18 Captain Sabine's Experiments on the 



time T' in which the same number of vibrations would have 

 been performed at any other temperature, t', adopted as a time 

 of comparison, T'=T [1 ± .00017 (t — £')] ; the sign + being 

 applicable when the observed temperature is lower than that 

 adopted as a mean, and — when it is higher. 



By the same means, needle 4 was found to lessen the time 

 of performing 170 vibrations 7".6 by a reduction of tempera- 

 ture of 21°, from 62° to 41°; and to increase it 16".8 by an 

 augmentation of temperature of 64°.5, from 57° to 121°. 5. The 

 sum of the two experiments 24".4 -f. 85°.5 = 0".285, the 

 increase for one degree of Fahrenheit ; and 0".285 -f- 15' 20" 

 the time of 170 vibrations s -0003 the multiplier. For this 

 needle, therefore, 



T'=T [1 ± -0003 (t-ty]. 



Needle 5 was found to lessen its time of performing 240 

 vibrations 20".25 by a reduction of 22°, from 64°.25 to 42°.25 ; 

 and to increase the time 25".4 by an augmentation of 39°, from 

 68° to 107°. The sum of the two experiments 45".65 -f59°.25 

 =0".75, the increase for one degree of Fahrenheit ; and r/ .75 

 -f- 31' 07", the time of performing the 240 vibrations qa -0004, 

 the multiplier. For this needle, therefore, 



V b= T [1 ± -0004 (t-t')~\. 



Needle 6 was found to lessen its time of performing 100 

 vibrations 2".78, by a reduction of 24°. 5, from 67°.5 to 43°; 

 and to increase it 4". 51 by an augmentation of 48°, from 65° 

 to 113°. The sum of the two experiments is 7".29 -f- 72°.5 

 = 0".l, the increase for one degree of Fahrenheit; and 0".l 

 -r 10' 38", the time of performing 100 vibrations = -00016 

 the multiplier. For this needle, therefore, 



T' = T[1 ±.00016 (*-*')]• 



When observations with horizontal needles are widely ex- 

 tended, so as to include a considerable range of intensity, and 

 consequently much difference in the time of performing a given 

 number of vibrations, it is not sufficient for the just relation of 

 the results, that the vibrations should be made on all occa- 

 sions in similar arcs : it is also necessary, in such case, that the 

 time of vibration at each station should be increased to what 

 it would have been had the vibrations been made in infinitely 



