56 PROF. OSBORNE REYNOLDS ON THE MANNER IN 



Suppose the drop to start having a weight ?<;, aucl a tem- 

 perature ti, and on reaching the earth to have a temperature 

 t^. Then the increase in the quantity of heat in the drop 

 would be {t^ — ti)w^ nearly. This heat would be developed 



bv the condensation of a weight of water (L — t.) — ~ nearly : 



so that, even supposing ^2. — ^, = ioo° F.^ which it could 

 not possibly be, the increase in the weight of the drop could 

 not be one tenth. 



It is obvious also that the drop would not have parted 

 with its heat to the air it passes through ; for it is assumed 

 to be colder than this air. Therefore the only way in 

 which it could have parted with its heat would have been 

 by radiation. Some heat might be lost in this way, but 

 only a very small amount, and one of which an approximate 

 estimate may be made. For after the drop had acquired a 

 considerable size, say one hundredth of a foot in diameter, 

 the time occupied in its descent would be very small. 

 Assume this to be one minute ; and assume that during this 

 time the drop is lOO degrees hotter than the surrounding 

 objects, although this is of course far beyond what could 

 possibly be. According to the most accurate data the 

 amount of heat it would then lose would not be sufficient 

 to condense ^r^ of a grain of water^ — an altogether 



* The surface of a drop whose diameter is '05 ft. is -000314 sq. ft. Now 

 if the temperature of the surrounding objects be zero Centigrade, and the 

 temperature of the drop be 60° Centigrade, then, assuming the radiation 

 from the surface of the drop to be tlie same as the radiation from the sur- 

 face of glass, we have (see Balfour Stewart on Heat, p. 228) : — 



R= io( 1*600770— I )A, 

 where R is the heat radiated from the surface A in one minute, the units 

 being the heat required to raise 1000 grains of water 1 ° C. This gives 



R = 6A 

 or R = "oo2 nearl5^ 



Now if R' be the same quantity of heat, the imif being the heat required to 

 raise one grain 1° Fahr., R'=:i8oo R, 



= 36. 



