814 
DR. T. R. ROBINSON ON THE DETERMINATION OF 
Table XYII. 
No. 
AV\ 
124 
+ 0-54 
125 
+ 1-24 
126 
+ 1-40 
127 
+ 1-94 
128 
+ 1-35 
129 
+ 2T8 
130 
+ 1-95 
131 
+ 1-81 
132 
+ 0-63 
133 
-0-27 
No. 
aV / . 
134 
+ 0-75 
135 
+ 0-37 
136 
+ 1-17 
137 
+ 1-00 
138 
+ 1-26 
139 
+ 1-33 
140 
-0-22 
141 
+ 0-33 
142 
+ 1T0 
143 
+ 0-04 
No. 
AV'. 
No. 
AV'. 
144 
-0-04 
152 
-(- 0*63 
145 
-0-82 
153 
-0-66 
146 
-1-09 
154 
-0-62 
155 
— 1T9 
147 
-0-54 
148 
149 • 
150 
151 
+ 0-87 
— 0T5 
-0-59 
-1-43 
156 
157 
158 
+ 0-38 
-1-40 
— 151 
Here also the entire set is nearly as well represented with y=0 as by the entire 
equation. The probable error of Table XYI. =q = 0‘630. The maximum value of 
AY' in it — + 2 '18 ; the minimum = — T51. In the other case the probable error 
= :p0 , 637 ; the maximum = -fl'66; the minimum = — 2T8124. It was observed 
on a different day from the rest of that series, and its difference from its neighbours 
seems to imply an excess of friction in the latter. The table might evidently be 
improved by farther approximation. 
(43.) The plotting of No. IY, Plate 69, resembles the other except in one notable 
circumstance. The dots of the first series (200 to 210) are lower than the rest, 
although their general direction is nearly parallel to that of the others. This 
indicates that the friction during their course was greater than on the following 
days. This may have been caused by bad oil, as already mentioned, and a rough 
measure of f taken then gave it =250 grains instead of 185, which I computed it to 
be from the disc measures. The viscidity of the oil would increase f ; but if, asis 
probable, it was also applied to the pivots of the brake, it would lessen the pressure 
of the rubbers and the brake friction. Both these effects seem to have taken place to 
such an extent that I find it impossible to derive from the observations any constants 
which will represent the entire set. It was scarcely to be hoped that minimum 
squares could give a good result. I tried them, omitting the first 11, and had 
a=3'682 ; /I=7'541 ; y= — 18T72. These are inadmissible; a is too far above my 
measures, and y far too negative. Assuming y=0 the result is no better. Taking, as 
in the others, a=0'9, the measured one for II., the result is still worse. It seemed 
however possible that though a and /3 were both astray, their ratio might approximate 
to the truth. This gives £C=1'0240; x 2 =z= 1'049. I computed by these AY', in- 
tending to correct them by the formula (YI.). The second series was well represented; 
in the first the V' was too small ; in the rest too great, and it was not possible by any 
correction of the constants to represent the whole. The constants just given for 
No. II. failed utterly ; but to my surprise those used for Nos. I. and III. were not 
