B ABBA GE'S NOT A TION. 249
writers upon subjects connected with horology, have employed a land of notation for showing the sequence of the wheels and arbors in clockwork. Willis has entered somewhat closely into this method of symbolization. The following, for example, shows the arrange- ment of the wheel-work of a common clock in a form which he himself adopted :
48
6 45
6 30
Here the numerals stand for numbers of teeth, the lines indicate the connection of two wheels by an arbor, the placing of one figure over another shows that the corresponding wheels gear together. Putting the names of the wheels beside the numbers of their teeth we should have : Great Wheel 48
Pinion 6 45 Second wheel
Pinion 6 30 Balance-wheel.
Other writers have used methods somewhat differing from this.* It is evident, however, that the object here is the representation of a portion only of an isolated case, and even that portion is not intended to include the general kinematic nature of the spur- gearing, but to cover merely the indication of its velocity-ratios, a very important matter, of course, in itself.
The method proposed by Mr. Babbage " for expressing by signs the action of machinery " was more important than these, and was indeed intended to be quite general in its application. Babbage, to whom no doubt the subject was suggested during the extremely difficult construction of his calculating machine, described his system in a small book, not much known,-)- in which he has illustrated it by two large examples, a clock with working and striking trains and a hydraulic ram. His method is as follows : The names of the whole of the moving parts are first put down in order, and then signs are placed in tabular form beside the name of
- Willis instances the following for the case supposed :
Oughtred (1677) Derham (1696) Allexandre (1735).
30 48)6-45)630 48
6)45 456
6)48 306
t A Method of Expressing by Signs the Action of Machinery, by C. London, 1826.
