1865.] Pendulum Base Observations for India. 431 



C. Correction for temperature. Two thermometers were fixed, one to 

 the lower, the other to the upper part of a brass bar, which was made by 

 Mr. Adie, of precisely the same form as the pendulums. 



The brass bar being fixed near the middle of the receiver, close to the 

 swinging pendulum, every, change in the temperature of the latter was of 

 course shared by the brass bar, and indicated by the two thermometers, 

 which were extremely sensitive and read to '05 of a degree. The readings 

 of these two thermometers were in the first instance corrected for index- 

 error. The instruments having been very carefully compared with the 

 Kew Standard, a table of index-errors was made from these comparisons, 

 and, by interpolation, giving the errors from degree to degree. Another 

 correction was applied for the observations in the exhausted receiver on 

 account of the eifect of exhaustion on the glass tubes of the thermometers. 

 This effect was determined very accurately by a series of experiments at 

 Kew, and found to be equal for both thermometers, and amounting to 

 0'43 for a decrease in pressure of 29'210 inches. This correction is 

 smaller than that assumed by General Sabine and the late Mr. Baily, who 

 make it | of a degree for the thermometers which they employed. 



Our experiments showed the remarkable fact that the correction is by no 

 means proportional to the decrease in pressure. The diminution of the pres- 

 sure from 30-080 inches to 13-610, that is, by an amount of 16-470 inches, 

 gave a correction of only 0< 0/>2, while a further decrease of 12-820, bringing 

 the pressure to 0790 inch, gave for one thermometer 0'377, and for the 

 other 0-385. 



The mean of the upper and lower thermometer reading will give the 

 temperature of the pendulum at the moment of the observations ; and if we 

 call t, t', t", t'" the temperatures found in this manner for the successive 

 observations, we have 



t_ + t_ t' + t" t" + t'" 

 2 ' ~~2~' 2 



as the most probable temperature during the interval between two con- 

 secutive observations. These intervals being of unequal length, we will 

 call n, ri , ri', ri", the number of coincidence-intervals which they contain ; 

 and calling t the mean temperature of the whole experiment, we have 



n-\-ri 



Table III. gives the mean temperature found in this manner for each ex- 

 periment, and shows the mean of all observed temperatures for each pendu- 

 lum, to which temperature all the experiments made with that pendulum 

 have been reduced. For this reduction it would have been best if we had had 

 an opportunity of swinging the pendulums at extremes of temperature, say 

 about 50 distant from each other. But the desirability of sending the appa- 

 ratus to India under the care of Mr, Hennessey, who left by the March mail, 



