36 *N THE STANDARD OF WEIGHT AND MEASURE, 



every practical application of the mathematics to the purpofes 

 of real utility, that I have no hefitation in undertaking the 

 humble office of commentator on lb valuable a text. 

 &eal cubic di- II. It is ftated in § 1 3* that the produft of the three mean rrtea- 



^"sTvelyS fures of the fldes ofthe cube > viz ' 1 *- 98882 X 4-9S955 X 4.98925, 

 folids. is 1 24. 189 17: this however is erroneous, it being in fact 



1 24. 1 92246. The folid content of the cylinder was 75.247 1 49, 

 as already ftated in the preceding paragraph, and that of the 

 fphere (§ 28) = 6.007 45 3 x .52359878 = 113.51914-7 cubic 

 inches. 

 CorteAionfor HI. Suppofing the brafs fcale and thefe bodies to be at the 

 thTkS" rC ° ^ ame degree °f neat > tne * r apparent dimenfions as meafured by 

 it would be the fame whatever was the temperature of both ; 

 the fcale being of the fame fubftance, and confequently ex- 

 panding and contracting with the bodies themfelves. Their 

 feal dimenfions however varying with the temperature, we 

 rauft aflfume fome certain degree of heat at which the gradua- 

 tions on the fcale are to be confidered as meafuring correfpon- 

 dent intervals of fpace. We will fuppofe this to be 6*0° of 

 Fahrenheit's thermometer. Now in order to afcertain the real 

 cubic meafure by the fcale when at 60°, of the quantities of 

 diftilled water difplaced by thofe bodies when they were 

 weighed in it, we mull add to or fubtraft from the nominal 

 cubic dimenfions of each, 3 millionth parts (vide Tab. I. in the 

 note on § 23), multiplied by the number of degrees above or 

 below 60°, at which they and the fluid were at each of thofe 

 times. 



At the time of their being refpeclively weighed in water, 

 therefore, the folid content of the cube at 60.2° (§ 22) was 

 124.192246 x 1.00000062= 124.192323 cubic inches of the 

 fcale when at 60°; that of the cylinder at 60.5° (fecond ex- 

 periment, § 23) 75.247149 X 1.0000015 = 75.247161 ; and 

 that of the fphere at 66° (§29) 113.519147 x 1.000019 = 

 113.521304. 

 Correction ne- IV. In appreciating the apparent difference of weight in £ 



ceffary for den- body when weighed in air or in vacuo, it has been ufual to 



fity and tempera- J . ° 



tire of the air. aflume, that air at a given temperature, and under a given 



* Thefe references with a § prefixed, are to the feclions fo num- 

 bered in Sir G. S. Evelyn's Paper, which it is thought proper te 

 mention here to fave the neceflity of repetition. 



2 preflure 



