A GREAT SOLAR OUTBURST. 



Now the time in which a projectile with this initial 

 velocity would traverse the upper half of its path is 

 not so readily determined in fact, the formula is not 

 altogether suited to these pages. 1 I must, therefore, 



extreme height reached by a projectile from the sun ; V the velocity of 

 projection. Then, a mile being the unit of length, and a second the 

 unit of time _ 



V = 379 A / J *L_ 

 Y K + H 



(379 miles per second is the velocity which would be required to carry 

 a projectile away from the sun altogether) ; and we have only to put 

 for H, 200,000 (miles), and for R, 425,000, to deduce the required velo- 

 city. 



1 Following, however, the plan adopted in my treatise on The Sun, 

 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 : 



E 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 Professor Young's observation, find- 

 ing the application of this formula rather wearisome (especially as the 

 formula had to be applied tentatively in dealing with the main problem, 

 for it tells us nothing as to the extreme height, when this is to be de- 

 termined from the observed time between certain levels), I was led to 

 consider whether a geometrical 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 ; they prevent 

 any serious errors of calculation, by affording a tolerably close approxi- 

 mation 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 witli singular ease, rapidity, and amiracy to all problems such 

 as the one we are upon. Let K Q E C be a carefully constructed half 

 cycloid, K being a cusp, E the vertex, and E C the axis. (The same 

 cycloid is to be used for all problems, the remaining constructions being 

 pencilled.) Divide C E in A so that C A represents the sun's radius, 



