588 REPORT— 1894. 



Now C.G.S. units are one of the innumerable metric systems of systematic 

 physical units thus placed at our disposal. This particular system is found to be 

 inconvenient for use by practical men ; which makes it desirable that they should 

 be able on many occasions to avail themselves of other metric systems equally 

 systematic and in closer relation to their work. This is the more to be recom- 

 mended since the translation from any such system into the C.G.S. system, in 

 which our best tables of physical units exist, or from the C.G.S. system into it, 

 can by the proposed nomenclature be made so conspicuous as to be always certain 

 and easy. The prefix hyper- and the affix -ein are designed to provide us with 

 facilities for doing this. 



Employing the word weights to designate the pieces of metal used with our 

 balances, it may be stated to be the usual practice of engineers and physicists to 

 measure forces by the gravitations of these weights, i.e., by the downward forces 

 exerted by them at the station where the experimenter works. Now the gravita- 

 tions or downward forces of all %ceights, and therefore of the metric series — the 

 gram weight and its decimal multiples and submultiples — vary slightly from one 

 station on the earth's surface to another; while the decimal series of systematic 

 forces (determined by the condition that they are the force which will produce an 

 acceleration of a metre per sec. per sec. in a mass of a kilogram, along with the 

 decimal multiples and submultiples of this force) is a .system of forces quite inde- 

 pendent of the place of observation, and therefore each of them maintains the same 

 value over the whole universe. Here, then, we have two decimal series of forces — 

 one the fixed series required in dynamical calculations, the other the gravitations 

 or downward forces of the metric weights, convenient in experiments but de- 

 pending for the amounts of these forces upon the situation where the experiment is 

 made. Now it so happens that the theoretic forces are close to — about two per 

 cent, more than — the laboratory forces ; and hyper-, when prefixed to the name of 

 a weight, is intended to signify the slight increase which has to be made in it to 

 make its gravitation become equal to the adjoining theoretical force. Thus in the 

 language of systematic measures the hektogram, kilogram, &c., are masses ; but the 

 hyper-hektogram, hyper-kilogram, and so on, are forces, viz., those forces of the 

 systematic decimal series which are about two percent, more than the gravitations 

 of the hektogram, the kilogram, and the other metric weights. The prefix 

 hyper- may accordingly be paraphrased into '10/^ times the gravitation of the 

 weight whose mass is a — .' The coefficient 10/^, which is indicated by hyper-, 

 (in which g is gravity at the station where the experiment is made, expressed in 

 metres per second per second), varies from 1'022 at the equator to 1-017 at the 

 pole, and is about 1'019 in England;' or, with more exactness, an observer at 



' The following is a convenient formula for the unit of absolute force : — 

 The hyper-hektogram = the gravitation or downward force in vacuo of 



(10197'8 + 26 cos 2\+ A) centigrams 



at latitude A., and at the height of h metres above the sea. 

 Hence the hyper-hektogram to the nearest milligram 



Grams used as ' 

 weights in va- 

 cuo and at 

 level of sea. 

 = 102-238 at the equator 

 = 101-978 at the latitude of 45° 



= 101-920 „ Greenwich, which is 51° 28' 



= 101-903 „ Dublin „ 53° 20' 



= 101-902 „ Manchester „ 53° 29' 



= 101-892 „ Belfast „ 54° 36' 



= 101-882 „ Glasgow „ 55° 51' 



= 101-881 „ Edinburgh „ 55° 57' 



= 1 01-718 at the poles, 



the extreme range, between the equator and the poles, being the gravitation of about 

 half a gram (052 gram). 



