18 Mr. W. Galbraith on the Experiments 



boiling point is = 0*0018709 part of itself. This gives for every 



degree of Fahrenheit ^~^ =0-0000104 part of itself, or 



0*00001 nearly the value of 8L, which agrees sufficiently well 

 with Capt. Kater's experiments. 



Substituting this in formula (3) it becomes A L = -^q^qJ^^) ; 



or, in words, shift the decimal point in the length L five 

 places to the left, and multiply by the number of degrees of 

 chance of temperature, the result will be the expansion at the 

 rate we have mentioned ; otherwise the actual variation by 

 experiment from formula (3) must be employed. If the 

 value of aL formula (5) be subtracted in formula (4-), we get 



^N=-^^ (6) 



^ 100000 ^ ' 



Or shift the decimal point in \ N five places to the left ; this 

 result, multiplied by the number of degrees of change of tem- 

 perature, will give the correction required. 



If N do not differ much from 86400, formula (6) would be- 

 come AN = 0*432« (7) 

 And this may be considered as sufficiently accurate, unless n, 

 the number of degrees of change of temperature, be consider- 

 able, or N differ above 100 seconds from 86400, the expan- 

 sion for each degree of Fahrenheit's thermometer remaining 

 the same. 



To exemplify these, let us suppose w = 6° Fahrenheit; then 

 by formula (7) AN = 0*432 x 6 = 2=*592, the retardation or 

 acceleration in a day for that expansion in a brass pendulum. 



At 62° Fahrenheit, Capt. Kater found the pendulum sent out 

 with Capt. Hall made 86235*98 oscillations in a day : it there- 

 fore, from an expansion answering to 6° of Fahrenheit's ther- 

 mometer, would be retarded 2'*592, and 86235°*98 — 2°*59 = 

 86233^*39, the number it would actually perform in the same 

 place at a temperature of 68°. 



Now, by our ordinary treatises on mechanics l:V::n": w" 

 we have, since Capt. Hall found the same pendulum made 

 86101*34 oscillations in a day at the Galapagos (86233*39)*: 

 (86101*34)-:: 39'"*13929: 39'"*019514, the length of the pen- 

 dulum oscillating seconds at the Galapagos at 62° of Fahren- 

 heit, that at London being 39'"*13929. This operation, how- 

 ever, is tedious. 



The formula will give an approximation to this for AN = 

 86233*39 — 86 101 -34 = 1 32*05. Hence from formula ( 1 ) A L = 

 L X AN _ 39139 2 9x132-05 _ _ ^.n, qs7 

 ■"In"- 43116-7 - uiiy»^ 



Hence 39*13929 — 0*11987 = 39*01942, which differs from 



the 



