198 



SCIENCE. 



[Vol. I., No. 7. 



Let M be the mass of body; N, moment of inertia 

 about the axis; Z, distance of centre of gravity of 

 body from the axis; g, acceleration of gravity; d, 

 angle of rotation, which is when body is at rest. 

 The motion is considered, first, under the condition 

 that the angular velocity vanishes for the value 9o of 

 d, and, secondly, under the condition that the angular 

 velocity vanishes for the value t — 9o of d. If t and t' 

 denote the times in these two cases, then 



-JNf— 1 = ZMg (cos e - cos So), 



iN [j-^ij = ZMg (cos e + cos flo). 



M. Lipschitz expresses t and t' in terms of elliptic 

 integrals of the first species, and proceeds to find the 

 corresponding integrals (w and w') of the second spe- 

 cies. He points out that these represent quantities to 

 which Hamilton gave the name accumulated living 

 force ; that is to say, in each case the element of the 

 integral is equal to the sum of the living forces of the 

 system multiplied by the element of lime. He shows 

 that if T and T', W and W, denote the values of t and 

 t', w and w', corresponding to the passage of the body 

 from the state of rest (when equal 0) to the state 

 when 9 is a maximum (which is flp in the first case, 

 and TT — do in the second case), then 

 TW' + WT' = 27rN-. 

 Whence it appears that this expression, involving the 

 four quantities T, T', W, W, for the two assumed 

 conditions of motion of the same body, has a value de- 

 pending solely upon the moment of inertia of the body. 

 — {Coiiqjtesrendus, Dec. 4, i8S2.) G. A. n. [415 



Changes in the teaching of mechanics. — M. 

 Yvon Villarceau observes, that what is usually and 

 vaguely termed 'rational mechanics' might with 

 more propriety be called ' general mechanics,' follow- 

 ing the example of M. llesal. The science, in M. 

 Villarceau's method of treating it, is based on two 

 principles, — the equation of the motion of a material 

 point projected upon a fixed arbitrary line, and the 

 principle of action and re-action. In treating ijrob- 

 lems which involve the Uuisims of points, a certain 

 rule, often neglected, should always be observed. 

 This rule consists in determirnng the values of all 

 the forces which are eliminated in effecting the solu- 

 tion of the problem, so that we may know whether 

 they are compatible with the properties of the matter 

 of which the bodies are composed; e.g., the intensi- 

 ties of the forces ought not to exceed the limits of 

 the resistance, strings ouglit not to be subject to a 

 compression, etc. Fi'om failure to observe this rule, 

 contradictory results may be reached in the case 

 of certain problems; although all the theorems 

 employed in the solution are incontestal)ly true. 

 As an illustration, M. Villarceau considers the mo- 

 tion of a solid of revolution turning about its axis 

 of symmetry, and left to itself. He is led to the 

 conclusion that the study of the motion of a geomet- 

 rical solid left to itself ought to be excluded from gen- 

 eral mechanics. — {Comptes rendus, Dec. 26, 1SS2.) 

 G. A. II. [416 



{Photography.) 



Quantitative photographic measurements. — 

 In connection with the above article a paper was 

 read by Mr. \V. H. Pickering, describing some experi- 

 ments on the absolute sensitiveness, and other im- 

 portant characteristics, of photographic dry plates. As 

 a standard of sensitiveness, ordinary white filter- 

 paper, which is salted and sensitized in standard 

 solutions, was selected. No toning or fixing is em- 

 ployed after the exposure; and the amountof light 



absorbed by the exposed portions is measured by a 

 photometer by gaslight. The paper and the plates to 

 be compared are exposed altogether to the direct light 

 of the sky, shining through diaphragms. The plates 

 are then placed in a standard developer for a given 

 time, and fixed. They are next measured by the pho- 

 tometer, and the per cent of li^ht absorbed by the 

 exposed portions determined. The amount of light 

 necessary to darken the paper and each plate 50 per 

 cent is calculated; and the reciprocals of the ratios of 

 these amounts tlien give the absolute sensitiveness of 

 each plate in terms of the paper taken as a standard. 

 This sensitiveness was found to vary between one and 

 ten million for the various plates measured. It was 

 shown that the plates most sensitive to faint lights 

 were by no means necessarily the most sensitive to 

 high ones, and that those most fogged by gaslight 

 were not proportionately so when exposed to the light 

 of the sky. It was found, that if we expose one por- 

 tion of a ijlate to a standard light for a standard 

 time, and then expose another portion to n times the 

 light for an nth the time, the same result will be 

 obtained. The largest value of n employed was 500; 

 but, if the law holds for all values, it can be shown 

 that an average plate exposed to direct sunlight will 

 be darkened perceptibly by an exposure of tujou iTiTunr 

 part of a second. The relative sensitiveness of the 

 paper and plates may perhaps best be illustrated by 

 the fact that to take a photograph of a landscape 

 under ordinary conditions requires an exposure of 

 about five seconds. Now, to take the landscape under 

 the same conditions on sensitive paper directly would 

 require an exposure of a little over one year of con- 

 tinuous sunlight, day and night. Measurements were 

 made of tlie amount of contrast obtainable by the 

 different plates, and also of the range of light through 

 which tliey would give gradations of shading. Great 

 differences were found to exist in them, and several 

 peculiarities in the development of the plates meas- 

 ured were noted. — (Amer. acad. arts. sc. ; meeting 

 Feb. 14.) [417 



Bicarbonate-of-soda developer. — A developer 

 very popular in Europe at present is that recom- 

 mended by Mr. John McKean, — a cold saturated 

 solution of bicarbonate of soda, 1 ounce; liquid 

 ammonia (.880), 1 ounce; water, 4 ounces. 



A few drops of the above in a three-grain solution 

 of pyro. will develop any good plate with less expo- 

 sure, and with more detail in the shadows, than has 

 ever yet been secured with the use of bromide. If 

 the shadows are not as clear as may be desired, in- 

 crease the proportion of bicarbonate. One or two 

 droits of nitric acid in the hypo, solution dispel any 

 trace of fog that may exist after a forced develop- 

 ment, in the case of under-exposure. — {Phot, times, 

 Jan.) w. II. P. [418 



Carbonate-of-soda developer. — A very popular 

 recent American developer is that given by Mr. H. J. 

 Newton. Stock solution No. 1: carbonate of soda, 

 500 grains; water, 10 ounces. Stock solution No. 2: 

 pyrogallic acid, 20 grains; oxalic acid, 30 grains; wa- 

 ter, 10 ounces. 



Take equal parts of the above solutions, thorough- 

 ly mixed, and flow over the exposed plate, whicli has 

 first been laid in water for a minute or two. If the 

 plate should be over-exposed, add a few grains of bro- 

 mide of ammonia; if under-exposed, use a stronger 

 soluticm of soda. Instead of oxalic, we may use gla- 

 cial phosphoric acid (IJ grains to the ounce) or con- 

 centrated formic acid (4 grains to the ounce). These 

 acids give rather better colored images than the oxalic, 

 but, even in large cities, are sometimes difficult to 

 obtain. —.{Phot, times, Feb.) w. H. p. [419 



