1847.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



195 



" Now, each cabic foot of water converted iuto steam exists in the cylin- 

 der before expansion begins under a pressure/;,, it therefore occupies a rela- 

 tive space by Equation (e), represented by 



1 

 « = — 



" Now, the number of cubic feet of water which is evaporated in the 

 boiler, and passes into the cylinder at every stroke of the engine in the form 



of Steam, is represented by -j^ ; therefore the space occupied in cubic feet in 



the cylinder when the valve is closed and expansion begins will bo repre- 



E/ 1 \ 

 aented by t-, i — - I ." 



There is an insuperable objection to any measure of the duty 

 of the engine, as estimated by tlie quantity of water diminished in 

 the boiler in a given time ; ;ind that is, that all tlie water removed is 

 not evaporated. In fact, a large portion of water, called " priming" 

 by engineers, is conveyed from the boiler into the cylinders in a state 

 of fine particles, possessed of no elastic force whatever. The propor- 

 tion which this bears to the amount evaporated seems to depend on 

 the violence of the ebullition and the form of the throttle pipe. Sub- 

 stances which have a tendency to modify the action of the boiling 

 water, such as butter or potato parings, likewise affect the quantity 

 of priming; and in tubular boilers the priming is found to be great- 

 est when tlie extent or firj-surfaee is greatest. All these disturbing 

 causes, which it is impossible to contemplate in theory, render uncer- 

 tain any formulEe for the work done bv the engine as deduced from tlie 

 decrease of water in the boiler. In p. Gi.ou the crank, the proof 

 given by Woolhouse, that the pow-er multiplied by the space which it 

 passes over is equal to the weight or resistance multiplied by the 

 space which it passes over, evidently assumes that the mass of the 

 connecting rod may be neglected, otherwise the proof would be incor- 

 rect. Mr. Woolhouse, as quoted by Mr. Hann, assumes that the pres- 

 sure against the crank is the resolved part of the pressure applied at 

 the lower end of the connecting rod. The following is a more accu- 

 rate investigation: — 



Let the length of the connecting rod =: r; the radius of the crank 

 =rp; and e and (p the angles they make respectively with a vertical 

 through the centre of the crank at time ;. Let this vertical be taken 

 for the axis of x. Let xy be the condinates of the centre of gravity 

 of rod at time t\ the origin, that point in the vertical which coincides 

 with the lower end of the rod when 8 = (|> = o; X, Y, reactions be- 

 tween rod and radius of crank parallel to the axes of x and y; m^ 

 mass of rod{ and X', Y', the pressures at lower end of rod parallel 

 X, y : then, 



a; = P (1 — cos (p) + s '^°^ *• 



y — ssinfl; 



also, r sin 9=: p sin ip. These are the geometrical relations 

 For the mechanical we have — 



^Jl2- -niS + X'-y.^ 



dt- 



y 



— Y'-Y 



IF 



d^ 

 dt' 



= (X + X') ~ 



(Y + Y')^C0S9; 



X=p(l 



{'-V 



-COS <t>) + ^ cos 9 := 



+ \ 



COS e. 



From these equations, X', Y', and Y can be obtained in terms of X, e' 

 also, since sin = ^ sin <f>, 9 and its differential cO' 



given, ^ 



!-«. and ^-11., 

 dl di^' 



efficients depend only on <p and its differential co-efficients; 



therefore, if the angular velocity of the radius of the crank be 



(2<P . . . • ■ de d-e . 



IS given, and ,p is given; ••• 6 j^ and jy^ a'e given. 



and .• . X', Y', and Y are known. When, however, m = o, X = X', 

 Y =: Y', X sin 9 - Y cos 9 =: o, — and Mr. Woolhouse's solution is 

 correct. 



We must here conclude our notice of Mr. Hann's treatise — Part L 

 We hope that before long. Part IL will make its appearance, and that 

 the author will be enabled to continue, without interruption, his useful 

 labours, which are alike honourable to himself and to the collegiate 

 body of which he is so distinguished a member. 



Practical Rules/or Ascertaining tlie Relations between the Alterations 

 in Gradients, and the Corresponding Changes in the Contents. By 

 Demzil J. H. Ibbetson, civil engineer. London: Weale. 8vo. 

 pp. 24. 



To the engineer and surveyor, the object of this little work will be 

 sufficiently obvious from its title. The increase or diminution of 

 earthwork on railways consequent on the alteration of gradients, is 

 here calculated on the supposition that the altered gradient is para'llel 

 to the original gradient. It is important to observe that the calcula- 

 tions are based on this hypothesis exclusively, because they are appli- 

 cable to no other. The case taken is a very unpractical one, and of 

 so rare occurrence, and so simple, that it is a very insufficient excuse 

 for rushing into print. Where gradients are altered at all, it is usually 

 their inclination which is subjected to the alteration. Our author at 

 page 11, gives incidentally a hint for modifying his furniulEe'to 

 these more general cases ; but the method is unsatisfactory and uncer- 

 tain — instances might be suggested in which it would give results which 

 were the exact reverse of the truth; that is, results which represented 

 the earthwork to be increased, where it was in reality diminished by 

 the alteration of the gradient; and conversely. 



Mr. Ibbetsou's formulce do not suppose the cross section to be known: 

 they depend on theinclinationof the slopes, butnotontheircomparative 

 height on opposite sides of the railway. No distinction is made be- 

 tween a cutting through a hill and one round it; and no special rules 

 are given for sidelong ground or open cutting. It is quite clear that 

 such a rough method of proceeding could never be permitted in 

 making the earthwork for ii'urkiiig or contract estimates. In these, 

 considerable accuracy is imperatively required, and can be ensured 

 by no method but that of taking out the quantities from the crosssection. 



For parliamentary purposes less accuracy is wanted. In the pre- 

 liminary investigations the distinction between equal cutting and side- 

 long ground, is considered unnecessary. Here then, perhaps, the pro- 

 posed method might sometimes apply. But, unfortunately, the very 

 cause (laxity of investigation) which would palliate the inaccuracies of 

 the method, at the same time excludes its comparatively inconsiderable 

 results. The results of Mr. Ibbetsou's formulce then would generally 

 be too minute for parliamentary purposes, and too inexact foi the pur- 

 poses of the contractor. 



However, the methods appear to be in themselves neat and simple 

 enough. The propositions are stated in that precise language which 

 always argues well for the correctness of them. There seems every 

 reason to suppose that if Mr. Ibbetson would write another book on the 

 practical cases of alteration of gradients, and confine himself to ob- 

 jects of practical utility, the result would be successfully obtained. 

 There are no diagrams or demonstrations in his treatise. Against this 

 method of giving mere recipes in the cookery-book fashion we always 

 protest. But he has taken up new ground, and one in which a quali- 

 fied labourer is much wanted; — if he will permit the above suggestions 

 to weigh witii him, he may gain the credit of having effected a 

 work, which though of great value and importance, has been hitherto 

 unattempted. 



yi Proposed System for the 'more ready and correct Valuation 

 of Carpenters' and Joiners' Works. By Henry B. Browning. 

 London: Weale. 



Though this work of Mr. Browning's is founded on Peter Nichol- 

 son's system, yet he has carried it out in a new way, and instead of 

 the labour employed, he proposes to calculate the quantities of mate- 

 rials used, and to give the elements of valuation in such minuteness, 

 as to enable the builder to calculate them in detail. For this attempt, 

 Mr. Browning deserves particular praise, for he has evidently taken 

 conscientious pains in getting up his work, and bestowed great labour 

 upon it; but we doubt whether the work will be extensively used by 

 practical men, for whom the Builders' Price Books are found to con- 

 tain more conveniently the information they want. The mode of 

 calculating each part is carefully shown by Mr. Browning, and tables 

 and forms are given with each example. In calculating the material 

 for joiners' work, the several thicknesses are all reduced to a standard 

 thickness of one inch, and then multiplied by the value of the inch 

 deal. Thus, according to the price of inch deal, the price of mate- 

 rials will be determined. Mr. Browning does not, however, in the 

 case of joiners' work, give the value of labour and nails, though, in 

 the case of carpenters' work, he gives new tables, instead of the usual 

 estimates. 



While we award great praise to Mr. Browning, we must observe, 

 that so far as experienced surveyors are concerned, the same minute- 

 ness of calculations is employed ; but the reason why builders gene- 

 rally do not apply it, is, not from want of appreciation of its value, 



