Mr. J. J. Waterston on Solar Radiation. 509 



Let us study the same differences with the cooling in air : — 

 At r-jw. have 695 beats lst Difference 2 « ^ ^^ „ 

 r=J0 „ 220 „ » 206 „ 22 



r = 7 we have 576 beats , . «:<»,««„«« o,m 



r-14 „ 336 „ 1st Difference 240 2nd Difference 23 



r = 28 „ 119 „ " ' 



r — 9 we have 484 beats 



18 „ 254 

 r = 36 „ 44 



1st Difference 230 2nd Difference 20 



Thus it appears that in air the cooling takes place in a ratio 

 greater than r, the first difference of the times diminishing and 

 the second difference slightly increasing between 247 and 210. 

 The limiting value of the first difference must be 294 when 

 r=0, and 294 minus the first difference increases nearly as\/r. 

 An empirical formula constructed in conformity with this ratio 

 cannot differ much from the observations*. 



Let A represent 1st difference, and g a constant, 

 A = 294-y y> 

 and 



294-247 liyifl0 294-210 Q , .. 

 9= — 7^- =17'162 = -^ =&c. (nearly). 



* That is, within the above limits of the value of r; but since it makes 

 A«=0 when r=294, it is not to be trusted in the upper part of the scale. 

 Another empirical formula of better promise may be constructed on the 

 hypothesis that the second difference is constant. If we lay off the first 

 difference as ordinate to the mean proportional between the values of r to 

 which it belongs, the curve traced out would be the logarithmic curve if 

 the second difference were constant. Now it has every appearance of being 

 so. The mean of the four is 21, the extremes being 19 and 23, and the 

 irregularities are evidently casual. The equation derived from this is 



20 

 A a =217 + ^~^(log20-logr a ), the second difference being assumed 20. 



The following Table is computed from this value of A a : — 



r a -\-p = r v . r a +p = r v . 



5+ 0-7= 5-7 50 + 27-4= 77'4 



10+ 2-5=12'5 C0+35'4= 95'4 



15+ 4-6=19-6 70 + 43-9=113-9 



20+ 7-1=27-1 80+53-2=133-2 



30+13 =43-0 90+63-2=153-2 



40+198=59-8 100+73-6=173-6 



The influence of the air in conveying away heat thus increases in a much 

 higher proportion than r. Further experiments are required to test this 

 at the higher parts of the scale, also to determine whether the ratio of 

 r a to r v is not affected by the size of the spherical reservoir. The actual 

 time of cooling must augment with the diameter of the sphere, but the 

 ratio of the times in air and in vacuo is probably not affected by the dia- 

 meter. 



