310 
MESSRS. ROSCOE AND THORPE ON THE RELATION 
artificial horizon of black glass, which was carefully levelled before each observation. 
The watch used could he read to quarter seconds, and the Lisbon mean time was obtained 
by regulating the watch by means of the time-ball of the Lisbon Naval Arsenal, which 
falls at 1 p.m., and afterwards ascertaining the amount of the watch’s daily variation. 
In cases in which the altitude could not be determined by experiment, it has been cal- 
culated from the following formula, 
cos <p = cos . cos t . cos sin £ sinjq 
in which 
h represents the sun’s declination, 
^represents the latitude of the place = 38° 40', 
and t represents the sun’s hour-angle. 
It was necessary, in the first place, to ascertain what error was introduced into the 
determination of diffused daylight by any accidental variation in the distance of the 
brass ball from the sensitive paper. A series of experiments were made with this object 
on August 8th, 18G7, at 9 a.m., the blackened ball being placed at distances varying from 
140 millims. to 230 millims. above the silvered paper. These experiments showed that 
the ball placed at 
140 millims. 
gave mean reading 143-3 
or Chemical Intensity 0-116 
160 
143-6 
55 
„ 0-116 
190 „ 
„ „ 14L9 
55 
„ 0-116 
230 „ 
„ „ 136-8 
55 
„ 0-118 
consequently the height of the blackened ball may safely vary between 140 and 190 
millims. without producing any appreciable error. 
The following gives the elements of an observation, and may serve as a sample of the 
others, 134 in number, which were all carried out in a manner exactly similar, and form 
the data from which are derived the conclusions drawn in this paper. 
August 5th, 1867. 
Determination of Altitude . — 
Observed Calculated 
Observed 
Sun's 
time. time, 
h m h m 
double altitude. 
O l 
altitude. 
O i 
1st Observation. 3 37 p.m. 3 57 p.m. 
71 42 
35 51 
2nd „ 3 41 p.m. 4 1 p.m. 
Determination of Chemical Intensity . — 
70 00 
35 00 
Observed time 3 h 39 m to 3 h 40 m . Calculated time 3 h 59 m to 4 1 '. 
Readings on calibrated strip. Mean. 
I. Total daylight 100, 97, 97, 105, 103, 106, 102 =101 
II. Diffused . . 110, 108, 112, 116, 116, 117, 108, 110 =112 
III. Total . . . 104, 100, 100, 97, 100, 102, 107, 105, 103=102 
IV. Diffused . . 108, 112, 113, 108, 115, 114, 107 =111 
