METHODS AND APPARATUS. 13 



the remaining constants were derived and the suitability of the apparatus 

 for the work assured. 



The potentiometer has a resistance of 15,000 ohms, which can be included 

 between the potential terminals in steps of 0.1 ohm. The galvanometer 

 resistance is about 50 ohms, and the sensitiveness such that a deflection of 0.5 

 millimeteris produced by a current of 15 X 10~ 10 amperes. The resistance of the 

 constantan wire as selected is about 14 ohms for each circuit; that of the 

 copper is negligible. The electromotive force of the copper-constantan couple 

 is taken as 40 X 10 -6 volts per degree centigrade. The voltage of the storage 

 cell is 2.0 volts, that of the standard cell 1.0197 volts. Most of the tempera- 

 tures to be measured are assumed to lie within the limits of 36 to 38 C, and 

 are desired to an accuracy of about 0.01 C. The apparatus, however, should 

 not be restricted to these limits but should be capable of measuring lower 

 temperatures, although with a somewhat decreased precision. 



The constant-temperature junction is kept at a temperature of about 40 C, 

 and as the other junction never rises to so high a temperature as this, it follows 

 that the net voltage of the thermal-junction system always acts in one direc- 

 tion. The temperature difference between the junctions is usually not less 

 than 2 C. nor greater than 4 C, so that under these circumstances the 

 voltage limits would be 80 X 10~ 6 volts and 160 X 10~ 6 volts, between which 

 the voltage should be determined to approximately 0.4 X 10 -6 volts. 



The necessity for a potentiometer shunt may be very easily shown. If the 

 apparatus is to be direct reading a change of 0.4 X 10 -6 volts involving a 

 change of 0.1 ohm in the potentiometer setting then a current of (0.4 X 10~ ) 

 -f- 0.1, or 4 X 10~ 6 ampere is required, and this, if a regular series circuit is used, 

 demands the use of a circuit resistance of 2-t- (4 X 10~ 6 ) or 500,000 ohms. 

 Since this is hardly practicable, it has been decided to shunt the potentiometer, 

 leaving the current in the potentiometer itself 4 X 10 -6 ampere, but taking 

 from the storage battery about 0.01 ampere, and causing the remainder to flow 

 through the shunt. For the main current a value of 0.0102 ampere has been 

 decided upon, as this permits the use at M of a 100-ohm coil. The value of S 

 is then (4 X 10~ 6 X 15000) 4- (0.0102) = 5.88 ohms. The total resistance of the 

 circuit is 2.0^-0.0102 or 196 ohms, 100 ohms being taken by M and about 6 

 ohms by S in parallel with P, leaving still 90 ohms necessary to be taken up in 

 R, Vi, V 2 , V 3 , and V 4 . 



To determine the proper value for each step of the variable resistances, it 

 must be noted that while voltages as high as 160 X 10~ 6 volts are to be meas- 

 ured, yet a deviation of 0.2 X 10 -6 volts will in itself produce an error in the 

 results sufficient to affect the nearest hundredth of a degree. From this it is 

 seen that the current must not vary by 2 parts in 1600, so that each step in the 

 variable resistances must not make more than this fractional change in the 

 resistance, or (2 -M600) X 196 = 0.25 ohm. This represents the maximum 

 allowable change; consequently the steps in the resistance as actually made 

 are smaller than this. The smallest steps are in the resistance V 3 , which is 

 composed of nine 0.1 ohm coils. Similarly V 4 comprises nine 1.0 ohm coils, so 



