STRANGE NEWS ABOUT THE SOLAR PROMINENCES. 
55 
would traverse the upper half of its path is not so readily 
determined — in fact the formula is not altogether suited to 
these pages.* I must, therefore, ask those readers who do not 
care to make the calculations for themselves, to accept on trust 
my statement that 25m. 56s. would he the time required for 
the upper half of our projectile’s course. 
It is already obvious, therefore, that the matter watched by 
Professor Young did not behave like a projectile in vacuo , 
having 200,000 miles as the limits of its upward course. It 
traversed a space in 10 minutes which such a projectile would 
only traverse in about 26 minutes. 
Now two explanations are available. We may suppose that 
the real limit of the upward flight of the hydrogen was greater 
than 200,000 miles, and that, therefore, the 100,000 miles next 
below that level were traversed with a greater velocity than 
would correspond to the case we have just been considering ; or 
* Following, however, the plan adopted in my treatise on ‘ The Sim,’ I give 
the formula for all such cases in a note, so that those readers whose tastes 
are mathematical may make the calculation for themselves, if they wish to. 
It runs thus : — 
ft being the sun’s radius, D the extreme distance of a projectile from the 
sun’s centre, X its distance at time t after starting from rest at distance D 
( from centre , be it remembered), then, 
In the course of my examination of Prof. Young’s observation, finding the 
application of this formula rather wearisome (especially as the formula had to 
be applied tentatively m dealing with the main problem, for it tells us 
nothing as to the extreme height, when this is to be determined frcm the 
observed time between certain levels), I was led to consider whether a geo- 
metrical construction might not be found which would at least afford a test 
of the calculative results. (For this, be it noticed, is the great value of 
geometrical constructions j they prevent any serious errors of calculation, 
by affording a tolerably close approximation to the truth ; and in calculation 
— crede experto — great errors are most to be feared). 
I presently lighted on the following construction, which may be applied 
with singular ease, rapidity, and accuracy to all problems such as the one we 
are upon. Let KQEC be a carefully constructed half cycloid, K being a 
cusp, E the vertex, and EC the axis. (The same cycloid is to be used for all 
problems, the remaining constructions being pencilled.) Divide CE in A so 
that C A represents the sun’s radius, A E the flight of a projectile. About 
centre C draw half circle ADL. cutting half circle on EC as diameter in D. 
Draw DM square to AC, rnd let M m L, a half circle on ML, cut KC in m. 
Then the time of descent from E to any point P in E A is represented by the 
ordinate PQ (parallel to KC), where mC represents 18 m. 40s., which is 
the time in which CA would be traversed, with a velocity of 379 miles 
per second. 
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