imiDGE. 



FLYING BRIDGE. 



in 



Leibniti had inserted Newton's method, changing its naine ami 

 tion. in tha Leipxig AcU. The article COXIUUK M take* 



up the hUtory at this (xiint. 



The ' Commerciuiu RpMaliMa ' ili<l not reach Leibnitz, who won 

 at Vicuna, fur a considerable time. In the mean while he wrote to 

 John UcrnuulU (who had received hia copy) for hi- opinion of the 

 work. This the latter gave, tint in a letter to Leibnitz, and after 

 wards (as Leibnitx asserts) in an anonymous tract published in July, 

 1713. Hut, a> in thu tract the author speaks in complimentary terms 

 of John Bernoulli, it has been supposed that at least it waa edited by 

 some one ebo. Tlii- 1. ti. ; H decidedly as unfair towards Newton as 

 the friends of the latter had been towards Leibnitz; it asserts the 

 method of fluxions to be a plagiarism from the Differential Calculus. 

 Keill printed a reply, and Newton and Leibnitz then appear as mutual 

 accuaers, in letters to Mr. Chamberlayne. Nothing remarkable arose 

 out of this correspondence, which terminated in the announcement of 

 Leibnitz that he also would prepare a ' Cominerciuin Kpistolicum.' 

 December, 1715, Leibnitz re-opened the matter in a letter to the 

 Abl.'- Aut-mio I'onti of Venice, then on a visit to England. Hu there 

 complains of the treatment he hod received, and attacks the Newtonian 

 philosophy in general. Newton wrote a reply, February 26, 1715-18? 

 in which he very much dwells on previous admissions made by Lcib- 

 iiit/. The latter, in a third letter to Conti, April 9, 1716, avows that 

 he always believed Newton upon hia word, but that, seeing him 

 connive at accusations which he must have known to be false, it was 

 natural that he (Leibnitz) should begin to doubt. Newton is also 

 reminded that he had made some admissions in favour of Leibnitz (in 

 the scholium) which he was now desirous of disavowing. This letter 

 was not sent directly to Conti, but first to Paris, that it might be there 

 seen and copied by a friend : on which Newton refused to send any 

 answer, considering it aa an insult that Leibnitz, though he com- 

 plamed of suppressions in the ' Commercium Epintolicum,' should take 

 means to preserve evidence to the whole of liis letters. But Newton 

 circulated some remarks among his friends, which he published imme- 

 diately on hearing of the death of Leibnitz, November 14, 1710. It 

 is in this last paper that the remarkable sentence occurs which we have 

 quoted above in connection with the scholium which it disavows. 

 Kaphson's ' History of Fluxions' being then ready for publication (its 

 title-page bean 1715), or perhaj>s published, the Conti correspondence 

 wan annexed aa a supplement. 



The history of the controversy ends with the death of Leibnitz, 

 and we shall conclude this article with a few additional quotations and 

 facts which bear upon the subject. 



1. The second letter of Keill (May 24, 1711) [CoMMEBcruM EPISTO- 

 I.ICUM], on which the whole of the subsequent dispute arose, was in 

 substance the statement of Newton himself. In the minutes of the 

 Royal Society, April S, 1711, it is stated that " the president gave a 

 short account of the matter, with the particular time of his first 

 mentioning or discovering his invention, referring to some letters 

 published by Dr. Wallis : upon which Mr. Keill waa desired to draw 

 up an account of the matter in dispute, and set it in a just light." 

 Tip- letter in question was the consequence, which was read at the 



ing of the 24th of May (its date). 



2. The original committee consisted of Dr. Arbuthnot, Mr. Hill, Dr. 

 Halley, Mr. Jones, Mr. Machin, and Mr. Burnet. This is what Newton 

 his been supposed to call " a numerous committee of gentlemen of 

 tereral nation* : " and singularly enough, no writer on the other side 

 has ever noted this apparent unfairness. But it has lately been dis- 

 covered that Newton was right During the investigation there were 

 added to the committee, Robarts, Aston, Brook Taylor, Jiunel, the 

 Prussian minister, and De Mature. The names of the committee were 

 n<>t published with the ' Commercium Epistolicum.' 



8. So far from the committee considering themselves as in any 

 judicial capacity, it appears, from a letter of Burnet above-named to 

 John Bernoulli (which the latter sent to Leibnitz, and the extract ia in 

 the published correspondence of the two), that the Royal Society was 

 busy proving by original letters that Leibnitz might have seen the 

 method of fluxions in the correspondence of Oldenburg, Ac. 



There was throughout the whole dispute a confusion between the 

 knowledge of fluxions or differentials and that of a calcuiut of fluxions 

 or differential/*, that is, a digested method with general rules. If the 

 dJKputo could be revived at the present time, it would be on entirely 

 different grounds : but of course, in describing the controversy as it 

 existed, we need only consider those ]<oints which were put in issue by 

 the parties themselves. 



KUYlNii mtlDOK. This consists usually of a boat or other vessel 

 which, lieitiK attached by a rope to a buoy, moored in the middle of a 

 river, is made, by the action of the current, to move across on an arc 

 i .-I.- of which the buoy is the centre. On large rivers, at places 

 h. -i c the communications across them are very frequent, such bridges 

 will probably, in future, \>a superseded by steam-vessels ; but, for 

 L"ini>rary purposes, and particularly to facilitate military upei.iti.nis 

 in countries where steam navigation in not in use, they may be of the 

 highest importance. 



Let A be a buoy securely MudkONd in the middle of a river, and I> a 

 boat to which, at a point about one-third of the vessel's length from 

 lip- head, is attaehi- I on cipl of HP- e >M>- or cli.dn n A : then j> ' indi- 

 cating the direction of the current, if the kwl u 6 of the boat be in- 



clined to that direction in any angle u p 6 a, the pressure of the water 

 against one side of the boat being resolved in a direction 9 a perpen- 

 dicular to p b, or across the river, will cause the boat to describe the 



arc CDE, whose centre is A. As far as the point n, in the middle 

 of the river, the boat descends, but afterwards it ascends obliquely 

 against the current ; for while He keel is kept by the rudder in a 

 position nearly parallel to 6 a, the force parallel to g a continues to act 

 and impel the boat towards E. If / represent the direct force of the. 

 current, and 8 the angle p b a, the force perpendicular to p h will be 

 expressed by /gin 1 9 cosO; and this will be a maximum when 8=54 44'. 

 It is evident that by increasing the length of the rope A B, the 

 length of the arc between c and E will be diminished ; the retai 

 arising from the action of the current, in ascending from the middle 

 of the river to E, will also be less : the length of the rope or chain 

 should, in fact, be such that the arc c D E may not exceed a quai 

 the circumference of the circle ; and when, for this purpose, the length 

 is very great, it must be supported aa at g, k, and Ic, on moveable buoys 

 or small boats. 



A flying bridge sometimes consists of a simple flat-bottomed vessel, 

 having a maat fixed to one of its sides in the middle of its length. 

 The cable passes through a block at the mast head, and is attached at 

 one end to the opposite side of the vessel, th other end being made 

 fast to the buoy. Two ropes connected with the cable lead one to the 

 head and the other to the stern of the vessel ; and, by pulling on one 

 of these, the other being let go, the vessel is placed in a position 

 oblique to the current : this position is retained by means of a steering 

 oar aided by a current-board which may be let down into the water at 

 the head or stern as the cose may require. 



In a rapid current it may be impossible to make the boat B move 

 up the ascending arc D E ; in which case a boat at F, by means of a 

 cable mode fast at a on the opposite bank, may be allowed to describe 

 the descending arc F o. On setting out from F, the boat takes with 

 her a coil of rope, of which one end is attached to a fixed object near 

 that place ; then, on arriving at. o, the boat is drawn up along the bank 

 to H ; and by the rope is hauled across the river to F, from whence it 

 set out. Again, a rope being made fast to an object near F, a boat 

 may be steered obliquely from some point aa K, till she comes to a part, 

 as H, of the river at which the current acts strongly upon her ; tln-n 

 letting go the rope and, by the rudder or steering oar, keeping thu 

 boat's keel at a proper inclination to the direction of the cm-rent, the 

 resolved force of the water will impel the boat to some point, aa o, on 

 the opposite bank. 



When the river is too wide* for a boat to swing over in a single arc, 

 two buoys may be moored in a direction across the river, at equal 

 distances from the banks and from each other, and two boats con- 

 nected with them by ropes may be impelled in circular arcs, one 

 extending over the first half of the breadth of the river, and the other 

 over the second : a raft being moored in the middle facilitates the 

 transference of the passengers, &c., from one boat to the other; <>r, 

 without the raft, one boat, on arriving in the middle of the river, may 

 transfer its passengers immediately to that which is to describe the 

 other half of the breadth. 



A triangular raft N P Q having its front, as N P, parallel to the direc- 

 tion of the current, and Vicing connected by a ring at N, with a lope 

 8 V stretched tightly across the river, may, by a resolved force of t h. 

 current on lQ, be impelled directly to the opposite lank; and, on 

 reversing its position so that P may be connected by a ring with the 

 rope s v, the raft may be impelled across in a contrary direction. A 

 boat running by a ring at one end, on s v, may, by being kept in a 



