1840.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



21 



CALCULATING BALANCE FOR ENGINEERS. 



BY M. I.KO LALANNE, C. E. 



(Tramlakdfiom the French.) 



It is often necessary to multiply by each other the terms of two se- 

 ries, and to iliviile tlie sum of tlie products l}y tlie sum of one of llie 

 series. Tllis calculution, wjiicli gives a kind of mean, is that used to 

 iind the centre of gravity, to determine certain prohabilities, and to 

 solve various questions, which occur in all the mathematical and phy- 

 sical sciences. M. Lalanne has conceived the idea of jierformiiig this 

 operation by means of a kind of Roman balance loaded witli different 

 weights, and on which the quotients required can be reailnrt'ona 

 scale, and obtained with that degree of approximation which allows 

 the representations of numbers by distances and weights. 



The plan of tliis machine is' formed on the following considera- 

 tions : — If we distribute on one of the arms of a balance weight, which 

 are proportional to the terms of a series, and if we place them at 

 distances from the point of suspension, which represent the terms of a 

 second series, if on the second arm of the balance we suspend an equal 

 weight to the sum of the weights already placed on the first arm, it is 

 clear that the distance at which this total weight nuist be made to act 

 for the equilibrium, will be the sum of the products of the op- 

 posed weights, multiplied respectively by their distances from the 

 axis, and divided by the sum of the weights. So nuich the more ex- 

 actness will be obtained in this result if the weights and tlistances are 

 more exactly proportional to the terms of the two series which are 

 to be operated upon, and iis the balance is made more sensible. 



M. Lalanne intends his instrument principally to assist engineers in 

 calc\ilating the mean distances of transports. We know that in these 

 calculations we must take the sum of the products of the cubes to be 

 transported by the distances which correspond to them, and divide 

 the sum of these products by the total cube. If, then, we take 

 weights which represent partial cubes, and if we place them on one of 

 the arms of the balance, at distances which represent those of the 

 transports ; if, at the same lime, we place a partial weight on one side 

 of the balance, an equal one is placed in a scale suspended from a very 

 precise point of the other arm, and this point may be moved about 

 until equilibrium is effected, its distance from the axis of suspension 

 will represent the mean distance sought. 



In M. Lalanne's balance, the upper part of the beam is divided into 

 150 compartments, each two millimetres broad ; upon it are placed 

 the weights — the distances thus taken from a hundred and liftieth 

 part nearly up to (JUU metres. The volumes are represented by tlie 

 weight, a cubic metre answering to five milligrammes, a total of 2U,0()U 

 cubic metres, may easily be operated upon witli the approximation of 

 one of these units. 



An experiment was made on the comparative duration of the times 

 necessary to obtain a mean by this instrument, and also by ordinary 

 arithmetical calculation — a calculation which required fifty minutes 

 to execute once without verification, was done by the machine in 

 twenty minutes, with only the chance of a very slight error. Thus the 

 time necessary is reduced at least by two fifths, giving besides a security 

 against great errors, and it would be reduced to a quarter if the ordi- 

 nary arithmetical calculations had been verified. Although the in- 

 strument can only give an approximation, and as in all grapliic oper- 

 ations, we have not the exact figure of the result, nevertheless the 

 saving of time is great enough to show the utility of it to engineers. 



BALISTIC CLOCKS, 



FOR ASCERTAINING THE POWER OF GUNl'OWDER. 



( Translakdfrom the Fniich.) 



These clocks were constructed in 1S3(), in the Arsenal of Metz, 

 the Woolwich of France, by Messieurs Piobert and Morin, and from 

 the nature of the experiments made with them, were formed so as to 

 fulfil the following conditions: — 



1st The suspension of the cannon clock must be susceptible of 

 receiving easily and at little expense, cannons and howitzers of every 

 calibre. 



2nd The machine must be sufficiently light for its susceptibility to 

 be great enough for small calibres, and small charges, and ne- 

 vertlicless the recoils must not exceed certain limits in heavy 

 charges. 



3rd The balistic receiver must be susceptible of receiving without 

 injury, the shock of projectiles of all calibres, propelled with the 

 greatest speed that powder can communicate to them, and be entirely 

 constructed of metal to avoid tlie effects of hygrometricitv and the 

 corrections which it necessitates for wooden clocks. 



4th The mechanical requisite of having the centres of oscillation 

 on the line of fin' being absolutely necessary for all calibres, required 

 easy means of effecting it. 



The detailed reasons which led the inventors to adopt forms almost 

 totally different from those of the old productions of Huttou, and th(jse 

 which had been estal)lished at the powder factory of Esquerdes, have 

 been already published by them. 



From a summary description of the apparatus, M. Morin shows, by 

 the results of experiments conducted by Captain Didion, Professor at 

 the School of Application at Met/,, how great is tlie accuracy of these 

 instruments. Thus, in the fire of asixteen-pounder, (about eighteen 

 English,) loaded with a charge of 41b. Coz., of four shots fired with 

 charges prepared with care, the speed given to the ball did not differ 

 more than 2 feet 7in, ^ of its mean value, 4l)2-7 metres. 



Among other remarkable experiments, these instruments have been 

 used by M. Didion to determine in an accurate manner the charge of 

 powder, beyond which the velocity ceases to increase in 12-povmdeis 

 (French), and which more than l7ilb., that is to say, much more than 

 the weight of the ball. 



Besides, this extraordinary fire, the same apparatus has been used to 

 measure results much superior, since by their means have been ascer- 

 tained velocities of (KJO metres in a second, communicated by particular 

 powder to a 24 pounder shot. 



In fine, by firing with a 12-pounder garrison gun, common shells of 

 12 inch calibre, weighing 4.U10 kil., with a charge of (i kil., they ob- 

 tained a velocity of 74j'3metres in a second, which is the greatest that 

 man has ever yet been able to communicate to moveable bodies. 



The machines have satisfactorily answered the purposes for whicli 

 they were intended, so that the Minister of War has had others made, 

 which have just been set up at the powder works of Bouchet, near 

 x\rpajon, and he has ordered a third set for that of Toulouse. 



In conclusion, the principle, and general arrangement, of these clocks 

 has been applied by M. Morin to the construction of a wooden clock, 

 of which the receiver closed with a wooden Ixirrel, five feet diameter, 

 will receive the shock of a projectile fired at variable distances of 

 5U, 100, or l.'iO yards to determine the effects of the resistance of the 

 air. These experiments are already in course of operation by Cap- 

 tain Didion, at Met/., and they afford positive data, and the bases of 

 experimental balistics, so necessary for artillery practice. 



PENZANCE HARBOUR. 



Ez tracts from tlie Report on the improvement of the Harbour of Penzance, by 

 Henry R. Palmer, F.R.S. 



Gkntlkmen, — In obedience to llic instnictiou of the Town Council, given 

 to me throagli ticorge IJ. John, Esq., the Town Clerk, I have endeavoured, 

 as far as lay in my power, to acciaaiut myself with all those circumstances on 

 which the imiirovcniciit of your harbour depends ; and by a careful consider- 

 ation of them to prciiare such suggestions as I trust may he coiifonnalile with 

 your wishes. 



The principal oljservations which I collected referred to an undulatory mo- 

 tion of the water which is invariably felt when the wind is high, and to an 

 occasional " lifting" of the waters arising from distant causes. 



The undulating motion of the water is cxiierieiiced at the extremities of all 

 hays, the beds of which form a gradual slope towards the shore, like that 

 which is under consideration, and the effect can only be reduced by an alter- 

 ation in the form of the surface, and by a protection from the action of the 

 winds. 



It being obvious that the iinprovcinciit of the harbour must consist mainly 

 in the erection of an addilioiml pier, I was anxious to have the opinions of 

 the nautical men as to the best sitnatioii and form of the entrance ; and, 

 also, upon the width of the opening. Upon the situation of the entrance 

 southward and northward, there was no important difl'erence of opinion ; hut 

 it was thought a<lvisahle to advance the entrance, if practicable, into deeper 

 water than tliat at tlie head of the present pier. The relative positions of 

 the pier head were discussed at some length; and there was a manifest dif- 

 ference of opiuion on that point It is, indeed, one on which it is very diffi- 

 cult to decide a priori. I am not acquainted with more than one pier har- 

 bour, the entrance to which was so designed originally as to he in all respects 

 satisfactory when carried into effect ; and in lajing down the plan, wliicli 1 

 have now the honour to sul)mit to the council, I have thought it prmlent so 

 to arrange the position of llic pier heads, as to admit of their lieiug finally 

 adjusted as evperience acquired in tlie progress of the work may dictate. 



For the satisfaction of the council, I have deemed it advisable to lay before 

 theiu plans of other pier harljours. By help of tliese, some comparisons may 

 be formed witli that [iroposed for Penzance, not only in relation to tlicir ex- 

 tent, hut also to their security. They ai-e as follow :— 



Rarasgate — Dover — Folkestone — Swansea. 



The harhour of Ramsgatc is entirely artificial; and is constructed on a 

 shore directly opjioscd to the prc\ailiiig winds. Its security is tliercfore ex- 

 clusively derived from the piers by which it is enclosed. The width of the 



