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ture from the “ pile” of iron, were shown. The finished bar differed in shape from 
that called the ‘‘ bridge” form, insomuch that it had additional flanches on the inner 
side, giving it the appearance of a square tube. It was suggested that deep, narrow 
girders might be rolled with facility on the above plan. 
On correct Sizing of Toothed Wheels and Pinions. 
By Ricuarp Rozerts of Manchester. 
Although much has been written on this subject, and on the best form of teeth, 
there is still much difference of opinion on both points, which difference is not con- 
fined to individuals, as it embraces the members of the trade or profession to which 
they belong; for instance, engineers, millwrights, and machinists in general, adopt 
the plan of extending the teeth of the pinion and wheel to the same distance beyond 
the pitch-line, and the majority of them are agreed as to the best form of teeth, 
namely, the cycloid for wheels to work in straight racks, and the epicycloid for 
wheels to work in other wheels or in pinions; they are not, however, so well agreed 
respecting the length of the teeth; whilst the makers of watches, clocks and chro- 
nometers, do not extend the teeth of the pinion, beyond the pitch-line, more than 
one-half as far as they do the teeth of the wheel: hence the preference given by those 
trades to the “ bay-leaf’’ form for the teeth of the pinion, as no other form would 
pitch with their sizing. 
Various rules are given in works on horology for sizing wheels and pinions; but 
I believe movement makers generally, English and foreign, use for that purpose an 
instrument (called a sector) resembling a two-feet rule, which is divided into equal 
parts throughout its length, commencing about half a division from the centre of the 
joint. The numbers up to 10 or 12 on the sector are usually subdivided, for the use 
of artisans who may prefer pinions a little larger than the corresponding number 
on the sector would give. 
Knowing it to be essential to the correct performance of any machine where wheels 
and pinions are employed that they should be properly sized, I have thought it might 
be useful to parties whose experience on the subject has been more limited than my 
__ own, to be informed respecting the plan which I have adopted for more than thirty 
_ years for sizing toothed wheels. It has long been the practice in Manchester to make 
those wheels which come under the denomination of clockwork with a definite number 
of teeth to the inch diameter, taken at the pitch-line, and to distinguish the pitch ac- 
cordingly. I have done this, and have adopted the same plan in respect to mill-gear, 
substituting the foot for the inch diameter in designating the pitch (naming the pitch 
_ by the number of teeth in a foot diameter), instead of naming it by the distance from 
_ the centre of one tooth to the centre of the next, which is, I believe, the universal 
practice. I may here mention, that, in the year 1816, I had a set of change-wheels 
made by a factory clockmaker, which were so much out of pitch as to direct my 
attention to the cause of the defect; and having found that the error had arisen 
from the defective principle of the sector, I immediately contrived a sector, which 
_ differed from the clockmaker’s sector, principally in the joint being adjustable like 
that of the proportionable compasses. The use of this kind of joint was to enable 
parties to pitch wheels correctly, and to suit themselves as to the depth of the teeth. 
_ After I had sold a number of sectors of this kind, I found that for all ordinary pur- 
poses a, fixed joint would answer equally well, provided the centre of the joint were 
equal to two of the divisions of the sector below zero. This circumstance led me to 
_ make sectors (if serrated bars of brass may be so called) of a cheaper kind, whilst 
they were better suited for the workshop. This kind of sector, which I believe is 
_ made by my firm only, has the tenth number at the twelfth division from the start- 
ing-point, the two divisions being added for the depth of tooth beyond the pitch-line. 
There are two scales on each of these sectors, one on each edge, which scales are 
marked according to the number of teeth to the inch diameter (pitch-line) they are 
adapted for. These sectors are made in sets, ranging from three to thirty in the inch. 
_ We use one set for sizing working-wheels, and another set for sizing pattern- wheels, 
the latter being one per cent. coarser than the former, to compensate for the con- 
_ traction of the metal in cooling. In a patent which I recently took out for improve- 
