152 THE TOP. 
Last winter I spoke of the curious tracings made on 
smoked glass by the point of a top when left to take its 
owncourse. I did little more than speak of their exquis- 
ite beauty, and exhibit some specimens by the photoen- 
graving process as shown on plate IV, vol. I1., of our 
Transactions. Although, unfortunately, the tracings are 
there reversed, and consequently not well adapted to ex- 
hibit the law which governs these movements, still they 
serve a useful purpose in some respects, and hence the 
plate is reproduced as plate II., in this paper. It repre- 
sents parts of three tracings. The largest, ornumber 1, 
shows only oneand a half gyrations, when for some 
reason, I forget what, the top was lifted from the glass 
plate. The axis was much inclined, and the point 
(about one-fortieth of an inch in diameter) a little “out — 
of true,’ hence the wavy, broken appearance. Number 
2 was made withthe same point, and with axis less in- 
clined, the waviness continued, but was more pro- 
nounced. This was due to the axis being more nearly 
vertical. The ‘‘point’’ jumped clear of the coating 
of lamp-black in case of number 1, but pushed it back 
in case of number 2. 
Number 3 was made with a needle point, better cen- 
tered. It is noticeable for its freedom from waviness. 
The axis, I think, was inclined about as in number 2. 
The following laws can be experimentally proved : 
1. The first spiralis the largest ; the others grow smaller 
with great uniformity till near the end of the top’s run- 
ning, when they begin to grow larger, but with far more 
rapid increase of size. In avery few instances I have 
seen the spiral commence small and increase to the 
end. 
2. On a pefectly level, and uniformly smooth sur- 
face the top does not travel. The point simply traces a 
series of concentric spirals. 
36 
