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(13.) Newton succeeded in determining the thickness of very thin laminæ of transparent substances by observing the colours which they reflect. A soap bubble is a thin shell of water, and is observed to reflect different colours from different parts of its surface. Immediately before the bubble bursts, a black spot may be observed near the top. At this part the thickness has been proved not to exceed the 2,500,000th of an inch.

The transparent wings of certain insects are so attenuated in their structure that 50,000 of them placed over each other would not form a pile a quarter of an inch in height.

(14.) In the manufacture of embroidery it is necessary to obtain very fine gilt silver threads. To accomplish this, a cylindrical bar of silver, weighing 360 ounces, is covered with about two ounces of gold. This gilt bar is then wire-drawn, as in the first example, until it is reduced to a thread so fine that 3400 feet of it weigh less than an ounce. The wire is then flattened by passing it between rollers under a severe pressure, a process which increases its length, so that about 4000 feet shall weigh one ounce. Hence, one foot will weigh the 4000th part of an ounce. The proportion of the gold to the silver in the original bar was that of 2 to 360, or 1 to 180. Since the same proportion is preserved after the bar has been wire-drawn, it follows that the quantity of gold which covers one foot of the fine wire is the 180th part of the 4000th of an ounce; that is the 720,000th part of an ounce.