312 Prof. Tyndall on the Reg elation of Snow -granules. 



.development by Balance of Errors, for it neither has a point of 

 sight nor a plane of projection, we have no such effect, but, on 

 the contrary, we have in it some of the circular arcs thrown into 

 lines of contrary flexure; and this I conceive is fatal to this 

 method of representing large portions of the earth's surface. 



For the projection of the surface of a hemisphere, the distance 

 of the point of sight which I have adopted is the best possible ; 

 for in it the distortion of form and the exaggeration of area — or, 

 as we may call these two defects of all projections, the misrepre- 

 sentation is a minimum ; but for extending the projection from 

 90° to 113° 30 7 , Captain Clarke has shown that the distance of 

 the point of sight to give the least misrepresentation should have 

 been JJ instead of \^ } in which case the misrepresentation would 

 have been 103*6 as compared to 100*0 in the projection by 

 Balance of Errors, the ratio in the projection as drawn by me 

 being 109*5 to 100*0. 



In deciding to adopt half the radius as the distance for my 

 point of projection, I knew that this was not the best possible 

 point, but that it was so near to it that, for all practical pur- 

 poses and the simplicity of its definition, it was the best to 

 adopt ; and it is the very best projection up to 90° from the 

 centre. For the same reason I adopted the limit of the tropics 

 for the position of the plane of projection, because this is very 

 definite, and near the limit which in prudence I could give to 

 the projection ; and I have called it a projection of two-thirds 

 of the sphere, whilst in reality the surface represented is seven- 

 tenths of the whole surface. 



A comparison of the two projections will satisfy any practical 

 person that, if the ratio of the misrepresentation in them is as 

 109*5 to 100*0, I should gain very little by making it in the 

 ratio of 103*6 to 100*0; in fact the eye would not detect the 

 difference. 



I have prepared a map of the world and a map of the stars on 

 my projection, each ten feet in diameter, for the Great Exhibi- 

 tion of this year ; and the public will have a full opportunity of 

 judging of its merits. 



XLIII. On the Regelation of Snow -granules. 

 By John Tyndall, F.R.S.* 



I THIS morning (March 21) noticed an extremely interesting 

 case of regelation. A layer of snow between 1 and 2 inches 

 in thickness had fallen on the glass roof of a small greenhouse, 

 into which a door opened from the mansion to which the green- 



* Communicated by the Author. 



