170 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[ J U N I 



corruption of the angular capilals of tlie temiile of Minerva I'ulias — is 

 one of the worst and the raost impure thai he could huve selected ; the 

 modillions do not belong to the order, and approach loo nearly to those of 

 the Corinthian. If one order upon another be ever admissible, the Co- 

 rinthian should mt ha>e been excluded for the purpose of introducing the 

 Composite. 



ON THE SCREW PROPELLER. 



In the f )llowing paper we propose to examine theoretically the beat 

 angle for the worm of the screw-propeller — taking for granted the theo- 

 retical forniultB for the resistance of fluids. At some future opportunity, 

 we propose to investigate the problem in a more practical manner, and to 

 supply conditions for the best form of the screw it.-^elf, with reference to 

 strcDgth and useful effect. 



L 



A I 



•B/^ 



ei/ 



Let BE D be a small plane rectangular lamina of rigid matter, attached 

 by means of a rigid rod A IJ, without weight, to an axis A L, which is 

 horizontal, and about which the rod A B can revolve in a vertical plane- 

 Let the rod A B be in the plane E B D and perpendicular to the sideE C D ; 

 also, let the small lamina E B D make an / 8 with the vertical plane 

 in which A B rotates ; and let the area of the plane E B D = fc. 



If the axis A L be fixed to a vessel floating in WHter or any other 

 fluid, and the point A be at such a depth below the surface that E B D 

 will always be in the fluid, and A B be made to revolve rapidly in the 

 direction C(/,— the resistance of the fluid upon BED, resolved iu a 

 direction parallel to A L, will cause the vessel to move in the direction A L. 

 Now, the worm of a screw, having A L for its axis (the plane of any 

 element of the worm being supposed to contain the line A B), may be 

 supposed to be made up of an infinite number of small elements, similar 

 to E B D. The rotation of such a screw would, therefore, cause the ves- 

 sel to move through the water. If the propulsion were caused not by one 

 unbroken worm, but by several portions of the same worm, symmetrically 

 and oppositely disposed about the axis, the resolved parts of the resist- 

 ances perpendicular to the axis will destroy each other, and the motion of 

 the vessel will be steady and in a straight line. M'lieu the vessel is moving 

 with an uniform velocity, the resistance of the water to its motion will 

 exactly equal the resistance to the screw, resolved in the same direction ; 

 and the sum of the moments of these two resistances about the centre of 

 gravity of the vessel will be zero. 



To return to the consideration of the single element E B D, supposing 

 the vessel moved has a velocity », and the resistance to its motion is R, let 

 us determine the value of the Z 9, when the amount of moving power 

 expended is a minimum. Let p be the density of the fluid ; r = distance 

 -A B ; m the angular velocity of E B D. Let Fr be the moment of the 

 pressure about A L, E B D exerts when moving with an angular velocity 



Fr 

 1 ; then, if the moving power be constant, — 'will be the moment of the 



pressure exerted by E B D when moving with an angular velocity m. 

 Consequently, the resolved part of the velocity of E B D perpendicular 

 to E B D is (in r sin. B — r cos. 6); and the resistance against E B D 

 J p At ^ m r sin. $ — v cos. 6 J.- ; B C being supposed indefinitely short com- 

 pared with A B. 

 The resolved part of the resistance parallel to A L is 



J p fc I m r sin. — i- cos. 6 \ - cos. 9 = R, 



siBce I), the velocity of the vessel, is by hypothesis uniform. Also, since 

 the motion of A B is uniform, 



Fr 

 Jpfc |mr6in. 9 — v cos. 9|=. sin. 9 x r = — ; 



Km 



■ F ■ 



cot. 9 : 



• . m = -- cot ( 

 H 



* We here suppose that no part of the power of the engiae is ezpended in overcoming 

 Mk friction and resistance to motion of its several parts. 



. • . J p. fc. { 1{ . COS. 9 — f COS. 9 } ' . cos. 9 =: R ; 



.■.Fr = Rr + ^^-^^^_3. 



In this expression, it is clear that F is least when cos. 9 is greatest— that 

 is, when cos. 9=1, aud . • . m = Q- The interpretation of this appar- 

 ently paradoxical result shows that the smaller the augle of the worm of 

 the screw, the less is the power lust iu transferring motion to the vessel. 

 There are, however, certain practical considerations which cannot be ne- 

 glected in delcrmiMing^he best value for 9 In the first place, we have 

 supposed the lamina E tJ D to be indefinitely ihiu, and that all the resist- 

 ance is perpendicular to E B I) ; this, in practice, is not the case : — the 

 resistance against E B D being very cousiderable, it follows that — in order 

 for the material connection of E B D with A L not to be destroyed by so 

 great a strain— E B D must he of appreciable thickness. 



Let the area of edge of E C B = /i ; then neglecting the eflect of the 

 mass of E B D and its weight, we should have trie following equations ; 

 ipk ^7nr sin. 9— i^ cos. 9 j. = cos. 9— \pli /mrcos.9 + i- sin. 9}= sin. 9= R 



f 1 F 



and, JpA-|mrsiu 9— f cos. 9}'- sin. 9 + Jp/i (inr cos. 9 + r sin. 9)- cos. 9 =- 



In these expressions we find that R is diminished, while F is increased ; 

 consequently, there is a double loss of power. F must be increased to 

 balance a resistance which not only dues not accelerate, but actually re- 

 tards, the motion. Also, the new terms introduced rapidly increase by 

 diminishing 9 : a value of 9 = 20" would probably make F nearly a mini- 

 mum. 



The whole theory of resistances is, however, so little to be depended 

 upon, that the results we have obtained can only be regarded as a rough 

 method uf approximating to the truth. In a futuie number of the Journal 

 we hope to be able to continue the subject, founding our investigations on 

 data of observation and experiment. 



[In the number for April, in the article " On the Motion of Fluids," 

 p. 9S, for •' the equal number for v," — read, " the equations for ti ;" and , 

 p. U8, col. 2, for the •' mean vertical velocity of the particles," — read " the 

 mean velocity of the particles in direction of the tube."] 



SEWAGE .\ND DRAINAGE. 



Since our last number, we have seen with the deepest regret, that the Go- 

 vernment have agreed to leave out from their sanitary measures for the pre- 

 sent year the metropolitan districts. It is most painful to (effect that two 

 millions are left exposed to the evils of a mo^t ineflicient system of sanitary 

 administration, at a time vihea the scarcity of food is sure to produce severe 

 disease, and when there is every likelihood of the .\siatic cholera spreading 

 through Europe to this country. 



If there be one fact that admits of no doubt in the public mind, and of no 

 doubt in the minds of any but aldermen and commissioners of sewers, it is 

 that the sanitary administration of the metropolis is most shamefully mis- 

 conducted, while it is imperative that the adniinistraticn should be concen- 

 trated and carried on with vigour. Whatever superiority we may have over 

 other countries in such matters, it is nevertheless true that we are miserably 

 behindhand, so far as our own enliglitenment is concerned. We want no 

 facts to prove this beyond the experience of every individual, though the re- 

 ports of the Registrar-General and of the officers of severs are convincing. 



One great good we expect from the abolition of the present .'■ystem — or no 

 system — is full scope for the exertions of able and intelligent engineers and 

 surveyors. Indeed, it is by such only that any amendment has been etfected, 

 as the labours of Mr. Roe, in the Finsbury Division, and lately of Mr. 

 Phillips, in the Westminster Division, fully show. We have now before us a 

 report of the latter gentleman, to which we shall direct attention in prefer- 

 ence to any other branch of evidence. 



This report is produced in pursuance of an order of the commissioners of 

 sewers, on the 1st May, 1840, and ordered to be printed 16th April last, 

 to ascertain the condition of a part of the eastern division of the sewers 

 north of Oxford-street, and east of Portland-place and Regent-street. This 

 district (called .\ll Souls) contains an area of about 130 acres, with a popu- 

 lation of 27,000 persons residing in 3000 tenements. The density of the po- 

 pulation is not great, considering the extent of the district and the number 

 of houses inhabited — being on an average nine persons to each house. Mr. 



