88 UEPOKT OF THE SECRETARY. 



infrequently. The procedure adopted has given the absokite loss by reflection at 

 the siderostat mirror for all wave lengths, and the relative loss for the several wave 

 lengths in the remainder of the apparatus. Without here detailing the procedure at 

 great length, it is sufficient to say that the operation consists of two parts. First a 

 second spectroscope is set up whose spectrum is formed at the slit of the first. Here 

 the bolometer is placed and its indications read for several points in the spectrum. 

 The bolometer is then replaced at its usual stand and energy curves of the small 

 portions of spectrum it has just been measuring are taken. These bits of spectrum, 

 it will be seen, have suffered absorption in the main spectroscope since the corre- 

 sponding deflections were first taken in the first spectrum at the slit. Therefore the 

 several quotients of the areas under the bits of energy curve to the deflections 

 obtained prior to absorption are in proportion to the transmission of the spectrost'ope 

 at the several wave lengths. 



In the second part of the procedure two freshly silvered mirrors are placed jiarallel 

 to each other ni such a way that the beam of the siderostat mirror strikes the first, 

 is reflected to the second, and thence to the spectroscope. This causes the spectrum 

 to be weaker at all wave lengths by loss experienced from two reflections than when 

 obtained with the beam from the siderostat mirror direct. Thus is the absorption of 

 the two mirrors determined, and by replacing the siderostat mirror temporarily by 

 one of them, its al)sorption follows at once. These determinations of the al)sorption 

 of the apparatus have been made several times, but I will not here give their results 

 more in detail, which are in general accordance with those already reached by you. 



Absorption of the atmosphere and selective absorption of imter vapor.— ^mcQ January 20 

 all favorable opportunities have been used to take quick speed energy curves. These 

 have been made with quite different altitudes of the sun. Sometimes as many as 15 

 have been taken in one day, and 160 were secured between January 20 and July 1. 

 These curves are studied from two points of view, first, as regards the variation in 

 height for single wave lengths with different altitudes of the sun; second, as regards 

 the variation in area and especially the areas of the great regions of water- vapor 

 absorption. The first kind of examination leads to the determination of the general 

 absorption of the air, the second to fixing the variations in amount of the solar radia- 

 tion and of the special selective absorption of water vapor. 



To illustrate the first method of study, let us suppose several energy curves to have 

 been taken in a single clear day, during which the barometer height was (B), and 

 let (Bq) be the standard barometric height, generally taken as 76 cm. From the 

 altitudes of the sun as com})uted from the hour angles and declination, the air mass 

 (m) is determined. This (juantity represents the ratio which the mass of air traversed 

 by the solar l)eam bears to that mass of air which would be traversed if the sun was 

 directly overhead. If we suppose [e) to represent the amount of radiant energy per 

 square centimeter of a certain wave length which reaches the earth's surface, and 

 (fj the amount prior to absorption by the earth's atmosphere, and let [a) be the 

 proportion transmitted per unit air mass, then by the well-known formula of 

 Bouguer:" 



B 

 e^e^a B^ 



But since the height {d) of the holographic energy curve at the wave length in 

 question is projjortional to {e), we may write: 



B 

 d^};e=ke,a^'^B, 



«As you have pointed out, this formula is grossly abused frequently in that (a) is 



treated as if constant for all wavelengths. Thus entirely erroneous results are 



reached. The present use of the forimda merely assumes {a) constant over the 



extremely narrow region of spectrum covering the bolometer strip at any given 



instant. As thus ap])lied it is bi^lieved that good results are reached. If single wave- 

 I ti... ; „.,*; — , ;* :.. i,,.i;„ 3 au. 



