18-lS.] 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL 



337 



To Rive some idea of tlie ni;inner in wliicli the miitbemntitMl c.ilcu- 

 lition of tlie newer exerted bv each stroke is ni;icl.-, we will take a 

 particular instance. We will suppose that at tl.e beginning of a cer- 

 tain stroke the exhaustion has been carried to siicli a point that the 

 pressure ofthe ail- in the main is lOlbs. to the inch, that is, the density 

 is two-thirds of that of the ext.-rnal air. We have then, on tlie 

 starling of the piston, a pressure of lOlbs. per inch in the direction of 

 "its motion in its favour ; in other words, the same amount of pressure 

 *.xists on the other side of the piston ; but it will be observed on ex- 

 amining the construction of the pump, that this latter pressure con- 

 stantly increases till it is equal to the external atmospheric pressure. 

 For the elTect of the motion of the piston is to compress the air in the 

 Dump till the valve C (or the valve V) open, that is, till the density in 

 the pump slightly exceeds that of the external air. Now, we suppose 

 the exhaustion has been can ied to two-thirds; it is clear then that 

 the compression we are speaking of r.quires that the piston perform 

 one-third of llie stroke. Wlien tlie piston is advanced thus far, the 

 air which before occupied the whole pump occupies only two thirds 

 of it ; and, therefore, the pressure in the pump is increased from lOlbs. 

 to 1 Jlbs., and the external valve begins to rise. It will be seen then, the 

 pressure resisting motion gradually increases up to a certain point, 

 and then remains constant. Now if we take the average of the first 

 pressure, and multiply it by the number of inches equal to one-third 

 the stroke, and add tlie pressure of 151bs. muliiplied by two-thirds the 

 stroke, we get tlie power exerted against the piston in terms of lib. 

 moved through so many inches. And if we'taketlie average pressure 

 on the other side of the piston, multiply it by the whole length of the 

 stroke, and subtract this product from the first, we clearly h .ve the 

 total work actu illy performed during the stroke. 



This is in effect done in the analytical calculation for each stroke ; 

 the amounts of work done during each stroke, addid together, give 

 the whole work done to effectllie preliminary exhaustion. It is found 

 that this total power is equivalent to lib. moved through 15,047,068 

 inches. 



In the second part of the calculation the train-piston is supposed 

 to have started, and in order that the degree of exhaustion may re- 

 main unchanged in the main, it is clear lliat for every cubic inch of 

 air pumped out the train-piston describes one cubic inch of space. 

 The averages are here taken as before to ascertain the work done by 

 the pump during the passage of the train. This is add 'd to the pre- 

 liminary work ; the useful effect or pressure on the train-piston mul- 

 tiplied by the distance traversed, and the preponderance, is, as has 

 been stated, one-third of the whole. According to experiments 

 actually made by Mr. Samuda and Mr. Stephenson, and published in 

 the last number of this Journal, the actual loss of power averages 8 J 

 per cent. It will be seen then from the above what proportion of the 

 loss is due to friction and leakage. 



n. C. 



REVIEW. 



Ekmenh of Physics. By C. F. Peschel, Principal of the Royal 

 Military College at Dresden, &e. Translated from the German, 

 with Notes, by E. West. Illustrated «itli Diagrams and Woodcuts. 

 London: Longman & Co., Paternoster-row. 1845. 

 There has been long wanted a manual of jihvsics, whicli should 

 . embrace something more than a mere detail of the facts of science, 

 although arranged in a systematic order, and yet d.stiuct from the 

 purely mathematical treatises which have at different times emanated 

 from the universities. The study of physics haa become of late a 

 VI TV important branch of education, arising from the practical appli- 

 cation of scientific principals in the details of almost every department 

 of manufacturing and agricultural industry. To civil engineers, ar- 

 chitects, surveyors, &c., a knowledge of physics is of the first import- 

 ance, and yet their ideas on scientific sulijects frtqueiitly displ.iy 

 incertitude and inexactness, which we think are traceable to the want 

 of sound mathematical knowledge. Practical men, generally, do not 

 feel disposed to subject themselves to the preparatory amount of 

 preparatory mental labour, which the acquisition of even the elenn'n- 

 tary mathematics implies; they imagine the toil ni ly be avoideil and 

 a sufficient acquaintance with science obtained from the study of 

 popular treatises. Wirks of this nature may do well enough for the 

 mere schoolboy tyro, but are totally inadequate for the education of a 

 scientific-praciical man. Scientific knowledge to be available must 

 be based on mathematics and chemistry. We are happy to see that 

 the jealousy wliicli once in no small degree existed between practical 

 and theoretical men, is now fast disappearing. The practical man 

 begins to see that Iheoreticd knowledge is not visionary knov^ ledge, 



and the theorist finds that his specul.itions, to produce any beiielicial 

 results, must be combined with the experience of practice. 



We have a large number of treatises of natur.d philosophy in our 

 langu.ige, but none which handles the subject both mathematically 

 and popularly. In this respect we are fir behind our continental neigh- 

 bours, whose works on science are models of simplicity and elegance. 

 Among the best works on natural philosophy recently published in 

 (ierrnanv, is Peschel's Elements of Phvsics; it is divided into twi 

 divisions : the first division treats on the physics of ponderable bodi's, 

 the second on the physics of imponderable bodies. The former is 

 the only part as yet translated. The first two sections contain a de- 

 scription of the properties of inaleri.ils, and of physical forces in 

 general, embracing molecnl.ir attraction and gravitation. This part is 

 illustrated by a variety of apposite experiuicnls. The laws of motion 

 and a sketch of the modern doctrines ol chemistry follow. The third 

 section is taken up with the properties of solid bodies, including the 

 pendulum, the elements of machinery, and friction. The theorems in 

 this section are clearly and satisfactorily proved, and contain besides 

 a great number of numerical illustrations, which practical men will 

 lind verv useful. The remaiidng sections contain the doctrine of 

 non-tHastiu and elastic fluids, vibrations, and acoustics, all of which are 

 most luminously and perspicuously treated. The translator has shown 

 good judgment in substituting the methods of Baily and Littrow for 

 determining the b.irometric measurements of altitudes in the place of 

 the author's, which is both long and intricate. 



The following extract gives a good general view of a subject 

 most important to the engineer— the strength of materials. 



" In consequence of its great tenacity, iron is the most important metal, 

 in a technical point of view. According to Tredgold's and Dulean's ex- 

 periments, a piece of the best bar iron I square inch across the end would 

 bear a weight of about 77,373 lb., while a similar piece of cast-iron would 

 he torn asunder by a weij;ht of from 16,213 to 19,46t lb. It is worthy of 

 remark, that thin iron wires, arranged parallel to each other, and present- 

 ing a surface at their cxtreudtj of 1 square inch, will carry a mean weiglil 

 of 120,340 lb. 



• All wood of the same name, however, is not of uniform strength ; for 

 such trees as grow in mouDtainuns districts are, in ihis respect, inucli supe- 

 rior to those which grow in a champaign country ; and in the same indi- 

 vidual there exists a great diirereiice in the trunk, branches, and roots. A 

 piece of well-dried pine-wood {Piiiiis sylL-estfis), presenting a section of I 

 sipiarc inch, is able, according to Ejleliveio, to support a weight of from 

 15,046 lb. to 20,408 lb., whilst a similar piece of oak will carry as much as 

 25,8.'J0 lb. 



" Theoretical investigations and actual experiments alike lead to this 

 result, that in a parallelopipedou of uniform thickness, supported ou two 

 points and loaded in the middle, the luteriU strength is directly as the pm- 

 duct of the breadth into the square of the depth, and inversely as the length. 

 Let \V represent the lateral strength of any material, estimated by the 

 weight, h the breadth, and d the de|ith of its end, and I the distance be- 

 tween the points of support ; then W =zfd'b-^l. 



" If tlie parallelopipedou be fastened only at one end in a horizontal 

 position, and the load be applied at the opposite end, W =fd''b-i-H. 



" It is to be observed that the three dimensions, d, A, and (, are to be 

 taken in the same measure, and tiwi h be so great that no lateral curvature 

 arise from the weight ;/ in each formula represents the lateral strength, 

 wliich varies in dillerent materials, and whicli must be learnt experiment- 

 ally. 



" A beam having a rectangular end, whose breadth is two or three times 

 greater than the breadth of another beam, has a power of suspension re- 

 spectively two or Ihree times greater than it; if the end be two or three 

 times deeper than the end of the other, the suspension power of that 

 which has ihe greater depth exceeds the suspension power of ihe other four 

 or nine times : if its length be two or three times greater than the length of 

 auolher beam, its power of su'-pension will be j or j respectively that of the 

 oiher; provided that in each case the mode of suspension, the position of 

 the weight, and other circumstances be similar. Hence it follows that a 

 beam, one of whose sides la|iers, has a greater power of suspension if 

 placed on the slant than on the broad side, and that the powers of suspen- 

 sion in both cases are in the ratio of their sides ; so, for instance, a beam, 

 one of whose sides is double tlie widlh of the other, will carry twice as 

 much if placed on the narrow si<le, as it would if laid on the wide one. — 

 Ajiplication in the beams of ships' decks, shoring houses, &c. 



" In a piece of round timber (a cylinder) the power of suspension is in 

 proportion to the diamelers cubed, and inversely as the length ; thus, .i 

 beam with a diameter two or three times longer than that of another, will 

 carry a weight 8 or 27 times heavier respectively than that whose diameter 

 is unity, Ihe mode of fastening and loading it being similar in both cases. 



" The lateral strength of square limber is to that of the tree whence it is 

 hewn as 10 : 10 nearly. 



'I'iie laieral strength of a beam supported at both ends, whatever be 

 Ihe stction it presents, is least when Ihe whole weight acts at the middle, 

 and greatest when placed near the ends ; hence the rule that considerable 

 weiglits are to be placed not in the middle but near the ends of Iheir sup- 

 ports, liy an equal distribution of the load over the entire length of the 

 timber, it can be made to bear twice at great a weight as it would ha\e 



