778 MR J. D. HAMILTON DICKSON ON 



These lines are shown on the diagram ; they cannot be said to meet in one point. A is 

 farthest out, F is next to it, the other four, however, are very nearly concurrent. On 

 looking- at the diagram, it will be seen that from —50° to - 150° the curve has been 

 allowed to fall somewhat below the observations, and therefore the series of mid-points, 

 a-y, . . .a, is rather more to the left than it ought to have been. This has the 

 greater effect, naturally, at the lower temperatures, and hence, as the lower a-points 

 are more correct, the upper ones tilt the top end of the A-line too much to the left and 

 make the lower end correspondingly swerve to the right. The same cause equally 

 explains the position of the F-line, so that one is somewhat justified in omitting the 

 A- and F-lines from the determination of the point where the lines meet (the centre 

 of the curve). Using therefore only the B, C, D, and E lines, the method of least squares 

 gives, as the most probable position of the centre of the curve, 



t= 44-307° C, E= -36073-6 C.G.S. units. 

 The curve thus determined is one branch of an hyperbola, with a sloping axis. The 

 inclination of the axis to the axis of E.M.F. can be determined from the lines A, B, C, 

 D, E, F ; but, as even slight variations in the inclinations of these lines cause abnor- 

 mally large variations in the value of this angle, seeing it depends not on the absolute 

 values of the angles of these lines but on their differences,* the results cannot be very 

 strongly maintained. 



Having accepted the curve as an hyperbola, and found its centre, attempts were 

 made both by calculation and mechanically to determine the slope of the axis. Three 

 separate calculations gave —5*63, — 5'44, —5*46 as the values of the tangent of the 

 (obtuse) angle made by the axis of the curve with the axis of temperature. The 

 mechanical process was carried out thus : — two rulers, one perpendicular to the other, 

 were laid upon the curve so that the edge of one should be opposite the mid-point of 

 the other; they were then carefully moved together, like a T-square, round the 

 centre of the curve, through which the former edge passed, until this edge was seen to 

 bisect the chord of the curve shown by the other perpendicular edge. Taking repeated 

 observations in this way, and combining their results with those already obtained by 

 calculation, it was found that the values of the tangent of the angle, made by the axis 

 of the curve with the axis of E.M.F. , converged round a central value 1/5 '45, which was 

 taken to be the final result. 



To get the semi-axes of the curve was now a simple matter. The length of the 

 transverse semi-axis was got by measuring along the axis the distance between the 

 vertex and the centre. The conjugate semi-axis was found thus : — If in the usual 

 equation for an hyperbola, x 2 /a 2 — y'/b 2, = 1 , we put x = aj1, the corresponding value 

 of y is 6. These two semi-axes were thus found to be 7 "156 inches and 2 "281 inches, 



* Suppose a cpiantity x were to be determined from two numbers such as 542-3 and 5487, each of which could be 

 depended on to one-tenth per cent., i.e. the}' might lie between 54T8 and 542-8, and 548-3 and 549-2 ; and suppose 

 that x depended on their difference. This difference, therefore, might vary from 549'2- 541 - 8 to 548'2-542 - 8 — that 

 is, from 7 - 4 to 5'4. Thus an error of inappreciable amount on the numbers themselves might cause a difference on the 

 values from which x was to be determined of from 25 to 33 per cent. 



