VOL. LXXVI.] PHILOSOPHICAL TKANSACTIONS. 53 



A piece of clean, straight-grained, well seasoned mahogany,, of about 2 feet 

 long, 3 inches thick, and 5 or 6 inches broad, is then to be well affixed to some 

 part of the general frame of the lathe, which must now have its position altered, 

 so that the platform will become horizontal ; and therefore the frame should be 

 originally made with this view.* The piece of mahogany is to be affixed so that 

 one of its larger faces shall be in a parallel plane to the face of the platform, and 

 so low as to clear the under side of the platform in its rotation ; and so far distant 

 from the centre, that an index may be fixed on this upper face of the piece of 

 wood, so as conveniently to drop into the holes of the hoop ; while the common 

 cutter frame of a clock-maker's engine shall be firmly attached on the same face of 

 the wood, and so fixed as to cut the edge of the dividing plate into teeth, answera- 

 ble to the several divisions of the hoop. The teeth need only to be cut with a 

 common cutter, making a parallel notch : and here it will be proper to observe, 

 that not only both the index and cutter are to be founded on the same piece or 

 base of wood ; but that the nearer they are together, the more free they will be 

 from the effects of all variations of expansions by variations of temperature. 



The Equalizing the Teeth of the Dividing Plate by Grinding. — The object of 

 transferring the divisions of the hoop to the teeth of the dividing plate, is still 

 further to equalize the teeth by grinding; especially those that, falling within the 

 compass of each set of 1 20 divisions, may be supposed, if any, to be mended by 

 it ; but as it may be incommodious to construct a curved screw, of such a length 

 and size, in Hindley's method, as would be sufficient for the purpose, I would 

 propose to use 2 screws of brass, cut from a cylinder in the way set forth by Mr. 

 Ramsden, each of which, with a very little grinding on this large circumference, 

 would lay hold of 10 or 12 teeth together. I would place the 2 screws, that is, 

 their middles, to be 90 divisions asunder; of consequence, when one of the screws 

 is between the 59th and the 6oth, or between the llQth and 120th division of 

 each set, the other will be in the middle of the space divided by the chaps only. 

 The threads of these screws I would advise to be cut a little taper, so that as they 

 grind in, they may fill the notches of the teeth ; which also, by this means, will 

 acquire a little tapering towards their extremities ; and by cutting the notches 

 parallel, as mentioned, the true ground part will always be certain of being at the 

 extremity. 



When the screws have been used in grinding till they are found to have the 

 effect of a perfectly equal and easy rotation all round, and all the teeth reduced to 

 a sensible taper, and regular bearing, I would then totally remove the screws 

 from the square block of wood, on whose upper face I suppose them to have been 



* After changing the position of the lathe, the collar of its mandrel should be removed, and the 

 neck made to move within three planes, so as to preserve an exact centre, in the manner of an equal 

 altitude instrument. — Orig. 



