810 
DR. T. R. ROBINSON ON THE DETERMINATION OF 
v=5 to v=9, a=10'896 ; £=11*360 ; y=5776 
All above 9 . 10*896 11-227 5*291 
All above 5 . 10‘896 11-830 2'437 
All .... 10-896 13-104 —6*505 
10-896 11-880 +1-600 
The values of - =x= T0903 ; —='?/= 0*1 468 ; and x^-\-y=z— 1"3356. 
a a J J 
(39.) The observations with No. I. constitute two series : the first (l"79) taken 
while there was only one roller to sustain the centrifugal pressure ; the other (80 "123) 
after two were applied. 
Plate 66 shows the plotting of the two : those of the first being represented by 
dots, those of the second by small circles. There is the same irregular distribution, 
and it is still more difficult to trace the curvature. It is to be remarked that the 
system of small circles falls below that of dots, which implies that the friction for it 
must have been greater than I assumed ; but for both the average curve is nearly 
the right line. 
In applying minimum squares, my previous experience made me omit those where 
v was very small. I obtained — 
First set 73. a=12-299; £=17-488; y= — 15*372; a'= 11*350 ; £'=13-401. 
Second set 39. a= 8*721; £=12-974; y= — 14-397; a'= 7753; £'= 8-990. 
Total 112. a= 11*183 ; £=16*954; y= - 19-862; a'= 9-880; £'=11*538. 
The second, as might be expected from the plotting, is not to be relied on ; and in 
all of them the negative value of y is too great. It wall be seen in the subsequent 
values of AY' that those for May 26 are too small, so as to confirm my suspicion that 
the F which I used was too small. This may have been owing to the engine having 
been stopped during part of the time, or else doing lighter work. I have already 
mentioned that a set of measures taken by Mr. IT, Grubb while the engine was not 
acting gave larger results than those in Table IY. For B=36 the excess was 406*4 ; 
the AY' for 123 would correspond to an excess of 291. Under the circumstances this 
set by itself is useless ; but as the earlier part of it seems correct, it may be retained 
in the total. But I give a double weight to the first. Using - x - 0 - measured a as before. 
First set 73 . a= 10706 ; £= 12-328 ; y=0’524 
„ reduced by (V) . . ,, 12 '269 ; 0"937 
,, omitting v<3 . . ,, 12778; 0 936 
Total 112 „ 13-193; — 2*991 
10-706 12-492 — 0*148 
Hence x— 1 "1648 ; y=— 0‘0138 ; 2=1-3414. 
In both cases £ seems tolerably certain ; but it is not so for y, especially in No. III. 
