61 
The Trochoided Plane. 
By Lawrence Hararave. 
[Read before the Royal Society of N.S.W., 6 August, 1884.] 
I nAveE been told that the subject of this paper is one that would 
interest the members of this Society, and therefore I have strung 
together my thoughts, experiments, and deductions, that refer in 
any way to the trochoided oe. pointing out where I see N ature 
working with it, and how it can be used by man for the trans- 
tapiditided plane 
The “trochoided plane” is a flat surface, the centre of which 
moves at a uniform speed in a circle, the plane being kept normal 
to the surface of a trochoidal wave, having a period equal to the 
time occupied by the centre of the plane in : completing one revolu- 
By “ Normal” is meant tangential to an undulating surface. 
“Orbit” is the path of any particle of a sibsainans, through 
which undulations are bein 
is the radius or radius-vector of the orbit. 
plane ; the ae of the connecting-rod is equal to the crank 
future call it the connecting-rod, unless some one points out its 
true mathematical designation ; geting, ig: the trochoid 
seems a good name also, but not $0 descriptive mecting-rod ; 
every one knows what a connecting-rod of a ipetating engine 
is, and i iliar motion. 
: ts fam 
“ Pitch, ” or length of wave, is the distance of waves from crest 
to crest, ‘measured in the a of propagation ; the length of a 
trochoidal wave is equal to the length of the orbit of a particle 
divided by the co-tangent it =e pitch-angle. 
