24 Prof. Snell on new articles of Philosophical Apparatus. 
wide and of about the same depth. Hach groove lies in a plane 
cutting the cylinder obliquely, and is of course an ellipse. But 
the several planes are not parallel. The second groove is revolved 
on the cylinder a certain number of degrees from parallelism with 
the first, the third holds the same relation to the second, and so of 
all the rest. |The slips of iron (ee) at their lower extremities are 
firmly attached to as many horizontal levers, which extend to the 
back side of the box, where they are confined by vertical pivots 
allowing free motion horizontally, but in no other direction. 
Each lever, passing just beneath the cylinder, is furnished with 
a short smooth iron pin projecting upward, which runs freely in 
one of the oblique grooves, and thus receives a horizontal oscil- 
latory motion. The ends of the levers near the front are sup- 
ported on a soft smooth edge, made by stretching morocco leather 
over a thin metallic plate, which extends through the length of 
the box. By this means the levers move silently and with little 
friction. Fig. 4 presents a cross section of the box; (e) is one 
of the vibrating pieces; (/) the lever to which it is attached ; 
(p) the pivot; (s) the leather edged support; (¢) csesncmngions 
cylinder. 
The ecnmumaaual ernitigenent of the grooves causes the 
vibrating pieces to arrive at a given phase of their oscillations in 
regular succession. The same remark might be made of the 
cams and iron columns in the other machine. Indeed, this reg- 
ular gradation of all possible phases, both in successive particles 
at the same time, and in the same particle in successive times, is 
the essential condition imposed on the vibrations of every con- 
ceivable kind of wave. It is a consequence of this condition 
that a wave always travels just its length during one vibration of 
any particle. This and all other relations that exist among the 
particles of an undulating medium, may be very satisfactorily 
presented to the eye by means of the instruments I have at- 
tempted to describe, or others of analogous construction. 
2. Instrument to exhibit caustics by reflection. 
The lecturer on optics, in illustrating the focal aberration oc- 
casioned by spherical mirrors, wishes to show the caustic curves 
as produced by reflection. He can indeed easily refer to exam- 
ples; since these curves are sometimes distinctly formed by a 
horizontal light on a white cloth beneath an inverted tumbler, 
