This writer seems to differ a good deal from Blith about the advantage of **interchanging** tillage and pasture.

Two relations R and R' are said to be ordinally similar, if a one-one relation holds between the members of the two fields of R and R', such that if x and y are any two members of the field of R, such that x has the relation R to y, and if x' and y are the correlates in the field of R' of x and y, then in all such cases x has the relation R' to y', and conversely, **interchanging** the dashes on the letters, i.e.

(7) **Interchanging** these values =m log r, 4, = mO, 4,+4,i =m log rei e (8) gives a state of vortex motion, circulating round Oz, called a straight or columnar vortex.

By testing the beam with the scale-pans attached and equal weights in the pans, and noting carefully the position which it takes up; and then **interchanging** the scale-pans, &c., and again noting the position which the beam takes up, a correct inference can be drawn as to the causes of error; and if after slightly altering or adjusting the knife-edges and scale-pans in the direction indicated by the experiment, the operation is repeated, any required degree of accuracy may be ob - tained by successive approximations.

Thus to divide by a fractional number we must multiply by the number obtained by **interchanging** the numerator and the denominator, i.e.