OF THE ATMOSPHERIC TEMPERATURE. 113 



The above tabular values are derived from more than 22 years of hourly observa- 

 tions made at eight stations. The assumption that the average oi hourly observations 

 equals the daily average, is so nearly correct as to require no further consideration; 

 thus at Thunder Bay Island, Mich., the mean of 24 observations taken at the full 

 hours is 42°. 84, the mean of 24 observations taken at the intermediate half hours 

 is 42°. 83, which is also the mean of the 48 semi-hourly observations. 



Times of Sunrise and Sunset in different Latitudes and for every tenth day in 

 each month. — We meet frequently, particularly in the older meteorological observa- 

 tions, with records taken at the times of sunrise and sunset ; this practice, now 

 generally superseded by better selected fixed epochs, still obliges us to resort to 

 tables of times of sunrise and sunset, Avith the day of the month and the latitude as 

 arguments, whenever we aim at a careful reduction of the recorded temperatures. 



In computing such a table for various latitudes and to answer for any year, the 

 deduced times can only be more or less close approximations on account of the small 

 variations, in different years, in the sun's declination, in its distance, and in the 

 equation of time, on the same nominal day. Fortunately a few minutes of error 

 witli a tendency to cancel itself for long series, are of little moment in the meteor- 

 ological record. The tabular quantities will generally be found correct within 2 

 or 3 minutes, excepting in the higher latitudes, where this limit may occasionally 

 be slightly exceeded. 



The times were computed by the formulae 



^^^ ^ ^ co^^--^in^sin^ ^j^^ i,' = 90° + 7- — 7t-f-s+fZ = 90°51 'nearly, 

 cos ^ cos 



where ^ = latitude, 



^ =: sun's declination, 

 ^ = sun's zenith distance, 

 t = hour angle, 



r = refraction in horizon, 

 s =^ sun's semidiameter, 

 7t = sun's horizontal parallax, 

 d = dip of horizon. 



The apparent time was changed to mean time by application of the equation of 

 time (JE). 



The value of S may vary in different years, for the same nominal day, by J^^ 9' 

 nearly, from its average amount; the value of s hardly varies as much as -}- 0'.5 ; 

 the variations in E for the same nominal day amount to less th an J^ i of a minute, 

 and the maximum half-daily change is of the same amount. The use of the value 

 of 8 for the meridian of Washington instead of any other meridian within the limits 

 of the United States, cannot occasion an error as great as that previously noted for 

 8. The changes in the horizontal refraction due to extremes of temperature (and 

 atmospheric pressure) may amount, at most, to about ^ S' from the mean state, 

 assumed at 35' (temp. 50° Fah.; pressure 30 inch.). The value of ^ was taken as 

 constant, S was taken from the ephemeris for the times of sunrise and set for those 

 parts of the year where the use of the meridional value would introduce a notable 

 defect. Both, 8 and E, refer to average years. 



15 February, 1875. 



