Galvanometer when used with the Thermopile. 421 



ually diminishing amplitude, as indicated by the first term. 

 Evidently r is the period of vibration of the needle, and 



— its logarithmic decrement. 



To test the above equation a series of observations was 

 made with a Thomson tripod galvanometer, every precaution 

 being taken to secure a constant source of heat, and to avoid 

 errors due to draughts of air, magnetic disturbances, etc. The 

 period of vibration of the needle, and its logarithmic decrement 

 (with the thermopile in circuit) were first determined by the 

 ordinary methods. Data for the curve shown in the figure 

 were then obtained by recording on a chronograph the times 

 of the successive maxima and minima, and the time at which 

 the needle passed each tenth division of the scale. Assuming 

 that the equation derived above truly represented the motion, 

 I then attempted to analyze the curve into its two components, 

 and after a few trials obtained the curves II and III of fig. 1. 

 These two, when combined, give exactly the motion that was 

 observed, while both are capable of being quite accurately 

 represented by equations of the form indicated in (6). For 

 example curve II was found to agree closely with the equation : 



0'~31O — 283 £-°- 037i (7 



the differences between observed and computed values of 6' in 

 no case exceeding two per cent. The time of vibration of the 

 needle, as computed from curve III, was found to be 6*1 

 seconds, while that observed when the needle was allowed to 

 swing freely, was 6*0 seconds. The observed and computed 

 values of the ratio of damping show a similar close agreement, 

 being equal to 1*28 and 1*31 respectively. 



The fact, which has already been mentioned, that the first 

 throw of the needle bears a constant ratio to the final deflec- 

 tion, is confirmed by equation (6). Since T is a factor of the 

 right hand member of the equation, and since the expression 

 inside the bracket is independent of T c , the only effect of a 

 change in the intensity of the source of heat would be to in- 

 crease or diminish all the ordinates of curve I in the same 

 proportion, the ratio of any two ordinates remaining the same. 

 If, therefore, the final deflection of the needle is proportional 

 to the quantity of heat received by the pile, the first throw 

 will also be proportional to this quantity, and may in all cases 

 be used instead of the final deflection. Experiments made in 

 1888 to test the above conclusion showed the ratio to be con- 

 stant for deflections ranging from I00 mm to 20 mm , but for 

 smaller deflections there was apparently a deviation from the 

 law. I have therefore repeated the observations, using great 



