1845.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



103 



" 16. For the gudgeons C. The pressure upon tbese will also be 

 uniform =: P, and the resislunce to motion = hi P." 



(15) is wholly vitiated by the same assumption as (12). An addi- 

 tional source of error is the assuming the pressure at B to lie along 

 B C. If this be so, what force thrusts the cylinder out of the vertical i 

 (16) also assumes the pressures at the two ends of B C equal and op- 

 posite, which could only be the case when the rod was at rest. Again, 



" 17. For the crank sha/t A. Making the angle B' A B =: fl, as in 

 Art. i:J, the constant force V upon the crank pin will resolve itself into 

 two, one to turn the crank round, and the other in the direction of the 

 length of the crank, which latter causes the friction upon the crank 

 shaft bearing. 



"While the crank pin is travelling from B' to B", this pressure will 

 be in the direction B A, and at B" it will vanish, and from B" to B'" it 

 will be in the direction of A B. 



This is all totally wrong. The reaction at A is assumed to be along 

 A B, whereas the direction of the pressure is a function of many 

 variables, as we have shewn for a similar case. 



We have not quoted the rest of the investigation. Assumptions, 

 which do not even approximate to the truth, can hardly lead to results 

 worth transcribing. 



" IS. We may now proceed to consider the 



DIRECT ACTION ENGINE, 



as the form shown in fig. 3, (or with the modiCoation as in fig 4,) is 

 generally termed, 



"The friction in this will arise from the strain upon the bearings A, 

 B, and C, and from that upon the guide at G. In each of these cases 

 the strain varies as the engine moves, and each will therefore require 

 the application of the calculus for its solution. 



" Let A B, =: the length of the crank, = r ; and B C, the length of 

 the connecting rod, = /. Let d ^= any angH B' A B described by the 

 crank, beginning from B', and (p = the corresponding angle B' C B. 

 Also let P be the uniform force exerted by the piston rod, and a, b, c, 

 the radii of the gudgeons A, B, C, respectively. 



" 19. For the bearing C. At this joint the pressure P resolves itself 

 into two, one in the direction C G, perpendicular to the resisting sur- 

 face of the guide (= P tan <p), and the other along the connecting rod 



o 

 CB = 



cos^ 

 nsistance from friction will therefore be 



The latter is the pressure upon the gudgeon, and the 



>»P „ 



cos <t> 



The web of error seems here beyond disentanglement. We may 

 however, be safe in saying that the pressure at C does 7Wl — P. Mr. 

 Pole has resolved a force at right angles to its own direction ! 



" 20. For the crank pin B. The pressure upon this gudgeon, and 

 consequently the remta7ice, will be the same as for the last-named, 

 _ otP 



008 ()> 



" While the crank is moving from B' to B", and the angle <p is in- 

 creasing, the differential of the space the rubbing surface moves through 



(cos <fr X 



1+ —====_)(?*; (NoteC.) 



V 



I' 

 aod theiefore the loss in this space 



. -1 r 



«m — - 



and the los3 



^,nPbr (A±+^ ^'^ Y 



"But when the angle 9 comes to decrease, or while the crank moves 

 from B" to B'", the differential is 



^b(l -^l^-_\a^, (NoteD.) 



— — sin ■ 9 



1 On reperiiaal of our remarkt, the error here alluded to appears to be fftT «^o\?2*' 

 " the gem ol' the collection.'* We once thoupht that many of Mr, Pole's errors arose iioin 

 his belierin^ by some Btranga halluctnatiou that he was discussing a statical instead of a 

 dyoamlcal problem. But the resolution of a force at right angles to Us length is rereruble 

 to no lystem of eitber sUtlcs or dynamlca wUii wblcb ita 4re acnuaioteU. 



= ,nPbr" (^ ^^= ) 



-1 r 



" NOTES." 



" (C.) Art. 20. Let fl, ip, r, I, b, be as in the text, and produce the 

 line C B to 6. Then the space the rubbing surface will have passed 

 througli during the motion of the crank from B' to B, will be =: 



6 X angle 6 B A. But 6 B A = (<p -f 9) and sin 6 =— sin <p. 



T 



/ . -w . \ 



.•. spacers 61 (/)-}- sm —sin 9 I 



and 



i. space = 6 I (^V-t- 



4 



. -1 I 



sm- <f> 



f9^ . 



"(D.) Idem. Beyond B",fl=7r — sin — sin <|>, therefore the second 



r 

 term of the differential changes its sign." 



Hero the impressed forces are equated without the effective, in 

 violation of D'Alembert's principle; secondly, the pressure is assumed 

 to lie along B C, in which case there would be no force to thrust it out 

 of the vertical. But we have quoted the above principally on account 

 of the notes. From note C it would seem that the geometrical con- 

 siderations of this paper are not conceived in a happier spirit than 

 the mechanical principles. We would humbly submit that if the 

 pressure lie along BC, the rubbing surface will move through a semi- 

 circle for a semi-revolution of the crank. When the crank is in its 

 lowest position A B', the highest point of the circular pivot presses 

 on the highest of the hole in which it works; when the crank is in its 

 highest position, the highest point of the pivot presses on what was 

 at fiist the lowist of the hole. Therefore, as the pressure is continuous, 

 the rubbing surface has described an angle = ir. It is remarkable 

 that in the exactly analagous case at (15) this error has not been 

 made. 



We omit several of the following articles ; not because they afford 

 no materials for comment — on the contrary they are every one erroneous 

 — but because they repeat errors which we have already exposed. The 

 last quotation we shall make is from (24), where the direct action 

 engine continues to be spoken of. After a totally ftiUacious investi- 

 gation of the friction against the guide, it is added : — 



" 23. In fig. 4, a friction roller is added to the preceding arrange- 

 ment, which causes the motion against the guides to be a rolling instead 

 of a sliditig one. The friction from the tolling will be very small if 

 the suifaces be hard and well faced, and may be neglected altogether. 

 That from the rubbing of the axle in its bearings will be to the amount 

 in the last Article as the radius of the axle is to that of the roller. 

 Let the former = v, and the latter = 11, then the friction will be, &c." 

 Here, again, all is wrong, the diminution of friction will not be in 

 proportion to the radii of the axle and roller only. The rubbing space 

 will be diminished in proportion to the radii, and the leverage 

 will be increased in such proportion to the radii. So, according to Mr. 

 Pole's own plan of making the total resistance equal to the friction mul- 

 tiplied by the rubbing space, the two frictions here will be as the 

 squares of their radii. If the radius of the axle be i that of the roller, 

 its friction will be -^ that of the roller — Mr. Pole would make it 1 : a 

 slight discrepancy truly. 



We shall not make any further extracts, because most of the subse- 

 quent errors seem to be of the same nature as those which we have al- 

 ready examined ; and we wish to be as brief as possible. We can, how- 

 ever, state circumspectly and with perfect confidence that in every para- 

 graph one or more of these errors occur. Had one single article been 

 tree from them we would have gladly quoted it here, in contrast to those 

 reviewed above. But, however ungracious may be the task of dwelling 

 on errors, we are compelled, after a careful examination of every para- 

 graph, to declare that not one approximates even in the remotest degree 

 to the truth. 



It will be observed that the errors which we here exhibit, arise, evea 

 if we admit that the considerations entertained by Mr. Pole are all 

 that affect the case. But there are two circumstance which power- 

 fully influence the question which we wish to mention, as no notice of 

 them has been taken in this paper. 



First, it was premised by Mr. Pole that he should omit all consi- 

 deration of friction arising Irom the tight working of joints. 

 Now if the cylindrical hole of a joint presses the axle on all 



