F. E. Stimpson on Farmer's Theorem. 373 
the rate of the gas consumed by the two burners ey 
one gave 3°66 cubic feet and the other 7:32 cubic 
Now from this it will be seen that the ratio of PERI 
was as 1 to 2, but the ratio of the lights being as the squares of 
the distances from the disk, becomes 200? : 80? or 1:16, and 
the result on the paper should stand, 
8°66* : 7'32+=1: and not 
3°66? : 7:32? =1:4. 
In other words, the lights were ‘proportional ie fourth 
powers of the consumptions and not to the squa 
In a 2, 8 and 4, the ratio of the s iss ares of con- 
periment 5, the ih ratio is certainly much nearer than the 
ratio of the squa 
hit eee tabi will, I think, suffice to show these various 
relatio 
leulated 
sy, | RS | ES | eo [geri ee 
Exp’t. | tion per sity by e | er ofcon- of 
hour. ae old laW-| squares. | sumption. | Old law. sans res. | power. 
3°30 A 1 iy 0 0 
9 4°35 21 1:32 13 2°098 —O°78 —0°37 | —0-00 
5-136 3°2 1°55 2°42 3°222 —1°65 —0.78 | +0°022 
5°556 4:0 1°68 2°83 3-995 — 2°32 —1:17 | —0-005 
3-72 1 L js eee 6 aoe 
3 4°884 z- 1°312 1-72 glee —0°628| —0°28 pa 
6°000 3° 161 2°60 meets —1°39 ~— 0°40 ee 
7-218 4 1:94 3-76 ees —2°06 —0°24 pigs <i 
4 5 18 § 3 +f ites te acne 
9°519 4 2114{ 446 es — 1886; +046 ade 
5 5-16 1°85 1°85 1°85 reeaena 0 0 ae 
1006 4:00 3°70 5°72 ae pa Ae +1°72 epee 
n experiment 6, the reductions have been made by applying 
Geta aes tion for the candle in both cases; the 
yori ate by Farmer’s Theorem being applied ae to the ¢ =e 
sumption of the gas, and so applied gives the most 
results, the enihanh shown by the old rule however, ie #4 
candles) is no greater than might have between 
SS even if the pensar. rege in both cases had teas 
[* Since the that tk 
pro gree of Cnt to 2”) but i in sp dig mci g of the posion of the disk — an 
It should twice as far from one flame as the other, i. e., the scree 
at 663, and thus the experiment supports the theorem. 
