[Footnote 6:  The following is a diagram of the first principal meridian, and of the base line running across southern Michigan.  A B is the principal meridian; C D is the base line.  The figures on the base line mark the range lines; the figures on the principal meridian mark the township lines.  E is township 4 north in range 5 east; F is township 5 south in range 4 west; G is township 3 north in range 3 west. [Illustration] As the intervals between meridians diminish as we go northward, it is sometimes necessary to introduce a correction line, the nature of which will be seen from the following diagram:—­ [Illustration:  DIAGRAM OF CORRECTION LINE.]]

[Footnote 7:  In Philadelphia the streets for the most part cross each other at right angles and at equal distances, so that the city is laid out like a checkerboard.  The parallel streets running in one direction have names, often taken from trees.  Market Street is the central street from which the others are reckoned in both directions according to the couplet

  “Market, Arch, Race, and Vine,
  Chestnut, Walnut, Spruce, and Pine,” etc.

The cross streets are not named but numbered, as First, Second, etc.  The houses on one side of the street have odd numbers and on the other side even numbers, as is the general custom in the United States.  With each new block a new century of numbers begins, although there are seldom more than forty real numbers in a block.  For example, the corner house on Market Street, just above Fifteenth, is 1501 Market Street.  At somewhere about 1535 or 1539 you come to Sixteenth Street; then there is a break in the numbering, and the next corner house is 1601.  So in going along a numbered street, say Fifteenth, from Market, the first number will be 1; after passing Arch, 101; after passing Race, 201, etc.  With this system a very slight familiarity with the city enables one to find his way to any house, and to estimate the length of time needful for reaching it.  St. Louis and some other large cities have adopted the Philadelphia plan, the convenience of which is as great as its monotony.  In Washington the streets running in one direction are lettered A, B, C, etc., and the cross streets are numbered; and upon the checkerboard plan is superposed another plan in which broad avenues radiate in various directions from the Capitol, and a few other centres.  These avenues cut through the square system of streets in all directions, so that instead of the dull checkerboard monotony there is an almost endless variety of magnificent vistas.]

[Sidenote:  and of Western counties.] If now we look at Livingston County, in which, this township of Deerfield is situated, we observe that the county is made up of sixteen townships, in four rows of four; and the next county, Washtenaw, is made up of twenty townships, in five rows of four.  Maps of our Western states are thus apt to have somewhat of a checkerboard aspect, not unlike the wonderful country which Alice visited after she had gone through the looking-glass.  Square townships are apt to make square or rectangular counties, and the state, too, is likely to acquire a more symmetrical shape.