1870.] 



On the Indian Pendulum-observations. 



101 



range of 34° ; as the correction is approximately equal to one vibration 

 for 2° of temperature, or seventeen vibrations for the extreme range, the 

 true value must necessarily be determined with the utmost possible 

 accuracy. 



(8.) In Section XIII. of my General Report on the Operations of the 

 Trigonometrical Survey for 1866-67, I have fully described certain mea- 

 sures which were taken to determine the coefficient of linear expansion. 

 Briefly, they were as follows : vibrations were observed, at high and low 

 temperatures, under the lowest pressure which could be obtained in the 

 vacuum-apparatus at Kaliana, and at the natural pressure at Masoori ; the 

 expansions were also determined at high and low temperatures by direct 

 micrometric measurement, with the following results : — 



Pressure, in Factor of expansion 

 inches. for 1° Fahrenheit. 



At Kaliana .. 3'5 000,011,10 } ' , 



„ Masoori .. 23-5 000,010,01 j b 7 Orations. 



„Dehra.... 277 000,009,73 by direct measurement. 



Thus the value of the expansion which was determined from vibrations 

 under a pressure of 3*5 inches was 14 per cent, greater than the value 

 determined by direct measurement, at the natural pressure. I stated in 

 my report that "whether this is due to an actual increase of expansion for 

 a decrease of pressure or to the action of other phenomena which are at 

 present unknown or only imperfectly known, is a problem for future 

 solution." 



(9.) Experiments have been made at the Kew Observatory for the 

 purpose of investigating this question ; they are described in the ' Pro- 

 ceedings of the Royal Society,' No. 113, 1869. Owing, however, to 

 difficulties which were experienced in working with artificial temperatures, 

 the results were not conclusive as regards the present difficulty, and the 

 hope was expressed that the question would find its best solution by our 

 labours in India. 



(10.) The temperature-coefficients which have been employed in the 

 preliminary reductions are those which were obtained from the observations 

 at Kaliana, viz. : 



For No. 4 pendulum 0*485 vibration per diem for 1° Fahrenheit. 

 „ No. 1821 „ 0-470 



(11.) The pressure-coefficient which has been employed hitherto is 

 the mean of the two values determined at Kew, or 0*32 vibration per diem 

 for each inch of pressure at 32° Fahrenheit. 



(12.) In the reductions to the sea-level, the surface-density has been 

 assumed to be half the mean density of the earth. Dr. Young's formula 

 has been used exclusively for stations situated on tolerably level plains, 

 but for stations on hills the observations have been first reduced to the 

 general level of the country by computing the vertical attraction of the 

 elevated mass down to this level, the mass being divided into a number of 



