the Heat-conductivity of Stone, 



259 



therefore the value of SE will, as a rule, depend on the value 

 of the trigonometrical expression in the last equation. Con- 

 sequently we have calculated, as follows, the values of the tri- 

 gonometrical expressions in equations (10) and (11) for 

 different values of a : — ■ 



*, in degrees. 



(sin*— aCOSa)(a— sin a COS a) 



& — sin « cos a 



« sin a (« 2 -}-« sin a cos « — 2 sin 2 «) 



a. sin 2 a 



o 



20 



64965 



0-67789 



30 



18-304 



0-69205 



50 



6-6181 



0-74277 



70 



3-5864 



0-83524 



J)0 



21975 



10023 



110 



1-5223 



1-3220 



130 



1-2369 



20740 



140 



11927 



2-9081 



150 



1-2356 



4-6616 



ItiO 



1-4506 



9-5326 



170 



2-7473 



35 073 



180 



a© 



00 



The curve A B, fig. 5, shows the scale of possible error in 

 K for different values of a ; and the curve C D shows the scale 

 of possible error in E. We see, therefore, that for given errors 

 in v and v the error in K is very great for small values of a ; 

 so that, for instance, values of « less than 50° are very unsuit- 

 able for use in calculations to determine K; and therefore, if we 

 had used such a size of ball as gave a value of a less than 50°, 

 we should have had to employ a new ball of more suitable size 

 to get a more correct answer. There is a diminution in the 

 possible error of K as a increases to about 140° ; and from 160° 

 the possible error increases rapidly and becomes infinite when 

 «=180 0, The error in E (the emissivity) is least for small 

 values of a, and it increases with a. Thus, to find K and E 

 with errors of approximately the same amount, we ought 

 to use such a size of ball as will make « about 120°. If K 

 only is wanted accurately, we ought to make a about 140° ; 

 but if E only is wanted, then a should be made as small as 

 possible. 



We here append a list of accurately determined values of a 



E?* 



for different values of ^, which Table, for reference further 



on, has been continued beyond ot equals 180°: — 



S2 



