VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 51 



for joining the two ends of the hoop, could scarcely have been wished for, in re- 

 gard to preserving the same equality of the space between the holes contiguous to 

 the joint, as in the other parts : for though, geometrically speaking, the two 

 saddle plates, in which the little cylindrical bolts are fixed, for bringing the ter- 

 minating holes of the hoop plate to their due distance, being one applied within 

 the hoop, and the other without, will belong to circles of different radii ; yet this 

 difference being exceedingly small in such thin metal, and so great a radius, and 

 one being as much too large for the hoop as the other is too little, when the 

 bolts are put in, and the hoop in that part set nearly to a circle by a mould ; the 

 mean between them assumed by the hoop, from the elastic compressibility of the 

 materials, will be the truth. It must however be remarked, that in the use of 

 the straps, the joining of the hoop should not be made at any part between a 

 ligth and a 120th division, as some inequality must be supposed there, unless 

 the saddle plates were adapted thereto. The method the most easily practised, 

 will be to continue the division on the hoop, about 20 more than the completion 

 of the number intended to form the circle, and to cut off all the overplus ones at 

 the beginning. 



The saddle plates I would recommend to contain 10 holes each ; so that if the 

 divisions are carried on to 20 more than what will be contained in the circle, 

 there will be a piece containing 20 to cut off; and this again being cut in the 

 middle will afford 1 holes to make each saddle plate ; so that there will be a 

 place for a bolt on each side the joint, and then putting a bolt through every 

 other hole, there will be 3 bolts at an end. The pieces destined for the saddle 

 plates, thus obtained, being broader than can be admitted when put to this use, 



1 would advise to divide the breadth of the plate into 3 equal parts ; and with a 

 cutting hook, which perhaps will be attended with the least violence in the sepa- 

 ration, to separate the 2 outside pieces from the middle piece : by this means the 



2 saddle plates, though double, will occupy 4- only of the breadth of the hoop in 

 the middle ; and 2 of the pieces cut off being applied, one on each side of the 

 saddle plate on the outside, will answer in like manner for the rivet plates. 



The last operation to complete the joining of the hoop is the putting on the 

 rivet plates; to complete this, I would advise a piece of brass, of 3 or 4 inches in 

 length, to be filed so as to answer to the inside of the hoop, when reduced to a 

 true circular form ; and being -§-, or -i- inch in thickness, to file the opposite side 

 somewhat nearly concentric to it ; apply the middle of its convex arch to the in- 

 side of the hoop at the joint, and then bringing on the middle of one of the rivet 

 plates to the joint of the hoop, confine the 3 together by a couple of narrow- 

 chapped hand vises, leaving a space between them capable of receiving a couple 

 of pins as rivets on each side the joint ; the holes for the rivets are then to be 

 drilled through all, and a little smoothed with a broach at their entry, into which 



H 2 



