Final answer:
No, a { extbf{sundial}} 100 miles directly north would not read the same time because of the difference in longitude and geographic latitude, as well as variation in the Sun's path with seasons. Sundials rely on the sun's position in the sky, which changes slightly with longitude and requires adjustment for latitude. Sundial time also differs from standard clock time due to time zones.
Step-by-step explanation:
No, a sundial will not read the same time 100 miles directly north due to several factors. The most notable is the difference in longitude between the two locations. As the Earth rotates, different longitudes experience noon at different times, with a general rule that every 15° of longitude corresponds to a one-hour difference in solar time. Since sundials are based on the position of the sun in the sky, a sundial located 100 miles north will generally show a slightly different time than one at your original position, unless both are at the exact same longitude.
Sundial time also differs from standard clock time due to the creation of time zones which have been established to keep time uniform within certain regions, irrespective of solar time. Also, the sundial's gnomon must point towards the celestial pole to work equally well throughout the year, and the angle of the gnomon will differ based on geographical latitude. This is because the angle between the gnomon and its base should equal the geographic latitude to accurately measure time.
Lastly, the shadow direction of the gnomon at noon will indicate the correct time, but at other times of the day, the shadow's direction and the angle it makes with the sundial's base (representing the hour lines) may vary with the seasons due to the Sun's varying path across the sky.