding to the 
 
 interior radius , and that due to the great radius > 
 
 9 9 
 
 and it approaches still nearer to this latter as the dia- 
 phragm or central newel is enlarged. Now we cannot 
 increase this diaphragm without reducing at the same time 
 the orifices of passage and lowering in proportion the 
 effective depression; but this danger diminishes with thin 
 seams, and we can understand that at its limit we must 
 admit for the theoretic value of the depression in the perfect 
 ventilator that which corresponds to the exterior radius, 
 
 *& 
 
 H.= , 
 
 and since w K is the tangential speed which we have expressed 
 
CENTRIFUGAL VENTILATING MACHINES. 53 
 
 up to this time by the letter u, 
 
 Jj.0 LZZ 9 
 
 g 
 
 an expression identical with that found for ventilators with 
 centrifugal force. From that we shall pass to the initial 
 depression, with the aid of a coefficient of reduction, 
 
 g' 
 
 in which the value, more or less high, forms the mano- 
 metrical result of the machine : with this exception, that 
 to different causes which reduce the result we must add the 
 difference of force which exists in practice between the 
 interior and the exterior radius. 
 
 Thus there is but one and the same theory for all depri- 
 mogen ventilators without exception. For machines with 
 direct force as for those with centrifugal force, the power 
 of depression is connected with the tangential speed, the 
 power of yielding volume to the orifice of passage by 
 identical expressions. For the one as for the other the 
 effective depression and the volume yielded result from two 
 formulae which I shall here repeat 
 
 h - s-> V = . 
 
 ('+) 
 
 I have not found in any industrial works experiments 
 sufficiently complete to allow me to make a calculation 
 with sufficient exactness of the manometrical result and of 
 the orifices of passage of a ventilator by direct impulsion. 
 I will content myself, then, by giving, as I did for centri- 
 fugal ventilators, a table of manometrical results drawn up 
 with the aid of all the experimental data relating to these 
 machines that I have been able to procure. 
 
THE THEOKIES AND PRACTICE OF 
 
 TABLE 
 
 No. 
 
 Date. 
 
 Mine. 
 
 Dimensions. 
 
 
 Exterior 
 Diameter. 
 
 Diameter. 
 
 Height. 
 
 
 
 
 ft. 
 
 ft. 
 
 ft. 
 
 PNEUMATIC SCREW 
 
 1 
 
 2 
 3 
 
 1842 
 Apr. 18, 1842 
 
 No. 2 Pit, Monceau-Fontaine 
 Ditto 
 
 2-624 
 2-624 
 3-936 
 
 095 
 095 
 
 2-624 
 2-624 
 
 
 Colliery of Chatelet 
 
 4 
 5 
 
 July 7, 1843 
 Nov. 2, 1849 
 
 Colliery Sauwartan-sur-Dour 
 Colliery of Pieton-Campagne 
 
 4-59 
 6-56 
 
 150 
 3-18 
 
 3-39 
 3-28 
 
 
 6 
 
 7 
 8 
 
 July 23, 1849 
 
 Ditto 
 June 1, 1843 
 
 Colliery of Monceau-Fontaine 
 Ditto 
 
 7-216 
 
 7-216 
 9-84 
 
 5-576 
 
 5-576 
 196 
 
 3-60 
 
 3-60 
 2-624 
 
 
 Colliery of Trieu-Kaisin 
 
 
 
 VENTILATORS 
 
 WITH HELICOIDAL 
 
 9 
 10 
 11 
 
 May 31, 1843 
 June 18, 1843 
 July 23, 1848 
 
 Colliery of Poirier 
 Ditto 
 
 5-576 
 6*56 
 7-54 
 
 1-968 
 1-64 
 4-26 
 
 3-54 
 3-93 
 918 
 
 
 Colliery of Vivier-du-Couchant 
 
 12 
 13 
 
 14 
 15 
 
 16 
 17 
 
 18 
 
 Aug. 14, 1849 
 Ditto 
 
 Oct. 26, 1848 
 Nov. 2, 1848 
 
 Colliery of the Reunion at Mont-sur- 
 Marchienne 
 Ditto 
 
 7-20 
 7-20 
 
 7-20 
 7-20 
 
 jATORS T 
 
 8-72 
 8*72 
 8-85 
 
 3-412 
 3-412 
 
 5-57 
 5-57 
 
 PITH VAN 
 918 
 
 918 
 918 
 
 623 
 623 
 
 656 
 656 
 
 ES OF A 
 
 
 Ditto 
 
 Ditto 
 
 VENTII 
 Grand-Bac 
 
 Ditto 
 
 Colliery of Val-Benoit, near Liege . . 
 
 VENTILATORS WITH HELICOIDAL 
 
 19 
 
 Aug. 2, 1860 
 
 Mines of Bethune, at Bully-Grenay . . 
 
 8-20 
 
 3-28 
 
 
 
 
CENTKIFUGAL VENTILATING MACHINES. 
 
 55 
 
 No. II. 
 
 
 Publications. 
 
 Authors. 
 
 Equivalent 
 Orifice. 
 
 Approxi- 
 mate Ma- 
 nometrical 
 Result. 
 
 Remarks. 
 
 
 
 
 sq. ft. 
 
 
 
 OF M. MOTTE. 
 
 
 Memoir on Machines 
 
 G. Glepin 
 
 3-583 
 
 050 
 
 Two helicoidal slides. This 
 
 
 applied to Ventilation 
 
 
 
 
 screw is the first constructed. 
 
 
 of Mines, p. 42. 
 
 
 
 
 
 
 Annals of Belgian Pub- 
 
 Gonot 
 
 2-872 
 
 084 
 
 The same machine. The mine 
 
 
 lic Works, Vol. L, 
 
 
 
 
 being narrowed, the result is 
 
 
 p. 236. 
 
 
 
 
 better. 
 
 
 Memoir on Machines 
 
 Glepin 
 
 1-883 
 
 121 
 
 Two helicoidal slides. 
 
 
 applied to Ventilation 
 of Mines, p. 40. 
 
 
 
 
 
 
 Ditto, p. 40 
 
 Ditto 
 
 3-034 
 
 183 
 
 Ditto. 
 
 
 Annals of Belgian Pub- 
 
 Jochams 
 
 3-72 
 
 208 
 
 Ditto. 
 
 
 lic Works, Vol. XI., 
 
 
 
 
 
 
 Ditto 
 
 Ditto 
 
 6-197 
 
 189 
 
 Ditto. The machine is fitted 
 
 
 
 
 
 
 with diaphragms which make 
 
 
 
 
 
 
 the air enter at the centre and 
 
 
 
 
 
 
 leave at the circumference. 
 
 
 Ditto 
 
 Ditto 
 
 3-292 
 
 230 
 
 Ditto. The mine had been 
 
 
 
 
 
 
 artificially narrowed, which 
 
 
 
 
 
 
 improved the result. 
 
 
 Memoir on Machines 
 
 Glepin 
 
 6-442 
 
 199 
 
 Ditto. An inverse current 
 
 
 applied to Ventilation 
 of Mines. 
 
 
 
 
 was produced towards the 
 centre of the machine. 
 
 VANES, BY M. PASQUET. 
 
 
 Memoir on Ventilating 
 
 Glepin 
 
 7-85 
 
 117 
 
 Three vanes in a conical form. 
 
 
 Machines, p. 64. 
 
 
 
 
 
 
 Ditto, p. 68 
 
 Ditto 
 
 2-162 
 
 120 
 
 Six vanes, same contraction as 
 
 
 
 
 
 
 last. 
 
 
 Annals of Public 
 
 Jochams 
 
 4-529 
 
 188 
 
 Type, Pasquet modified. 
 
 
 Works, Vol. XL, p. 1. 
 
 
 
 
 
 
 Ditto 
 
 Ditto 
 
 6-56 
 
 131 
 
 Ditto. Helicoidal passage. 
 
 
 Ditto 
 
 Ditto 
 
 4-163 
 
 182 
 
 Same machine. The mine 
 
 
 
 
 
 
 being narrowed increases the 
 
 
 
 
 
 
 result. 
 
 
 Ditto 
 
 Ditto 
 
 7-42 
 
 123 
 
 Ditto. 
 
 
 Ditto 
 
 Ditto 
 
 3-658 
 
 197 
 
 Ditto. The mine being reduced 
 
 
 
 
 
 
 increases the result. 
 
 WINDMILL, BY M. LESOINNE. 
 
 
 Treatise on Working 
 
 Trasenster 
 
 13-66 
 
 080 
 
 Six vanes inclined to the 
 
 
 of Mines, by POD son. 
 
 
 
 
 centre. 
 
 
 Ditto 
 
 Cabany 
 
 15-49 
 
 069 
 
 The mines were large, giving 
 
 
 
 
 
 
 a bad result. 
 
 
 Ditto .. 
 
 Trasenster 
 
 10-32 
 
 131 
 
 Ten vanes inclined through 
 
 
 
 
 
 
 the whole length. 
 
 VANES, BY M. DAVAINE. 
 
 
 Annals of Mines, Vol. 
 
 Sens 
 
 4-633 
 
 161 
 
 Four vanes of wood, forming 
 
 
 XVIL, p. 425. 
 
 
 
 
 a screw. 
 
56 THE THEORIES AND PRACTICE OF 
 
 The results in this table are all very feeble. The highest 
 does not exceed 0*230. We must not be astonished, for 
 none of" the machines named realise the conditions which are 
 so clearly required by the theory ; none of them have their 
 vanes straightened to the plane of the axis, and they do not 
 throw out the air into a diffuser. 
 
 Another cause occurs to still further diminish the result 
 obtained the insufficiency of the orifice of passage. The 
 largest of these ventilators is no more than 9*84 feet 
 diameter, and so, if we deduct from that the surface occupied 
 by the diaphragm or the central spindle, there remains only a 
 very narrow passage, which absorbs in pure loss a great part 
 of the depression, We see this at once if we reduce or 
 enlarge the equivalent orifice of the mine ; at the Pit No. 2 
 of Monceau-Fontaine (Nos. 6 and 7 in the table), a small 
 reduction suffices to increase the result from 0*189 to 0*230. 
 It is the same at the colliery Keunion (Nos. 14 and 15), where, 
 from the same cause, the result rises from 123 to * 197. 
 
 These observations warrant the assumption that if the 
 average of the " approximate results " in our table attains to 
 0*145, the exact manometrical result, based on the initial 
 depression, would certainly exceed 300. 
 
 It is impossible to say which is the best of the four types 
 of ventilators examined, for our. observations were neither 
 sufficiently regular nor sufficiently numerous to demonstrate a 
 marked superiority. The only thing which appears to be 
 at all clear is that the large diameters are favourable to 
 yield. It was to such machines as this that recourse was had 
 for the purpose of ventilating the large hall at the Palace 
 of the Trocadero for fetes. In the excellent communica- 
 tions made by M. Bourdais to the Members of Congress 
 at Paris, he said that they obtained very remarkable results 
 with the employment of machines of the helix type. 
 Are these facts, then, in opposition to what I have shown? 
 
CENTKIFUGAL VENTILATING MACHINES. 57 
 
 I think not. The truth is that the ventilation of a large 
 hall is incomparably more easy than that of a mine. It is 
 sufficient for M. Bourdais to have a pressure of 23 inch 
 of water in order to obtain a circulation of 2000 cubic feet of 
 air per second, but these figures correspond to an equivalent 
 orifice of about 97 square feet. Besides, the work was divided 
 between two machines, each of which had no more than 
 0'12 inch of pressure to produce. Under such conditions 
 we may say that all ventilators are good, provided that they 
 possess a sufficient orifice of passage. The motive power 
 required is the smallest possible; its economy becomes a 
 secondary consideration ; and one is naturally led to choose 
 the most simple machine, the least cumbersome, and especially 
 the least noisy. 
 
 It appears from these considerations that ventilators 
 by direct impulsion whilst good for ventilating buildings, 
 could only give very feeble results upon collieries. Is it 
 then possible entirely to proscribe them ? I would not say 
 so. Up to the present time there has been so little regard 
 paid in their construction to the requirements of theory, 
 that we may hope that with more intelligent arrange- 
 ments we may approach as high results as a Guibal 
 ventilator. Besides, these machines possess in some respects 
 an important advantage, which, under certain circumstances, 
 might lead the balance to be given in their favour: they 
 do not occupy in the plane perpendicular to their axis, 
 an area greater than their exterior circumference. To 
 fully understand this advantage, we must assume for a 
 moment that under certain circumstances we might have 
 to place a ventilator within the mine. A Guibal would 
 require an enormous space, not only for its circumference 
 but for the eccentricity of its cover and chimney. A 
 ventilator by direct impulsion would only require a circular 
 chamber equal to that of its vanes. 
 
58 THE THEORIES AND PRACTICE OF 
 
 This hypothesis of a ventilator below the surface, if it has 
 never yet been, might still be realised. Constantly we 
 see in mines currents of water descending unutilised from 
 great heights to reach the sump. Would it not be rational 
 to utilise this force to turn a turbine placed on the axis of a 
 ventilator ? 
 
 5. MOTIVE POWER. 
 
 To complete the theoretical study in which we are engaged, 
 it remains for us to determine the motive power necessary to 
 drive the depriinogen ventilators. I mean by motive power 
 the work to be applied to the shaft of a ventilator to set it 
 in motion. 
 
 Suppose, then, a deprimogen ventilator attached to a mine 
 where the equivalent orifice is known, and turning with a 
 given tangential speed. To determine the exact condition, 
 let us suppose that it is a centrifugal ventilator, and that its 
 vanes are bent in the direction of the radius as theory 
 requires, what would be the motive power required by this 
 machine ? 
 
 If we wish to make this determination by rational and 
 direct method, it will be necessary first to establish a 
 polygon of acting forces for any element of the profile of 
 the vane ; then to project the resultant on the trajectory of 
 the element ; to multiply this projection by the space passed 
 through ; and then to pass by an integration of the element 
 to the entire vane. I will content myself here with the 
 following a posteriori method : Let us admit for a moment 
 that our ventilator is a perfect machine, as we have often 
 done during this study. The result will be 100 for 100 ; 
 or, otherwise, the motive power shall be equal to the power 
 utilised, and as this latter is obtained it follows as a well- 
 
CENTKIFUGAL VENTILATING MACHINES. 59 
 
 known rule in multiplying the volume by the depression 
 that I have for the motive power the simple product 
 
 H being the theoretical depression expressed in inches of 
 water and V the corresponding value. 
 
 If, now, we call to mind machines more or less imper- 
 fect, the observed depression will be notably inferior to 
 the theoretical value H , and the volume afforded reduced 
 in proportion. But recalling what was said when we com- 
 menced we shall remember that this diminution is only 
 apparent the imperfect ventilator developed the theo- 
 retical depression equally as well as the perfect ventilator, 
 only that a certain portion of this depression was absorbed 
 by frictions, losses of duty, and other imperfections in the 
 machine. 
 
 In the first of the two factors of motive power H there is 
 no change ; the second V becomes the effective volume given, 
 V. Now add the work of passive resistance inherent to every 
 machine made by human hands, and we shall have for the 
 expression of effective motive power 
 
 Thus the motive power to be applied to a ventilator with 
 centrifugal force and with radial vanes is equal to the 
 product of the theoretical depression by the volume yielded, 
 increased by the work of passive resistance. 
 
 All the terms of this expression may be easily calculated 
 in advance, or at least with an approximation sufficiently 
 accurate for the constructor. 
 
 The theoretical depression for ventilators with radial vanes, 
 expressed in inches of water, is given by the formula 
 
60 THE THEORIES AND PRACTICE OF 
 
 We shall find in the additional note (E), a table of the 
 results of calculations, in which this depression is given for 
 all practical values of the tangential speed. 
 
 When the vanes are inclined to the radius, the value of 
 the theoretical depression is modified a little and becomes 
 
 U? 8 u V 2 cos a $ 
 
 H = 
 
 9 9 
 
 V 2 being the relative speed of the air leaving the vanes. It is 
 modified in the same way for ventilators by direct impulsion, 
 or, correctly speaking, the theoretical depression is due not 
 to the tangential speed, but rather to the speed of a certain 
 average point, of which the distance from the axis has for 
 its value 
 
 _ 
 
 But the superiority of the ventilators with centrifugal 
 force and the radial vanes appears to be generally recognised, 
 so that the first expression of H is alone necessary. 
 
 The knowledge of the volume given V results, either 
 from the formula established above, or from a simple 
 hypothesis. 
 
 As to the passive resistances they are of two kinds, 
 easily determined by methods familiar to engineers, viz. : 
 
 The friction of the shaft on its bearings ; and 
 
 The friction of the air drawn in by the vanes against the 
 fixed sides of the ventilator. 
 
 For this latter friction it is well to observe that of the two 
 components of the air moving in the machine, one only 
 interests us, that which follows the direction of the circum- 
 ference described by the vanes. The component parallel 
 to the radius need not in effect increase any resistance to 
 the load of the propulsive vane, since it is perpendicular 
 
CENTRIFUGAL VENTILATING MACHINES. 61 
 
 to its movement. This fact much simplifies the matter, 
 for it permits us to reduce the complex movement of 
 the air to a simple rotation round the axis, as in the 
 case when the mine is shut off and the air turns in its 
 place. 
 
 Thus the calculation limits itself to measuring the fric- 
 tion surfaces, estimating the average speed of friction, and 
 applying to these data the coefficient of friction based upon 
 experimental knowledge, in which, according to Aubuisson, 
 the value will be equal to about '0032. To these two 
 frictions the passive resistances are reduced, which affords 
 the work to be applied to the shaft of the ventilator. 
 
 But if we mean by the motive power the work of the 
 steam acting on the piston of the machine as it is measured 
 with the indicator of Watt, it is necessary to add to the 
 passive resistances all the shocks and frictions on the part 
 of this machine, not forgetting the important work absorbed 
 by the belt where this kind of transmission exists. 
 
 I have insisted on a simple means of motive power 
 being employed by constructors in this calculation, because 
 they often employ for this object very fantastic methods. 
 I may cite amongst others that which consists in taking for 
 the work of opposing forces the product of the depression 
 by the surface of the vane, but this method is doubly 
 erroneous, for it neglects the yield, which is one of the 
 factors of work, and introduces the surface of the vane, 
 where the influence is nothing. 
 
 We may remark, however, that the motive power in- 
 creases rapidly when we increase the speed of rotation 
 of the ventilator, the volume V varying as the simple 
 speed, the depression H as its square, and the first term 
 of the work of the motor, and also the most important, 
 VH increasing as the cube of the speed. So it is less 
 easy to make this latter vary within large limits than might 
 
62 THE THEORIES AND PRACTICE OF 
 
 at first sight appear. If, on the contrary, we suppose the 
 speed of rotation to be invariable, H becomes constant, 
 and the motive power depends only on the yield V. This 
 has the singular effect, which at first appears almost para- 
 doxical, that the more we increase the resistance to the 
 passage of the air, the more the work is reduced, and the 
 ventilator increases in speed. And if, on the contrary, we 
 give the air free access to the machine, the work becomes 
 greater, and the speed of the ventilator is reduced. We 
 observe just the reverse with the volumogen ventilator. 
 
 The expression that we have now to find for the engine 
 power to be applied to deprimogen ventilators enables us to 
 establish the mechanical yield of these machines. I say 
 mechanical in opposition to the manometrical useful effect, 
 of which we spoke just now. We know the work useful 
 effect ; it is the product V h of the effective volume by the 
 effective depression ; the motive power is yet to be deter- 
 mined. Then the mechanical yield is the proportion of useful 
 work to the motive power and it takes the form 
 
 We may replace in this expression the quantities V^ and 
 Ho by their values in a function of the given characteristics 
 of machines and of the mines which they ventilate (equivalent 
 orifice, tangential speed, &c.), but the term T p of the deno- 
 minator not admitting of reduction, we should have a com- 
 plicated expression, and consequently not to the point. We 
 may also with the slightest reflection observe in the pre- 
 ceding expression the influences of different kinds which 
 vary the results. 
 
 We may ask, for example, what becomes of the mechanical 
 yield of a ventilator, when we increase its speed of rotation. 
 The useful work V h and the first term V Ho of the motive 
 
CENTRIFUGAL VENTILATING MACHINES. 63 
 
 power will both increase as the cube of this speed, so that 
 if we can admit that the term T p of passive resistances in- 
 creases with the same rapidity, the yield will be obtained 
 independent of the speed. But in reality the term T p 
 increases much less quickly, hence the yield improves as 
 the speed increases. This is proved by different experiments 
 where care has been taken to vary the speed of the ventilator. 
 I may cite, for instance, the numberless experiments made by 
 MM. Grille and Franeau on the G-uibal ventilator of Crachet, 
 to be found in the treatise on ventilation by M. Devillez, 
 page 227. 
 
 If, supposing the speed of rotation to be invariable, we 
 increase the equivalent orifice of the mine from zero to 
 infinity, we shall find at first no result, the useful effect being 
 nothing itself. Beyond, the result increases by degrees, but 
 remains feeble in consequence of the importance of the term 
 T p of passive resistance. In proportion as this influence weakens 
 the yield and the result continue to increase. But then 
 there occur rapidly increasing frictions of the air traversing 
 the machine ; quickly this new influence predominates, and 
 having reached a certain maximum the yield begins to 
 decrease, and finally attains a point where it becomes nothing. 
 
 This work of the yield is very clearly shown by the experi- 
 ments of the Commission of Gard, to which I refer the reader. 
 It shows that for every deprimogen ventilator there corres- 
 ponds a given mine for which its yield is greatest, and to 
 which it is especially appropriate. 
 
 As to the influence of the manometrical yield, and of the 
 orifice of passage, it is easy to see that the mechanical yield 
 varies in the same direction as these. When they are 
 weakened, it is because the frictions, losses of quantity, 
 and other imperfections increase, all causes which assist to 
 weaken the yield. 
 
 The experiments made to measure the mechanical yield of 
 
64 THE THEORIES AND PRACTICE OF 
 
 ventilators are much less abundant than those which are 
 limited to measure the yield and depression. 
 
 In many cases they have sought to establish the motive 
 power by applying to the surface of the piston the 
 pressure observed on the boiler gauge; but this method 
 is based on the employment of coefficients more or less 
 arbitrary, and does not appear to me to merit any confidence. 
 I cannot admit as important data results not obtained with 
 the aid of the Prony friction brake, or of the Watt indicator. 
 The use of the former is much more limited than the latter, 
 besides it supposes that we may break the connection between 
 the power and the resistance, a circumstance which does not 
 happen except in machines where the motive power is trans- 
 mitted by a belt. These inconveniences are unfortunate, for, 
 from the point of view of results, the brake presents a great 
 advantage over the indicator. It measures exclusively work 
 transmitted to the shaft of the ventilating machine, whilst 
 the indicator includes at the same time all the passive resist- 
 ances of the motive power ; the numbers obtained in the result 
 will be different also according to the instrument for measure- 
 ment to which we have recourse, they will be weaker with the 
 indicator in consequence of the exaggeration of the term T^, of 
 passive resistances. 
 
 I have included in the table on pp. 66-69 a certain 
 number of observations of yield selected from industrial 
 works. In general the observations are repeated a certain 
 number of times for each machine, varying sometimes the 
 speed and sometimes the resistance of the mine, and I have 
 reproduced the minimum and maximum results in the table. 
 The signification of these numbers varies with the dynamo- 
 meter employed ; I have been careful to specify this latter 
 in the column observations. The ventilators by direct impul- 
 sion are placed at the head of the table in order to follow as 
 nearly as possible the order of increasing yield. 
 
CENTRIFUGAL VENTILATING MACHINES. 65 
 
 As we may see (Table III.), the ventilators by direct 
 impulsion give only a very poor mechanical result ; the 
 highest deduction being made for passive resistance, it does 
 not exceed '824. 
 
 The ventilators without cover present some very irregular 
 results, the cause of which is not clearly seen. Thus it is 
 surprising that the ventilator of Crachet, which is 22 96 feet 
 in diameter, does not exceed 22, whilst the turbine of Lalle 
 rises to 47. We may see from these results that if there 
 has been any progress with ventilators by direct impulsion 
 the advantage gained is small. This progress continues 
 pretty equally with covered ventilators, from ventilators 
 with rectangular chimney up to ventilators properly called 
 Guibal, which are at present the most efficient. 
 
 If we take as a characteristic of the yield of each type of 
 ventilators the arithmetical average pure and simple of the 
 figures shown in our table, we shall obtain the following 
 series : 
 
 Ventilators by direct impulsion 260 
 
 by centrifugal force, without cover . . 278 
 with centrifugal force, covered, without 
 
 chimney 0-284 
 
 Ventilators with centrifugal force, with cover and 
 
 rectangular chimney 0'379 
 
 Ventilators with centrifugal force, with cover, slide, 
 
 and evasee chimney 0'467 
 
 Certainly it is rather the order of these values than their 
 absolute magnitude which we should consider here ; but even 
 with this reserve the series is still very interesting and 
 explicit. The most important of these averages is that of 
 the Guibal ventilators, for they result from a number of 
 already important observations. Still I think it rather poor 
 compared with the minimum of our table results in general, 
 though this may be a consequence of taking observations 
 
 F 
 
66 
 
 THE THEORIES AND PRACTICE OF 
 
 TABLE 
 
 No. 
 
 Date. 
 
 Mine. 
 
 Dimensions. 
 
 Exterior Diameter of 
 Diameter. Ouw. 
 
 Width. 
 
 
 
 ft. in. ! ft. in. i 
 
 ft. in. 
 
 VENTILATORS BY 
 
 Apr. 7, 1843 
 Aug. 2, 1860 
 
 Motte screw, at No. 1 Pit, Sauwartan- 
 sur-Dour. 
 
 Davaine's Ventilator, with helicoidal 
 vanes, at Bully-Grenay. 
 
 4. 7'1 1-8 
 
 6 6-7 
 
 3-9 
 
 2 4-7 
 
 UNCOVERED VENTILATORS BY 
 
 Mar. 28, 1844 , Combes' Ventilator, Grand Hormi .. ! 5 6-9 
 
 Nov. 25, 1842 , Letoret Ventilator, Colliery of St. Vic- 
 toire, at Frameries. 
 
 Sept. 24, 1876 ' Turbine Ventilator, Mines of Lalle and 
 
 Apr. 30, 1865 
 
 10 3-6 
 
 12 5-6 
 
 Guibal Ventilator, Colliery of Crachet 22 11-5 
 
 and Picquery. 
 
 Lambert Ventilator, Ormont Colliery, 26 2 9 
 at Chatelet. 
 
 4 5-511 1-4 
 
 5 3-013 0-6 
 
 4 4-7 
 
 9 10-1 
 
 4 1-2 
 
 4 7-1 
 
 4 7-1 
 
 Aug. 10, 1859 
 
 Nov. 28, 1865 
 
 COVERED VENTILATORS, WITHOUT 
 Grisceil Colliery, No. 10 Pit .. .. 13 1'4 5 3-0 j 5 0'2 
 
 Guibal Ventilator, Crachet and Picquery 
 
 22 11-5 
 
 9 10-1 
 
 4 7-1 
 
 COVERED VENTILATORS WITH 
 
 10 
 
 11 
 
 12 
 
 Mar. 22, 1859 
 July 29, 1877 
 
 Jean Bart Pit .. .. 
 Creal Mines, Besseges . 
 
 Grand Buisson Colliery 
 
 11 9-71 5 3-0 
 19 8-211 5-8 
 
 22 11-5 
 
 9 10-1 
 
 4 11-0 
 3 7-3 
 
 5 6-9 
 
CENTRIFUGAL VENTILATING MACHINES. 67 
 
 No. III. 
 
 Publications. 
 
 Authors. 
 
 Manometric 
 Yield. 
 
 Observations. 
 
 Min. 
 
 Max. 
 
 DIRECT IMPULSION. 
 
 
 Memoir on Ventilating 
 Machines. 
 
 Glepin 
 
 0-220 
 
 0-230 
 
 Prony brake. 
 
 
 Annales des Mines, 
 1860, p. 425. 
 
 Sens, Mining 
 Engineer. 
 
 0-264 
 
 0-324 
 
 Watt indicator, motor with- 
 out load deducted or the 
 result would not exceed 
 0-253. 
 
 CENTRIFUGAL FORCE. 
 
 
 Treatise on Mine Work- 
 ing, by Ch. Combes. 
 
 Glepin 
 
 0-270 
 
 0-290 
 
 Prony brake. 
 
 
 Memoir on Ventilating 
 Machines, p. 46. 
 
 Ditto 
 
 0-160 
 
 0-180 
 
 Ditto. 
 
 
 Bulletin of Society of 
 Mineral Industry, 
 2nd Series, Vol. VII., 
 p. 477. 
 
 Aguillon, 
 Fumal, and 
 Murgue 
 
 0-277 
 
 0-470 
 
 Watt indicator, by Commission 
 of Gard. 
 
 Ventilation of Mines, 
 by M. Devillez, 
 p. 227. 
 
 Gille and 
 Franeau. 
 
 0-160 
 
 0-220 
 
 Type, Guibal, before 
 covered. 
 
 being 
 
 Ditto 
 
 Devillez and 
 Letoret, &c. 
 
 0-354 
 
 0-398 
 
 Prony brake. 
 
 
 CHIMNEY, BY CENTRIFUGAL FORCE. 
 
 
 Annals of Public 
 Works, Belgium, Vol. 
 XVII. 
 
 .. 
 
 0-267 
 
 0-390 
 
 Watt indicator. 
 
 
 Ventilation of Mines, 
 by Devillez, p. 228. 
 
 Gille and 
 Franeau. 
 
 0-170 
 
 0-310 
 
 Ditto, same as No. 6. 
 
 
 CHIMNEY OF CONSTANT SECTION. 
 
 
 Notes of M. Cabany. 
 
 A. Cabany 
 
 0-334 
 
 0-342 
 
 Ditto, Guibal, early type. 
 
 Bulletin of Society of 
 Mineral Industry, 
 Vol. VII., p. 477. 
 
 Aguillon, 
 Fumat, 
 and Murgue. 
 
 0-422 
 
 0-517 
 
 Ditto. Part of work restored 
 by a canal vasee. 
 
 Ventilation of Mines, 
 by Devillez. 
 
 
 
 0-320 
 
 0-334 
 
 Ditto, Guibal, but the chim- 
 ney of constant section. 
 
68 
 
 THE THEORIES AND PRACTICE OF 
 
 TABLE 
 
 No. 
 
 Date. 
 
 Mine. 
 
 Dimensions. 
 
 Exterior 
 Diameter. 
 
 Diameter oi 
 Ou'ie. 
 
 Width. 
 
 
 
 
 i ft. in. 
 
 ft. in. 
 
 ft. in. 
 
 COVERED VENTILATORS WITH SLIDE AND 
 
 13 
 
 June 25, 1862 
 
 Verger Pit, Anzin 
 
 16 4-8 
 
 8 2-4 
 
 6 6-7 
 
 14 
 
 Aug. 11, 1861 
 
 Grosse-Fosse, Anzin 
 
 16 4-8 
 
 8 2-4 
 
 6 6'7 
 
 15 
 
 July 22, 1877 
 
 Grangier Pits, Besseges 
 
 16 4-8 
 
 8 2-4 
 
 6 6-7 
 
 16 
 
 Apr. 22, 1866 
 
 Mine of Forchier 
 
 19 8-2 
 
 9 10-1 
 
 "' 
 
 17 
 
 18 
 19 
 20 
 
 July 31, 1865 
 Mar. 1866 
 Mar. 25, 1866 
 
 Colliery of Crachet and Picquery 
 Ditto . .. 
 
 22 11-5 
 22 11-5 
 22 11-5 
 22 11-5 
 
 9 10-1 
 9 10-1 
 9 10-1 
 9 10-1 
 
 5 6-9 
 5 6-9 
 5 6-9 
 5 6-9 
 
 Ditto 
 
 Grand Buisson 
 
 21 
 22 
 23 
 
 24 
 25 
 
 Sept. 11, 1870 
 1866 
 Oct. 24, 1869 
 
 May 17, 1869 
 June 21, 1869 
 
 Grand Mambourg 
 
 22 11-5 
 22 11-5 
 29 6'2 
 
 29 6-2 
 29 6-2 
 
 9 10-1 
 9 10-1 
 9 10-1 
 
 9 10-1 
 9 10-1 
 
 8 2-4 
 5 6-9 
 6 6-7 
 
 6 6-7 
 6 6-7 
 
 RieuduCoeur 
 Louviere . . . . . 
 
 Grand Buisson 
 
 26 
 
 Mar. 25, 1877 
 
 Crachet and Picquery 
 
 39 4-313 1-4 
 
 1 
 
 8 2-4 
 
 WORKSHOP 
 
 27 
 
 .. 
 
 Uncovered Fan of M. Tournaire 
 
 2 9-5 
 
 1 6-9 
 
 
 28 
 
 July 22, 1855 
 
 Ventilator given to Exhibition by M. 
 de Lacolonge. 
 
 3 3-0 
 
 10-2 
 
 6-0 
 
 29 
 
 
 
 Ventilator made for charcoal furnace 
 by M. Rittenger. 
 
 5 3-0 
 
 1 2-2 
 
 3-5 
 
CENTRIFUGAL VENTILATING MACHINES. 69 
 
 No. III. continued. 
 
 Publications. 
 
 Authors. 
 
 Manometric 
 Yield. 
 
 Observations. 
 
 Min. 
 
 Max. 
 
 EVASEE CHIMNEY (GUIBAL TYPE). 
 
 
 Notes 
 
 Cabany 
 
 0-418 
 
 0-460 
 
 Watt indicator. 
 
 Ditto 
 
 Ditto 
 
 0-510 
 
 0-640 
 
 Ditto. 
 
 Bulletin of Mineral 
 
 Aguillon, 
 
 0-250 
 
 0-494 
 
 Ditto. The small yield was 
 
 Industry, Vol. VII. 
 
 Fumat, and 
 
 
 
 obtained on a thin mine. 
 
 
 Murgue. 
 
 
 
 
 Ventilation of Mines, 
 
 Stoesser and 
 
 0-413 
 
 0-455 
 
 Ditto dittot 
 
 Devillez. 
 
 Devillez. 
 
 
 
 
 Ditto 
 
 Gille and 
 
 0-380 
 
 0-610 
 
 Ditto, same far as No. 6, com- 
 
 
 Fraueau. 
 
 
 
 plete. 
 
 Ditto 
 
 .. 
 
 0-307 
 
 0-749 
 
 Ditto. Experiments made 
 
 
 
 
 
 when mine much altered. 
 
 Ditto 
 
 Stoesser and 
 
 0-440 
 
 0-501 
 
 Ditto. 
 
 
 Devillez. 
 
 
 
 
 Ditto 
 
 .. 
 
 0-426 
 
 0-725 
 
 Ditto, same fan as No 12, 
 
 
 
 
 
 chimney complete. 
 
 Ditto 
 
 De Poitier 
 
 0-426 
 
 0-534 
 
 Ditto. This fan is of great width. 
 
 Unpublished 
 
 C. Brice 
 
 0-230 
 
 0-410 
 
 Ditto. 
 
 Ventilation by Devillez 
 
 Brunin and 
 
 0-452 
 
 0-580 
 
 Ditto. 
 
 
 others. 
 
 
 
 
 Ditto 
 
 Roger and 
 
 0-279 
 
 0-513 
 
 Ditto. 
 
 
 Halley. 
 
 
 
 
 Ditto 
 
 
 0-382 
 
 0-382 
 
 Ditto. 
 
 Revue Universelle, 
 
 Hubert, 
 
 0-538 0-555 
 
 Ditto. 
 
 July 1877. 
 
 Devillez. 
 
 
 
 
 BLOWING FANS. 
 
 AnnalesdesMines,1860 
 
 Tournaire 
 
 0-240 
 
 0-500 
 
 Prony brake. 
 
 The "Genie Industrie!" 
 
 Experiments 
 
 0-132 
 
 0-646 
 
 Ditto. 
 
 
 at Conser- 
 
 
 
 
 
 vatoire des 
 
 
 
 
 
 Arts et 
 
 
 
 
 
 Metiers. 
 
 
 
 
 Ventilation, by Ritten- 
 ger, 1858. 
 
 Rittenger 
 
 0-110 
 
 0-230 
 
 Ditto. Equivalent orifice very 
 small and so yield and effect 
 
 
 
 
 
 is poor. 
 
70 THE THEORIES AND PRACTICE OF 
 
 under inconvenient working conditions and often those 
 unfavourable to the yield. I think that we may accept 
 the number 0*500 as representing with sufficient exact- 
 ness the average yield of this kind of machine under the 
 conditions in which they generally work. It is the result of 
 experiments made with Watt's indicator, the only dynamo- 
 meter possible with direct-acting machines. If we could 
 have measured the motive power on the shaft itself with the 
 aid of dynamometers, or even by the torsion on the shaft as 
 has been proposed by M. Him, we should certainly have 
 obtained a higher yield. 
 
 6. CONCLUSIONS. 
 
 I will now give a resume, in a few lines, of the theoretical 
 views developed in the preceding paragraphs. In theory 
 every deprimogen ventilator turning under the action of a 
 motor, gives a certain depression depending entirely on the 
 tangential speed, and consequently independent of the 
 volume of air which it yields. This depression has for its 
 value 
 
 H - " 2 - 
 
 H ~g 
 
 In practice two causes occur to prevent the effective 
 depression yielding this ideal value. 
 
 First, imperfections of different kinds, independent of 
 yield, oblige us to apply to the preceding expression a 
 coefficient of reduction K, which we have named the 
 manometrical yield. 
 
 Second, the frictions and losses of the load of air traversing 
 the machine, losses proportional to the square of the yield, 
 and expressed by the area of the orifice of passage o. 
 
CENTRIFUGAL VENTILATING MACHINES. 71 
 
 From these two enfeebling^ causes, the value for the 
 effective depression becomes 
 
 (+5) 
 
 From the knowledge of the effective depression and the 
 equivalent orifice of the mine, there is deduced by the appli- 
 cation of a formula for the flow in a thin medium, the 
 volume of air yielded 
 
 V = ' 65 
 
 Finally the product of volume by the theoretical depres- 
 sion which virtually subsists, and gives to the motor the 
 same load as if it had been manifest, gives, in taking account 
 of passive resistances, the value of the motive power 
 
 T - V H -4- T 
 
 -*-m - LJ -o \ *-$ 
 
 In the first part of this study, published in 1872, 1 stated 
 in the following terms the problem of mine ventilation : 
 
 To make a given quantity of air traverse a given mine. 
 
 Then, having proposed to represent mines by their equiva- 
 lent orifices, I thus modified this statement : 
 
 To make a given volume of air circulate through an orifice 
 in a thin medium. 
 
 I cannot pretend that it is always in these terms that the 
 problem presents itself to those studying it; but it is at 
 least the most general one, and it cannot give any difficulty 
 in the treatment of it under different forms. 
 
72 THE THEOEIES AND PRACTICE OF 
 
 Let a volume V be made to pass through an orifice a. 
 
 Let h be the necessary depression to cause this circulation, 
 a depression which will be immediately given by the formula 
 of the flow through a thin medium 
 
 The engineer should then decide upon the type of 
 machine that he intends to adopt. Theory and experience 
 show that the best deprimogen ventilator is the ventilator 
 with centrifugal force, in which the air expelled by the 
 vanes is received in evasee channels, like those of the Guibal 
 ventilator. Let us admit, then, that choice is made of the 
 Guibal ventilator. For comparison with existing machines, 
 we observe that the manometrical yield in these ventilators 
 may be estimated at 750. As to the orifice of passage, it 
 is more difficult to decide, this element depending especially 
 on the width, on the eccentricity, and on the ouie. I have only 
 given three examples of the orifice of passage, those of the 
 ventilators of Besseges, Creal, and Lalle ; they may assist in 
 suggesting a provisional hypothesis, and then, introducing 
 these two data K and o in the formula for effective 
 depression, 
 
 K'+S) 
 
 we have an equation from which it would be easy to deduce 
 the value of the tangential speed u. 
 
 This is the exact method arising rationally from our 
 theory ; there is another, more approximative but more 
 simple, and in fact sufficient for the application ; it is based 
 on the knowledge of the approximate manometrical yield. 
 This yield, according to our first table, is on an average, for 
 
CENTRIFUGAL VENTILATING MACHINES. 73 
 
 Guibal ventilators, 650. This figure increases a little for 
 thin seams and diminishes for thick ones. Dividing the 
 effective depression by this coefficient, always, it is true, 
 somewhat arbitrary, we obtain the theoretical depression 
 
 whence we deduce easily the value of the tangential 
 speed u. 
 
 This tangential speed is a most important factor in the 
 construction of deprimogen ventilators. We may see this 
 either in a small ventilator turning with great speed, or in 
 a large machine turning slowly. On this point the con- 
 structor is altogether free, and may be guided by con- 
 siderations of the place for which it is required, of economy, 
 and of mechanical simplicity. 
 
 The form to be given to the vanes has been described 
 before. They should present to the circumference of the 
 ouie an inclination following the resultant of their move- 
 ment of rotation and of the movement of the air pene- 
 trating their spaces. From this they should incline by a 
 gentle curve, and terminate by a part directly following the 
 radius. As to their number, it seems to me that it is an 
 advantage to make them numerous; they guide the air 
 better and shake less. The only objection is that by the 
 thickness being repeated they rather reduce the orifice of 
 
 The motive power to be applied to the machine so defined 
 will be given by the formula 
 
 whence it suffices to make an hypothesis on the value of the 
 passive resistances as far as it is known ; but that is all the sim- 
 plification possible. We have seen that the average value of 
 
74 THE THEORIES AND PRACTICE OF 
 
 the mechanical yield observed at the indicator with Guibal 
 ventilators is 500 ; it is sufficient, then, if we have the 
 elements of useful work YA, to double them in order to 
 obtain with a sufficient approximation for practice the work 
 to be applied to the piston of the motive power. 
 
 There remain to be determined the diameter of the ouie, 
 the width and the eccentricity, &c., but these elements result 
 from considerations altogether different from those which I 
 have enumerated, and I will return to this study for the 
 fourth occasion, and I hope the last one, if circumstances 
 permit me to establish the theoretical and practical conditions 
 which exist in the best ventilators. 
 
 BESSEGES, January 17, 1880. 
 
CENTRIFUGAL VENTILATING MACHINES. 75 
 
 ADDITIONAL NOTES. 
 
 NOTE A. 
 The Theory of Bernoulli. 
 
 This theory, which forms the base of hydraulics, may be 
 thus expressed: When a fluid vein where there is an 
 established condition flows in any given form, if we make 
 abstraction of the frictions which occur on the sides, at each 
 point, the generative height of the speed, the pressure mea- 
 sured in column of fluid, and the height above an arbitrary 
 horizontal plane, form a total constant 
 
 V 2 
 
 - f- H -f- Z = constant. 
 
 ^9 
 
 In the questions relative to ventilation the fluid veins in an 
 atmosphere of the same character and the same density as 
 themselves are not affected by the action of their own 
 weight. Consequently a vein moving primitively in the 
 horizontal plane may be inclined in any direction whatever 
 without being affected by the vertical displacement of its 
 molecules. 
 
 This remark enables us to eliminate the term Z of the 
 preceding expression, and to reduce it to the simple 
 
 binomial 
 
 V* 
 
 (- H = constant. 
 
 ^9 
 
 Thus in the vein of air the generative height of the speed 
 and the pressure mutually compensate each other, the one 
 increasing as the other weakens. 
 
 Let us consider two points, more or less distant from one 
 another, in the same vein of air, their pressures and speeds 
 
76 THE THEOBIES AND PRACTICE OF 
 
 being H and V for the first point, H' and V for the second. 
 We may then write 
 
 or rather, by calling h the increase H' H of the pressure, 
 
 an expression which may be thus translated : When the speed 
 of a vein of air gradually diminishes from one point to another, 
 the increase of the pressure is equal to the diminution of the 
 generative head of the speed. It is this statement which I 
 assume to be present to the mind of the reader whenever 
 in the course of this study I made reference to the theory of 
 Bernoulli i. 
 
 NOTE B. 
 
 Of the law of Proportionality between the Volume yielded and 
 the speed of Rotations, and between Depression and the 
 Square of this Speed. 
 
 All the published experiments, and all those which I have 
 made myself on the ventilator of the mine of Creal, agree as 
 to the evidence of this double proportionality. I will record 
 two of the latter experiments taken promiscuously. 
 
 The first, on the 26th August, 1876, includes three observa- 
 tions of the volume yielded at three different speeds of the 
 ventilator. Measurements were made with the aid of the 
 anemometer of Combes. Twenty-three observations of speed 
 made in twenty-three spaces being regularly divided over the 
 section of measurement have allowed us to establish an 
 average speed with a very satisfactory exactness. The 
 numbers of the last column indicate the proportion of the yield 
 
CENTKIFUGAL VENTILATING MACHINES. 
 
 77 
 
 to the speed of rotation, or, if we prefer, the number of cubic 
 feet yielded per revolution of the machine. 
 
 
 
 Revolu- 
 
 Volume 
 
 Proportion 
 
 
 
 No. 
 
 tions per 
 Minute. 
 
 per 
 
 Second. 
 
 of Yield to 
 
 Speed. 
 
 
 
 1 
 
 40-8 
 
 315-4 
 
 7'73 
 
 
 
 2 
 
 49-2 
 
 386-9 
 
 7-86 
 
 
 
 3 
 
 .58-3 
 
 454-6 
 
 7-79 
 
 
 The regularity of the final proportion leaves no doubt, 
 especially if we take account of the difficulty in every 
 particular in this kind of observation. 
 
 This proportional increase will evidently continue as far as 
 it is possible to push the speed of the ventilator. Still, it is 
 difficult to understand the opinion which we sometimes hear 
 expressed that beyond a certain speed the yield ceases to 
 increase, or rather only increases very slowly. It cannot be 
 based upon any experiments which are sufficiently exact. 
 
 The volume yielded per revolution of the machine remains 
 constant so long as the resistance of the mine itself does 
 not vary ; but it is clearly connected with this resistance, 
 so that every variation in the value of the equivalent orifice 
 shows itself by a corresponding variation almost proportion- 
 ally to the yield per revolution. This observation suffices to 
 show how irrational it is to seek to establish, as some writers 
 have done, a more or less constant relation between the 
 volume yielded and the volume generated by the rotation 
 of the vanes. This kind of relation has no serious signi- 
 ficance except for volumogen ventilators. 
 
 The second series of observations which I produce here 
 was made on the 14th January, 1872 ; the depressions alone 
 have been observed with a somewhat doubtful approxima- 
 tion to the extent of ^^ of an inch. The second column 
 gives the squares of the speeds of rotation, and the last the 
 proportion of the depressions to those of the square of the 
 
78 
 
 THE THEORIES AND PRACTICE OF 
 
 speed, a proportion of which it is necessary to verify the 
 regularity : 
 
 
 No. 
 
 Revolu- 
 tions per 
 Minute. 
 
 Square of 
 Number of 
 Revolutions. 
 
 Water 
 Gauge. 
 (Inches.) 
 
 Proportion of 
 Depression to 
 the Square of 
 
 
 
 
 
 
 
 
 
 
 1 
 
 33-8 
 
 1142-44 
 
 0-323 
 
 000282 
 
 
 
 2 
 
 39-8 
 
 1584-04 
 
 0-444 
 
 000280 
 
 
 
 3 
 
 49-0 
 
 2401-00 
 
 0-670 
 
 000279 
 
 
 
 4 
 
 56-8 
 
 3226-24 
 
 0-893 
 
 000276 
 
 
 
 5 
 
 64-0 
 
 4096-00 
 
 1-134 
 
 000276 
 
 
 Here, again, the regularity of the final proportion proves 
 itself in a sufficiently clear manner, having regard to the 
 difficulty of measuring the depression with certainty in the 
 midst of incessant oscillations. 
 
 We observe that the numerical value of this proportion 
 falls in a regular slowly decreasing progression. There is here 
 a certain indication of a natural action which was easily 
 accounted for at the time the experiment was made. The 
 chimney of the ventilator gives rise to a certain amount of 
 aspiration, which is added to the effect produced by the 
 vanes affecting relatively more the cases of weak depressions. 
 When the natural movement is lively it affects very strongly 
 the double proportionality which we seek to establish by 
 experimental verification. To see it most distinctly in the 
 case of the depression the best plan is to make a drawing of 
 it, with the squares of the speeds for abscissae and the observed 
 depressions as ordinates. The points so obtained arrange 
 themselves in a straight line, which, instead of coinciding 
 with the origin itself, passes above or below it, at a distance 
 which gives the exact measure of the action which is so 
 troublesome. In the case of the volume where this action 
 has an influence still greater we place in the abscissae not 
 the speed itself, but its square, and in the ordinates the square 
 of the yield. In effect, if h represents the depression due to 
 the natural action, and h that due to the ventilator alone, 
 
CENTRIFUGAL VENTILATING MACHINES. 79 
 
 the volume yielded, given by the formula of escape in the 
 thin medium, would have for expression 
 
 V = 0-65 a J2g(h A ), 
 and by raising it to the square 
 
 V 2 = (F65 2 a* 2 g (h h }. 
 
 Remarking that h is proportional to the square of the speed, 
 and that the product 65 a 2 2 g is constant, I may thus 
 transform this equation 
 
 If for the present we take <o 2 in abscissae and V 2 in 
 ordinates, we have a straight line passing above or below 
 the origin at a distance which will measure in size and in sign 
 the value of the square of the yield which exists when the 
 ventilator is stopped. 
 
 NOTE D. 
 
 Calculation ~by the Direct Method of the Motive Power to le 
 applied to Ventilators by Centrifugal Force. 
 
 This note is of such a highly theoretical character that it 
 seems hardly necessary to repeat it in full. It may be 
 summed up by saying that for every ventilator by centrifugal 
 force and with radial vanes the motive power, deducting 
 passive resistances, is equal to the product of the volume 
 yielded by the theoretical depression expressed in inches of 
 water, confirming the exactness of the indirect method given 
 in the body of the work. 
 
 NOTE E. 
 Of the Theoretical Pressure. 
 
 The theoretical depressions which ventilators with centri- 
 fugal force develop in the hypothesis of absolute perfection, 
 constitute an interesting and useful study. We see in the 
 
80 
 
 THE THEORIES AND PRACTICE OF 
 
 preceding note that it forms one of the factors of motive 
 power, and in this respect this knowledge is indispensable for 
 a constructor. Besides, it serves as a term for comparison to 
 establish the exact or approximate manometrical yield of 
 deprimogen ventilators. In the case of a ventilator giving 
 a certain depression it is sufficient to refer to the theoretical 
 depression, and to take the proportion, to obtain this test of 
 prime importance of the value of the machine. We give in 
 the following table, expressed in inches of water, the values 
 of the theoretical depression corresponding to the tangential 
 speeds comprised between the practical limits of 49 and 114 
 feet per second, and in spaces of about -j-J^ of an inch. These 
 values have been calculated with the aid of the formula 
 
 in which S, the density of the air, has been supposed to be 
 1-200. 
 
 VALUES OF THE THEOEETICAL DEPKESSION EXPRESSED IN INCHES. 
 
 Speed in feet of 
 the Periphery 
 per second. 
 
 Theoretical 
 Depression in 
 inches. 
 
 Speed in feet of 
 the Periphery 
 per second. 
 
 Theoretical 
 Depression in 
 inches. 
 
 Speed in feet of 
 the Periphery 
 per second. 
 
 Theoretical 
 Depression in 
 inches. 
 
 49-2135 
 
 ]-0839 
 
 56-4315 
 
 4248 
 
 63-6495 
 
 1-8126 
 
 49-5416 
 
 1-0980 
 
 56-7596 
 
 4413 
 
 63-9786 
 
 1-8315 
 
 49-8697 
 
 1126 
 
 57-0877 
 
 4583 
 
 64-3056 
 
 1-8504 
 
 50-1978 
 
 1276 
 
 57-4158 
 
 4752 
 
 64-6337 
 
 1-8693 
 
 50-5259 
 
 1415 
 
 57-7438 
 
 4917 
 
 64-9618 
 
 1-8881 
 
 50-8540 
 
 1555 
 
 58-0719 
 
 5091 
 
 65-2899 
 
 1-9075 
 
 51-1821 
 
 1714 
 
 58-4000 
 
 5260 
 
 65-6180 
 
 1-9263 
 
 51-5102 
 
 1870 
 
 58-7281 
 
 5427 
 
 65-9461 
 
 1-9455 
 
 51-8383 
 
 2024 
 
 59-0562 
 
 5600 
 
 66-2742 
 
 1-9647 
 
 52-1664 
 
 2177 
 
 59-3843 
 
 5779 
 
 66-6023 
 
 1 9846 
 
 52-4944 
 
 2331 
 
 59-7124 
 
 5953 
 
 66-9304 
 
 2-0043 
 
 52-8225 
 
 2484 
 
 60-0405 
 
 6129 
 
 67-2585 
 
 2-0240 
 
 53-1506 
 
 2642 
 
 60-3686 
 
 6307 
 
 67-5865 
 
 2-0436 
 
 53-4787 
 
 2795 
 
 60-6969 
 
 6484 
 
 67-9146 
 
 2-0638 
 
 53-8068 
 
 2952 
 
 61-0247 
 
 6661 
 
 68-2427 
 
 2-0838 
 
 54-1349 
 
 1-3114 
 
 61-3528 
 
 6842 
 
 68-5708 
 
 2-1039 
 
 54-4620 
 
 1-3272 
 
 61-6809 
 
 7024 
 
 68-8989 
 
 2-1240 
 
 54-7910 
 
 1 3433 
 
 62-0090 
 
 7205 
 
 69*2270 
 
 2-1445 
 
 55-1191 
 
 1-3594 
 
 62-3371 
 
 7386 
 
 69-5551 
 
 2-1645 
 
 55-4472 
 
 1-3755 
 
 62-6652 
 
 7571 
 
 69-8832 
 
 2-1850 
 
 55-7753 
 
 1-3921 
 
 62-9933 
 
 7756 
 
 70-2113 
 
 2-2059 
 
 56-1034 
 
 1-4083 
 
 63-3214 
 
 1-7941 
 
 70-5394 
 
 2-2264 
 
CENTRIFUGAL VENTILATING MACHINES. 81 
 
 VALUES OF THE THEOEETICAL DEPRESSION (continued). 
 
 Speed in feet of 
 the Periphery 
 per second. 
 
 Theoretical 
 Depression in 
 inches. 
 
 Speed in feet of 
 the Periphery 
 per second. 
 
 Theoretical 
 Depression in 
 inches. 
 
 Speed in feet of 
 the Periphery 
 per second. 
 
 Theoretical 
 Depression in 
 inches. 
 
 70-8674 
 
 2-2472 
 
 85-6325 
 
 3-2811 
 
 100-4055 
 
 4-5098 
 
 71-1955 
 
 2 2681 
 
 85-9596 
 
 3-3062 
 
 100-7336 
 
 4-5394 
 
 71-5236 
 
 2-2890 
 
 86-2877 
 
 3-3315 
 
 101-0617 
 
 4-5693 
 
 71-8529 
 
 2-3098 
 
 86-6158 
 
 3-3567 
 
 101-3898 
 
 4-5988 
 
 72-1798 
 
 2-3305 
 
 86-9439 
 
 3-3822 
 
 101-7079 
 
 4-6287 
 
 72-5079 
 
 2-3518 
 
 87-2719 
 
 3-4079 
 
 102-0360 
 
 4-6589 
 
 72-8360 
 
 2-3736 
 
 87-6000 
 
 3-4335 
 
 102-3641 
 
 4-6880 
 
 73-1641 
 
 2-3953 
 
 87-9281 
 
 3-4594 
 
 102-6912 
 
 4-7179 
 
 73-4922 
 
 2-4165 
 
 88-2569 
 
 3-4854 
 
 103-0203 
 
 4-7488 
 
 73-8203 
 
 2-4381 
 
 88-5843 
 
 3-5104 
 
 103-3484 
 
 4-7791 
 
 74-1483 
 
 2-4598 
 
 88-9124 
 
 3-5368 
 
 103-6764 
 
 4-8094 
 
 74-4764 
 
 2-4819 
 
 89-2405 
 
 3-5574 
 
 104-0045 
 
 4-8401 
 
 74-8045 
 
 2-5039 
 
 89-5686 
 
 3 5838 
 
 104-3326 
 
 4-8705 
 
 75-1326 
 
 2-5256 
 
 89-8967 
 
 3-6101 
 
 104-6607 
 
 4-9012 
 
 75-4607 
 
 2-5480 
 
 90-2248 
 
 3-6365 
 
 104-9888 
 
 4-9319 
 
 75-7888 
 
 2-5701 
 
 90-5528 
 
 3-6629 
 
 105-3169 
 
 4-9630 
 
 76-1169 
 
 2-5925 
 
 90-8809 
 
 3-6897 
 
 105-6450 
 
 4-9941 
 
 76-4450 
 
 2-6150 
 
 91-2090 
 
 3-7164 
 
 105-9731 
 
 5-0248 
 
 76-7732 
 
 2-6373 
 
 91-5371 
 
 3-7432 
 
 106-3012 
 
 5-0563 
 
 77-1012 
 
 2-6598 
 
 91-8652 
 
 3-7699 
 
 106-6293 
 
 5-0868 
 
 77-4292 
 
 2-6827 
 
 92-1933 
 
 3-7971 
 
 106-9573 
 
 5-1189 
 
 77-7573 
 
 2-7055 
 
 92-5214 
 
 3-8204 
 
 107-2854 
 
 5-1504 
 
 78-0854 
 
 2-7277 
 
 92-8495 
 
 3-8514 
 
 107-6135 
 
 5-1819 
 
 78-4135 
 
 2-7506 
 
 93-1776 
 
 3-8786 
 
 107-9416 
 
 5-2134 
 
 78-7416 
 
 2-7744 
 
 93-5056 
 
 3-9056 
 
 108-2697 
 
 5-2453 
 
 79-0697 
 
 2-7955 
 
 93-8337 
 
 3-9398 
 
 108-5978 
 
 5-2772 
 
 79-3978 
 
 2-8209 
 
 94-1618 
 
 3-9673 
 
 108-9259 
 
 5-3090 
 
 79-7259 
 
 2-8441 
 
 94-4899 
 
 3-9933 
 
 109-2540 
 
 5-3409 
 
 80-0540 
 
 2-8677 
 
 94-8180 
 
 4-0228 
 
 109-5821 
 
 5-3729 
 
 80-3831 
 
 2-8909 
 
 95-1461 
 
 4-0508 
 
 109-9101 
 
 5-4051 
 
 80-7101 
 
 2-9146 
 
 95-4742 
 
 4-0787 
 
 110-2382 
 
 5-4378 
 
 81-0382 
 
 2-9386 
 
 95-8023 
 
 4-1067 
 
 110-5663 
 
 5-4700 
 
 81-3663 
 
 2-9623 
 
 96-1304 
 
 4-1350 
 
 110-8944 
 
 5-5018 
 
 81-6944 
 
 2-9862 
 
 96-4585 
 
 4-1630 
 
 111-2225 
 
 5-5350 
 
 82-0225 
 
 3-0081 
 
 96-7865 
 
 4-1917 
 
 111-5506 
 
 5-5677 
 
 82-3506 
 
 3-0342 
 
 97-1146 
 
 4-2201 
 
 111-8787 
 
 5-6008 
 
 82-6787 
 
 3-0586 
 
 97-4427 
 
 4-2484 
 
 112-2068 
 
 5-6334 
 
 83-0068 
 
 3-0831 
 
 97-7708 
 
 4-2772 
 
 112-5349 
 
 5-6665 
 
 83-3349 
 
 3-1074 
 
 98-0989 
 
 4-3053 
 
 112-8630 
 
 5-6996 
 
 83-6630 
 
 3-1313 
 
 98-4270 
 
 4-3346 
 
 113-1919 
 
 5-7327 
 
 83-9910 
 
 3-1567 
 
 98-7551 
 
 4-3638 
 
 113-5491 
 
 5-7661 
 
 84-3191 
 
 3-1811 
 
 99-0832 
 
 4-3939 
 
 113-8472 
 
 5-7996 
 
 84-6472 
 
 3-2059 
 
 99-4113 
 
 4-4220 
 
 114-1753 
 
 5-8331 
 
 84-9753 
 
 3-2311 
 
 99-7384 
 
 4-4512 
 
 114-5034 
 
 5-8659 
 
 85-3034 
 
 3-2599 
 
 100-0775 
 
 4-4807 
 
 
 
 UNIVERSITY 
 
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 On Lathes Turning Tools Turning Wood Drilling Screw Cutting Miscellaneous 
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 Treatise on Watchwork, Past and Present. By the 
 
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 Algebra Self-Taught. By W. P. HIGGS, M.A., 
 
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 Spons Dictionary of Engineering, Civil, Mechanical, 
 
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PUBLISHED BY E. & F. N. SPON. 15 
 
 Notes in Mechanical Engineering. Compiled prin- 
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 Proceedings of the National Conference of Electricians^ 
 
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 CONTENTS: 
 
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 List of Tests (Reagents], arranged in alphabetical 
 
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 EDITED BY ERNEST SPON, MEMB. Soc. ENGINEERS. 
 
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 Indicators, and Slide 
 Rule. 
 
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 and Machinery. 
 
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 Integral. 
 
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 Limes, and Mortar. 
 
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 Washing. 
 
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 Magneto-Electric Ma- 
 chines. 
 
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 Electrical Engineering, 
 Telegraphy, Electric 
 Lighting and its prac- 
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 Engines, Varieties of. 
 
 Explosives. Fans. 
 
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 the practical work of 
 the Foundry. 
 
 Gas, Manufacture of. 
 
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 other Power. 
 
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 tors. 
 
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 Beacons. 
 
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 tion. 
 
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 Processes employed to 
 Dress. 
 
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 WORKSHOP RECEIPTS, 
 
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 BY ERNEST SPON. 
 
 SYNOPSIS OF CONTENTS. 
 
 i Freezing. 
 
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 and Pastes. 
 
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 Oils. 
 
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 Bronzes and Bronzing. 
 
 Candles. 
 
 Cement. 
 
 Cleaning. 
 
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 Concretes. 
 
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 Drawing Office Details. 
 
 Drying Oils. 
 
 Dynamite. 
 
 Electro - Metallurgy 
 
 (Cleaning, Dipping, 
 
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 description). 
 Enamels. 
 Engraving on Wood, 
 
 Copper, Gold, Silver, 
 
 Steel, and Stone. 
 Etching and Aqua Tint. 
 Firework Making 
 
 (Rockets, Stars, Rains, 
 
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 Fluxes. 
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 Stains, Fluxes, Ena- 
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 Scouring. 
 
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 Solders. 
 
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 Taxidermy. 
 
 Tempering Metals. 
 
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 o'-Pearl, and like sub- 
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 and Use of. 
 
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Crown 8vo, cloth, 485 pages, with illustrations, $j. 
 
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 SECOND SERIES. 
 
 BY ROBERT HALDANE. 
 
 SYNOPSIS OF CONTENTS. 
 
 Acidimetry and Alkali- Disinfectants. 
 
 Isinglass. 
 
 metry. 
 
 Dyeing, Staining, and 
 
 Ivory substitutes. 
 
 Albumen. 
 
 Colouring. 
 
 Leather. 
 
 Alcohol . 
 
 Essences. 
 
 Luminous bodies. 
 
 Alkaloids. 
 
 Extracts. 
 
 Magnesia. 
 
 Baking-powders. 
 
 Fireproofing. 
 
 Matches. 
 
 Bitters. 
 
 Gelatine, Glue, and Size. 
 
 Paper. 
 
 Bleaching. 
 
 Glycerine. 
 
 Parchment. 
 
 Boiler Incrustations. 
 
 Gut. 
 
 Perchloric acid. 
 
 Cements and Lutes. 
 
 Hydrogen peroxide. 
 
 Potassium oxalate. 
 
 Cleansing. 
 
 Ink. ' 
 
 Preserving. 
 
 Confectionery. 
 
 Iodine. 
 
 
 Copying. 
 
 lodoform. 
 
 
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 Crown 8vo, cloth, 480 pages, with 183 illustrations, 5^. 
 
 WORKSHOP RECEIPTS, 
 
 THIRD SERIES. 
 
 BY C. G. WARNFORD LOCK. 
 Uniform with the First and Second Series. 
 
 SYNOPSIS OF CONTENTS. 
 
 Alloys. 
 
 Indium. 
 
 Rubidium. 
 
 Aluminium. 
 
 Iridium. 
 
 Ruthenium. 
 
 Antimony. 
 
 Iron and Steel. 
 
 Selenium. 
 
 Barium. 
 
 Lacquers and Lacquering. 
 
 Silver. 
 
 Beryllium. 
 
 Lanthanum. 
 
 Slag. 
 
 Bismuth. 
 
 Lead. 
 
 Sodium. 
 
 Cadmium. 
 
 Lithium. 
 
 Strontium. 
 
 Caesium. 
 
 Lubricants. 
 
 Tantalum. 
 
 Calcium. 
 
 Magnesium. 
 
 Terbium. 
 
 Cerium. 
 
 Manganese. 
 
 Thallium. 
 
 Chromium. 
 
 Mercury. 
 
 Thorium. 
 
 Cobalt. 
 
 Mica. 
 
 Tin. 
 
 Copper. 
 
 Molybdenum. 
 
 Titanium. 
 
 Didymium. 
 
 Nickel. 
 
 Tungsten. 
 
 Electrics. 
 
 Niobium. 
 
 Uranium. 
 
 Enamels and Glazes. 
 
 Osmium. 
 
 Vanadium. 
 
 Erbium. 
 
 Palladium. 
 
 Yttrium. 
 
 Gallium. 
 
 Platinum. 
 
 Zinc. 
 
 Glass. 
 
 Potassium. 
 
 Zirconium. 
 
 Gold. 
 
 Rhodium. 
 
 
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WORKSHOP RECEIPTS, 
 
 FOURTH SERIES, 
 
 DEVOTED MAINLY TO HANDICRAFTS & MECHANICAL SUBJECTS, 
 BY C. G. WARNFORD LOCK. 
 
 250 Illustrations, with Complete Index, and a General Index to the 
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 Leather Polishes. 
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 Musical Instruments the preservation, tuning, and repair of pianos, 
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 Clock and Watch Mending adapted for intelligent amateurs. 
 
 Photography recent development in rapid processes, handy apparatus, 
 numerous recipes for sensitizing and developing solutions, and applica- 
 tions to modern illustrative purposes. 
 
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JUST 
 
 In demy 8vo, cloth, 600 pages, and 1420 Illustrations, 6s. 
 
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 MECHANICS' OWN BOOK; 
 
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 CONTENTS. 
 
 Mechanical Drawing Casting and Founding in Iron, Brass, Bronze, 
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 Soldering, Brazing, and Burning Carpentry and Joinery, embracing 
 descriptions of some 400 Woods, over 200 Illustrations of Tools and 
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 Marble, Metals, and Wood Varnishing Mechanical movements, 
 illustrating contrivances for transmitting motion Turning in Wood 
 and Metals Masonry, embracing Stonework, Brickwork, Terracotta, 
 and Concrete Roofing with Thatch, Tiles, Slates, Felt, Zinc, c. 
 Glazing with and without putty, and lead glazing Plastering and 
 Whitewashing Paper-hanging Gas-fitting Bell-hanging, ordinary 
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 Pavements, and Bridges Hedges, Ditches, and Drains Water 
 Supply and Sanitation Hints on House Construction suited to new 
 countries. 
 
 London: E. & F. N. SPON, 125, Strand. 
 
 New York : 12, Cortlandt Street. 
 
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