On the Icy Crust formed oh Glass Windows, &c. 19I 

 describes this space c + d, and its velocity is greater than 



that of the lamina in the ratio of -?+ 1 to 1. that is — ; — 



a v 



la « . . /a , \ h 



+ 1 or - b + 2 to 1, becom.ng»( i -+ ») v(aa + t) =»« 



0, 4* * • 1 a 



; which, when h vanishes, becomes m V" r > as 



in Lagrange's theorem, and, when h is small, m ( *J - -f -- 



— tt — ttt^ , or m - — 7-— : but if a were small, it would 



approach to m ^ l 9 the velocity due to the whole height of 

 the wave. 



XXXIII. On the Icy Crust formed on Glass .Windows du- 

 ring a severe Frost : — with a few Remarks on Marine Ve~ 

 getables. By Mr. James Graham, of Berwick-upon- 

 Tweed, 



To Mr. Tilloch, — Sir, 

 If you think the following observations on the crust formed 

 on windows during a severe frost merit a place in your 

 very useful and entertaining Miscellany, they are much at 

 your service. 



This curious phaenomenon is so common, that I believe 

 there are very few who have not taken some notice of it ; 

 but, like many of the other appearances in nature, which 

 strike the mind of the philosopher or the contemplative ob- 

 server with wonder and astonishment, with the great bulk 

 of mankind it excites not the least surprise. Such seem* 

 to be the general weakness of the human intellect, that 

 we all require some friendly hand or kind assistant to 

 first " rear the tender thought, or teach the young idea how 

 to shoot. " The appearance to which I wish to call the at- 

 tention of your readers is the various figures which are re- 

 presented on the glass where this crust is formed. T have 

 found some, whose curiosity was in a certain degree excited, 

 suppose that all was merely accidental, .or formed by what 

 we often call chance: but, on a closer observation, this v. ill 



