Heat by the Method of Mixtures. 273 



Draw CE parallel to axis of t. Then 

 ab=ao + ob ; cd=co + od, etc., etc. 



.'.'%\=n(ao)-t-bo + do+ -{-no 



=n± 1 +t&ng8{0 mt -t i +$ m „-t A + +$ m «- tl ) 



(n-1 $4-0 ) 



= /2A 1 +tang8J %0 + JLLJi-ntA 



Then to find tang 8 we have 

 or as a final result 



A —A 

 tang8—-r — — ■ (from fig. 1) 



iA a= nA 1+ ^j^ + ^i»-^[ (8) 



and true temperature after equalization will be 



0=0 n + SA 2 



i 



Other precautions which are of advantage will be readily 

 noted by observing that loss by radiation depends upon three 

 factors : 1st, excess of temperature of calorimeter above the 

 temperature of the surrounding air. This excess will be 

 diminished by making the mass of water M large, so that the 

 rise in temperature, 6— t, will be small. This cannot be car- 

 ried too far, however, because when the interval becomes small 

 the difficulty of reading temperature to the required degree 

 of accuracy is greatly increased (see 5A and 5C). 2d, surface 

 exposed. Theoretically the best form of calorimeter vessel 

 would be a sphere ; but as that is difficult of construction the 

 next best form is that of a cylinder of maximum capacity per 

 superficial area, viz : one in which the altitude equals the dia- 

 meter of the base. 3d, time. The time element will be re- 

 duced by keeping the water well agitated and by using the 

 body in the form of flat strips or wires rolled up into a ball 

 instead of a solid mass. 



Finally, there is an error in the observed temperature 

 due to the thermometer itself, which, when its stem is exposed 

 to a temperature below that of the bulb, indicates a lower read- 

 ing than it should. This error can only be determined in any 

 given case by careful experimental observations of the " time 

 lag" and "stem lag" of the thermometer. To make it as 

 small as possible, the thermometer should be of the smallest 

 possible size, and immersed so deeply in the calorimeter that 

 only enough of the stem projects to make the readings possible. 



Am. Jour. Scl— Fourth Series, "Vol. IY, No. 22.— Oct., 1897. 

 19 



