HYDRODYNAMICS. 



435 



/ = the temperature when the liquid is weighed. 

 t" = the temperature reckoned from the point of maxi- 

 mum density, or t" = I 3.42. 

 a = the weight of volume of dry or moist air in the 



glat* vessel at the time the liquid is weighed. 

 (<i)=the weight of a cubic centimetre of dry air, at the 

 temperature of 32, and the pressure of 0.76 

 metres, or 29.99+ inches. 

 K = the cubical dilatation of glass for every degree of 



the centigrade thermometer. 

 p = the he : cht of the column of mercury when the 



A tinned. 



p' the height of the column of mercury in the baro- 

 meter, reduced to the temperature of 32 of 

 Fahrenheit. 

 ' = the relation of th weight of air to that of water, 



at the temperature If. 

 T = the tension of the vapour of water in the air where 



the liquid is weighed. 



- = the wright of a cub : c centimetre of the liquid at 

 the temperature of 32 of Fahrenheit. 



Then we hare 

 =; 0.0000063*750r * 0.00000008708 t" 



(1 +f . 0.00375)0-76 



_() 

 (t 



No. 1. 

 No. 2. 



'. No. S. 



+1.0.00375)0- .76 

 (L + )(!+>) 



No. 4. 

 No. 5. 



The use of these formula; will be best seen by ap- 

 plying them, as M. Biot has done, to the following expe- 

 riments on mercury and water by him and M. Arago. 



In calculating the value of V, from the formula No. 

 S, we have 



(o)=0.001299541 grammes, and Log. (o)=3.1 137902, 

 and by the formula No. 1. 



y =0.0017017forExp.S. sincer=20.l 30.42=16.68 

 Y =0.00 18654 for Exp. -t. t'^O .93 .42=17 .48 



The height of the mercurial columns, or p, being re- 

 duced to the temperature of 32 of Fahrenheit, we 

 have 



ff = 0.760 0.0028 = 0.7572 Exp. S. 

 p' = 0.7589 0.0089 = 0.7560 Exp. 4. 

 With these values, and the temperature /' observed 

 at the time of the weighing, we have by the formula 

 No. 2. 



' = 0.001206079 

 ' = 0.001192953 



Now K<- = 0.0005281 

 K t' = 0.0005431 



. 3. 

 Exp. 4. 



Speciti, 

 Gruvitic.. 



I lence ' K f = 0.0000006369, ' + ' K (' K f = 0.00067861 Exp. 3. 

 'K/' = 0.0000006551, ' + ' K t' Kt' = 0.00064451 Exp.*. 



By substituting these values in the formula No. 3. we have, in cubic centimetres, 



= 98.7*1 + 0.1679935 + 0.0671518 = 98.9561453 Exp. S. 

 V = 98.716 + 0.1841449 + 0.0637819 = 98.9639268 Exp. 4. 



The arithmetical mean between then remits is 



V = 98.960036. The 

 vessel at the temperature of 92* of Fi 



The abMtaU weight of mercury or any other liquid 

 weighed in the same glass vestel, at a given tempers), 

 lure, mar now he easily deduced from the formula No. 5. 

 We shall follow M. Biot in applying the formula to 

 Kxperunents 1. and S. on mercury. 



In order to calculate the value of a, we have 

 (a) V=0,1286201 grammes, or the weight of dry air 

 contained in the glass vessel at the standard temperature 

 of 3S of Fahrenheit, and 0-.76 or 29.994 inches of aU 



I fence we shall have by the formula No. 4. 



Eip. 1. 



f L=l 



1 - 



(L+a 1 



Hence 



a=0,120Oi Exp. 1. and a=0.11872. Exp. 2 

 L= 1342,989 grammes, f L= 1340,93 



lgOM LExp.2.4 = '" 878 



L+a 1343.109M j (L+a 1341,01172 



As these weights contain a great number of grammes, it is necessary to calculate the corrections with regard 

 to K t and A more exactly than would otherwise have been necessary. We have 



(L+a) 

 =L+ * 



K< 



i 



The second of these term*, which U always very small, is the correction sought. Now 

 j ' + *= 1 14^10004 0,44091 9= 1 342,668 1 2 Exp. 1. 



- = 1341,01172 0,725363=13*0,286357 Exp. 2. 

 -f rvr 



