Notices respecting New Books. 171 



Kirchhoff, and tested experimentally by Strehlke; and the latter 

 may therefore be disposed to reject the theory in toto. But it is 

 necessary here to distinguish two distinct questions : it is one 

 thing to deduce the logical consequences of premises generally 

 admitted, and another to inquire how far those premises are 

 really applicable to the case in hand. With respect to the first 

 point there can, I apprehend, be no doubt that the theory deve- 

 loped in the present paper stands on as high a level as that of 

 Kirchhoff relating to a circular plate. It satisfies the same dif- 

 ferential equation over the area, and the same boundary-condi- 

 tions, and is indeed in one respect* even less open to doubt. 

 But ijt may be that the fundamental equations are for some 

 reason less applicable to a square than a circular plate, though I 

 do not see why this should be the case. On the other hand it is 

 possible that, in spite of all Dr. Strehlke's care, some error may 

 have crept into his measurements. If this be so, the cause of 

 error must be of a systematic character, not eliminated by repe- 

 tition or by changing the plates. One suggestion I may be 

 allowed to make : it appears to me that experimenters have not 

 been sufficiently careful to touch the vibrating plates only at the 

 nodes. In the present case it is, I believe,, not unusual to damp 

 the plate by touching the middle point of one of the sides — a 

 method which would be legitimate on the old view that the node 

 passes, or ought to pass, through the points referred to, but 

 which certainly cannot be justified for purposes of measurement 

 without an experimental or theoretical proof that no error is 

 thereby introduced. One would suppose that the action of the 

 finger or other damper must in part resemble the effect of a load 

 applied at the point touched; and there can be no question that 

 such a load would produce a disturbance. 



XVII. Notices respecting New Books. 



Astronomical and Meteorological Observations made during the year 

 1870, at the United-States Naval Observatory. Washington : 1873. 

 rPHIS volume, which commences with the report of the Super- 

 ■*■ intendent of the Observatory, Bear-Admiral Sands, contains ob- 

 servations with the transit-circle, the meridian transit-instru- 

 ment, the mural circle, and the equatoreal. From the report we 

 learn that the equatoreal was under the charge of Professors 

 Newcomb and Hall, who observed with it the minor planets, comets, 

 and occultations. The transit-circle was under the charge of 

 Professor Harkness, who also had charge of the telegraphic appara- 

 tus and connexions by which correct time is furnished to the 

 Navy department, the city of Washington (by striking the fire bells 



* The relation of the constants and rigidity and compressibility. 



N2 



