102 Mr. W. Baily on a New Automatic 



The edge of one of the fixed disks is graduated, as shown in 

 fig. 4 ; and the nearest moving disk carries a vernier, the zero 

 of which for the position of the scale given in the figure must 

 be in the direction K T. It is convenient to mark 5° of cir- 

 cumference as 1° of graduation, since the disk moves five 

 times as fast as the prisms open out from one another. The 

 reading may then be made to give the angle between conse- 

 cutive j)risms. Motion can be given to the instrument by 

 connecting the moving and fixed disks by a rack and pinion. 



It may be necessary to adopt some contrivance for keeping 

 the pins always pressing against the same sides of the slits 

 through which they pass. I ensure pressure against the 

 inner sides of the curved slits in the disks by fixing pegs in 

 the disks somewhat in the positions a, (3, 7, 8 in fig. 3, and 

 passing an elastic band romid each pin and the corresponding 

 peg. The bands and pegs are placed on the sides of the disks 

 remote from the prisms, so as not to interfere with the rest of 

 the machinery. To ensure pressure always against the same 

 sides of the slits in the arms, a peg is inserted at E in the fixed 

 disk, fig. 4, and pegs are inserted at F, G, H, I in the arms ; 

 the pins P, Q, R, S are connected with the pegs E, F, G, H 

 respectively by elastic bands ; and thus the pins P, Q, P, S 

 are drawn round K in one direction, and the arms K P, K Q, 

 K R are drawn in the opposite direction. It will be found 

 that there is not much variation in the length of the band. In 

 order to pull the arm K S by a band which shall not vary 



much in length, a slit whose middle line is r = F ( - j should be 



cut in each of the fixed disks, and a slit r = F ( 7; j (that is, a 



straight slit along the initial line K T) should be cut in each of 

 the moving disks ; then, if T be a pin passed through these 

 slits, T will be at the same distance from K as the other pins, 

 and a band round T and I will be of the same length as the 

 other bands. This additional pin is not given in the model 

 exhibited ; but one of the bands connects an arm with a fixed 

 point, and therefore undergoes a good deal of stretching, 

 which it is better to avoid. 



The form of F(^) is arbitrary ; but there is an advantage in 

 giving it the form ae~^^, so as to make r = F(^) an equian- 



gular spiral. Since all the curves will be of the form r = ae~^mj 

 they will all be equiangular spirals ; and therefore in fig. 1 

 the angle A Tp will be constant, and the angle d Fp will 

 also be constant, and consequently the angle AT d will be 

 constant. Similarly it may be shown that the angles B Q c, 



