The results given in the above table are probably true to the fifth place. The length of the standard bar was determined by comparing it with the standard yard. For this purpose the yards and bar were placed side by side in the same box, and the comparator readings taken on both of them, temperature being taken at the same time. The comparator readings were then reduced to what they would have been if the temperature had been 62°. The difference in the reduced comparator readings was the difference in the length of bar and yards at 62°. The yards were placed in regular order, and their ends kept in contact with spiral springs exerting a pressure of two pounds. Of all the observations taken, 93 were selected which were called good. The mean of these observations showed the yards to be .00107 shorter than the bar. The length of the yards, as previously determined, was 179.99890; hence the length of the bar would be the sum of these two quantities, (179.99997 United States inches.) The above observations were taken through a range of temperature from 29 to 6. During the time of the observations, the yards were taken apart and relined eight times. The probable error from observation of final result is .00002. There is, however, an uncertainty of .00100 in the total length of the five yards, when placed end to end, owing to irregularities in their end surfaces. These irregularities were discovered first by a difference in the total lengths of the five yards when placed in different orders; and again by a series of observations made on the central and diag onal lines of each yard. There is no means of obtaining a correction for the irregu larities; hence the uncertainty in the length of the yards, and consequently the bar still remains. The lengths given above were adopted for use until better means for comparisons are obtained.

Summary of results obtained.

The thermometers have been found to differ considerably from the standard. Their corrections are tabulated on page 2.

The coefficient, by which the readings of the Baumann comparator No. 1 must be multiplied to reduce them to American inches, is 1.0872..

The same for the Wurdemann comparator No. 1 is 1.0021.

The expansion of the brass standard bar for 1° Fahrenheit is .00174.

The same for five standard yards

The same for tube No. 1

The same for tube No. 2

The same for comparators..

.00176

.00014

.00002

.00008

The comparative lengths of the yards differ very much from the lengths marked on them, in one case .00065 inches. Their ends are not planes, but irregular surfaces, making in one case an angle of eight minutes, with the perpendicular to the axis. The sum of the central lines is 179.98890 United States inches, assuming yard No. 5 to be an exact yard.

The length of the standard bar is 179.99997 United States inches, with the uncertainty of .00100 inch. owing to the irregularity of the end surfaces of the yards. Very respectfully, your obedient servant,

Major CYRUS B. COMSTOCK,

Corps of Engineers, United States Army.

E. S. WHEELER,

Assistant United States Lake Survey.

Appendix E.

OFFICE UNITED STATES LAKE SURVEY,
Detroit, September 30, 1871.

SIR: I have the honor to submit the following report on the meteorology of the lake survey:

In March of the present year, a vacancy having occurred in this department, I was instructed by you to take charge of its computations and to inspect the accuracy with which the observations were being made.

It is but just to state that I found many and perplexing inaccuracies in the records of the observers, and the reductions, especially of the water gauges, were not in all cases satisfactory.

Having had other duties to perform, being in charge of the computing department of the Lake Survey, and having also an unforeseen amount of astronomical observations to make during the summer, I have had but little time to give to the study of results. I give herewith, for the years not already published, the results in tables, with as much accuracy as was possible from the data. In accordance with instructions from you bearing date August 7, I visited the stations to the east of Detroit and determined

Superior.
Milwaukee

Detroit

Cleveland

Erie.

Charlotte.

64 E

with care the zeros of water-gauges with reference to permanent bench-marks. Where the old bench-marks were to be found the zeros were again referred to these. The amount of error at any one of four stations was not less than half a foot. The heights of the cisterns of the barometers were also determined with reference to the zero of the water-gauges.

*

Very respectfully, your obedient servant,

General C. B. COMSTOCK,

Superintendent United States Lake Survey.

O. B. WHEELER,

Assistant Lake Survey.

Station.

The following table gives the mean monthly water level below the high-water mark of 1838, in feet and decimals of a foot, taken from the bi-five day means, for the months from April to November, inclusive, of the year 1870.

Formula for the temperature curve, placing the origin at January 15.

Ado+a cos 0+ a2 cos 20+ as cos 30;

for the Nth day, 0=.

N 365.25

X 3600+ b, sin + b, sin 20+b3 sin 30

TABLE 2 of the constants in this formula and the mean errors computed from Table 1.

The same formula under the following form, placing the origin at the beginning of the year: A=A+B sin (0+ C) + B2 sin (20+ C2) + B3 siu (30+ C3)

TABLE 4.-Minima, maxima, and vernal and autumnal mean.

SUPERIOR CITY, WISCONSIN.

Percentage of winds from the different points of compass for the year 1870.

Percentage of winds from the different points of compass for the year 1870.

Percentage of winds from the different points of compass for the year 1870.

Percentage of winds from the different points of compass for the year 1870.