180 



Transactions of the Horticultural Society. 



directly, and the equivalent head is. inversely as the area of the section of 

 the pipe; consequently, 



3-U\6dlfv-- ^^Ifv'- ^ ^^^ j^g^j equivalent to the friction, 

 •7854 di d ^ 



But, in a pipe near the top, the head producing the velocity and overcom- 

 ing the friction is the quantity the fluid rises by expansion, ov he; there- 

 fore. 



xihe J—l\:=v'^; whence \/ . 



A he d 



d + 4 A // 



The effect of the cohesion of the fluid does not produce a sensible effect in 

 practical cases ; but, if it had been considered, the result would have 

 shown that the pipe might be so small in proportion to its length as to 

 render the velocity nothing. 



" 8. The coefficients to be obtained from experiment are denoted by 

 A, e, and/. That denoted by a depends only on the form of the tube or 

 pipe at its junction to the boiler, being the same for all fluids. 



"For the common mode of joining (j%. 22.) it is a=42; but, for a 

 pipe with a conical entrance (Jig. 23.), it is a =62. Now, the expense of 



23 



the conical form renders it probable that it will seldom be used ; hence, 

 42 may be inserted in any rule for general purposes. 



" 9. The expansion of liquids not being perfectly equable by equal in- 

 crements of temperature, and not the same for all liquids, the easiest mode 

 for obtaining it for any particular case will be by means of a table. 



Table of Expansion of Liquids. 

 Expansion by 1° of heat at the temperature in the first column. 







Water satu. 







Temperature. 



Water. 



rated with 

 common Salt. 



Spirit of Wine. 



Olive Oil. 



o 



62 



•00009 



•00010 



•00059 





72 



•00014 



•00015 



•00061 





82 



•00017 



•00018 



•00063 





102 



•00025 



•00027 



•00068 



•0007 



122 



•00029 



•00031 



. ^00075 





162 



•00034 



•00037 



•00081 





182 



•00036 



•00039 







212 



.00038 



•00041 







If the difference of temperature, for example, be 8°, and the mean temper- 

 ature 172°, then, for water, 8 X •00035=^0028 is the expansion of water by 

 8" of heat, and 8 x •00038=^00304 is the expansion for a saturated solution 

 of salt. 



" 10. The friction of fluids, and particularly the effect of change of tem- 

 perature, has been investigated only in a very partial manner. [Here Mr. 



